Split (1)

train · ~1.24B rows (showing the first 1.67M)

text stringlengths 8 1.01M
This well-accepted introduction to computational statistics with MATLAB is a textbook for high-level undergraduate and low-level graduate courses. The focus is on the implementation of the statistical methods and algorithms. Hence the book is well suited for students in computer science and engineering. Some of the methods in computational statistics enable the researcher to explore the data before other analyses are performed. These techniques are especially important with high-dimensional data sets. Moreover, modern insights in computational statistics are used to provide new solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational statistics, as well as several more advanced topics (jackknife method, spatial statistics, some techniques for statistical pattern recognition, etc.), are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. Finally, the authors provide detailed algorithms by MATLAB code for the methods presented in the book. Reviewer: J.Martyna (Kraków)
Math Module: Quadratic Equation, Quadratic Function and Inequality Other than in Junior High School, the material on quadratic equations are also studied back in high school. Likewise with quadratic functions and quadratic inequalities. Mathematical material is a material basis for the subsequent material, so that this material should be given since junior high. While in junior high, given the material was basic and not yet in high school complex. Quadratic functions and quadratic inequalities is also not too much given in junior high. Several times to teach quadratic equations, one difficulty is when students want to factoring, without using the abc formula or the quadratic formula. Even until the 12th grade high school students were still experiencing difficulties in factoring. Is required for factoring a lot of practice experience. Also logic and reasoning power is needed. Although such materials has ever been given in junior high, sometimes when repeated again in high school (grade 10), still many who forget, or do not remember at all, but the problems associated with these materials is also in the UN. Whose fault is it? Maybe you've had an interesting experience while teaching the material? Or the difficulties in explaining to the students? Write your comment below. Your comments will be useful for teachers in other schools in Indonesia. Well, this time I will make a link to download the module mathematics: quadratic equations, quadratic functions and quadratic inequalities. Comments [...] I've provided a link to download square root form exercies. There are 10 problem and i will give you the answer. But I apologize for not accompanied by a discussion, because i have limited time. These questions for grade 10. Hope can help you in learning mathematics. [...] Currently you have JavaScript disabled. In order to post comments, please make sure JavaScript and Cookies are enabled, and reload the page.Click here for instructions on how to enable JavaScript in your browser.
Search Journal of Online Mathematics and its Applications: Journal of Online Mathematics and its Applications Power Maths by Sidney Schuman Power Maths is a pre-calculus investigation designed to enable students to discover the integral and differential power rules numerically. The investigation leads the student to conjecture a simple ratio of areas, from which the rules are then deduced for the restricted domain [0,x]. A hardcopy version of Power Maths includes calculator/graph-based investigations for both power rules. If you would like a copy, or if you have any comments, please click the Worksheet link on the Investigation page. Power Maths (both parts) appeared originally as a booklet used while teaching at Lewisham College, London UK. Editor's note, 11/04: When published, this investigation included only the integral power rule, and there was a separate investigation for the differential power rule. The author has since combined these in the present version. Acknowledgements: Grateful thanks to David A. Smith for his encouragement and to Lana Holden for the applet.
10 Units 2000 Level Course Available in 2013 Provides an introduction to modern algebra through a detailed study of linear algebra. Thus students acquire fresh understanding of the algebraic ideas underlying modern mathematics - which is especially useful for those intending to teach mathematics - and at the same time learn about an important branch of mathematics with applications throughout the Sciences, Engineering and Information Technology. This course contains essential background for many 3000-level Mathematics courses, and is compulsory for all students in the BMath program. Objectives At the successful completion of this course students will have 1. an in-depth knowledge of the subject of linear algebra. 2. an understanding of what constitutes a rigorous mathematical argument and how to use reasoning effectively to solve problems.
Algebra/Linear Algebra: A Course In Algebra by E.B. Vinberg (gives an integrated introduction to both linear and abstract algebra with lots of applications,especially to geometry:VERY readable and reaches a very high level of coverage by the end), Michael Artin's Algebra (more intense,but similar in spirit,a second edition coming out later this year,can't wait for it) Topology: A First Course In Topology:Continuity And Dimension by John McCleary (the best introduction to the subject) Overview of Mathematics: Mathematics:It's Content,Methods And Meaning by A.N.Kolomogrov,etc. (The great classic by 3 Russian masters of mathematics,will give you the best bird's eye view of the subject) That should get you started and give you the tools needed to go forward. Good Luck and welcome to the sorcerer's guild!
Modelling with Fourier series This unit shows how partial differential equations can be used to model... This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations. After studying this unit you should be able to: understand how the wave and diffusion partial differential equations can be used to model certain systems; determine appropriate simple boundary and initial conditions for such models; find families of solutions for the wave equation, damped wave equation, diffusion equation and similar homogeneous linear second-order partial differential equations, subject to simple boundary conditions, using the method of separating the variables; combine solutions of partial differential equations to satisfy given initial conditions by finding the coefficients of a Fourier series. Contents Modelling with Fourier series Introduction This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations
Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of middle school mathematics curriculum with a "C" or better Course Description: This class will cover fundamental algebraic skills such as: operations, algebraic expressions, solving equations, graphing, ratios and proportions, quadratic functions, probability and statistics, and geometric connections. Algebra 1-2 is a college prep mathematics course that is required for graduation. In addition, it satisfies the first year mathematics requirement for many colleges and universities. Course Description: Strategic Algebra Support (SAS) is a standards-aligned course designed to give students the skills and support they need to meet the California Algebra 1 Standards and be successful in the Algebra 1-2 class. Additionally, the class is focused on giving students the skills and support needed to score at the proficient level on the California High School Exit Exam. On a regular basis, SAS teachers will engage in meaningful collaboration with the Algebra 1-2 teachers at their school site to guide the pre-teaching and re-teaching throughout the year. Students will be assessed on a regular basis to determine how well they are meeting the Algebra 1 standards. The class will support mastery of the standards for Algebra 1 using materials that are appropriate to the students' abilities and experience. Following the pacing guide for Algebra 1-2, the class is organized around nine-week instructional periods. Major Projects/Assignments: Varies by instructor. Approximate homework assigned daily: Varies by instructor Graduation Requirement: elective UC/CSU a-g Requirement: none Geometry 1-2 Year Course 10 Credits Grade level: 9-12 Prerequisite: Algebra 1-2 Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of Algebra 1-2, with a grade of "C" or better. Course Description: This class will cover basic geometric skills such as: congruent triangles, quadrilaterals and their properties, circles, logic and proof, volume and surface area, and using algebraic methods to solve a variety of equations among many other concepts. Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of Algebra 1-2, with a grade of "D" or better. Course Description: This class reviews the topics covered in Algebra 1-2. An introduction to basic geometric concepts (points, lines, planes, triangles, quadrilaterals, circles, etc.)Integrated Mathematics 3-4 Year Course 10 Credits Grade level: 10-12 Prerequisite: Geometry 1-2 Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of Geometry 1-2, with a grade of "D" or better. Course Description: This class reviews the topics covered in Geometry. An introduction to basic advanced algebra topicAlgebra 3-4 Year Course 10 Credits Grade level: 9-12 Prerequisite: Algebra 1-2, Geometry 1-2 Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of Algebra 1-2 and Geometry 1-2 with a grade of "C" or better. Students should also exhibit strong algebraic and reasoning skills, Course Description: This class is a college prep elective mathematics course, which satisfies the third year mathematics requirement of many colleges and universities. The covered topics include systems of equations, rational expressions, conic sections, combinatorics, probability, functions, sequences and series, logarithms and exponents. It is NOT an algebra review course, and students with weak Algebra 1-2 skills may have to seek extra work and assistance to succeed in this course. Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of Algebra 1-2, Geometry 1-2, and Algebra 3-4 with a grade of "B" or better in each preceding course. Course Description: This course is broken down into two major areas of study: Trigonometry and Math Analysis. Trigonometry is covered during the first 2/3 of the first semester, including topics such as properties of trigonometric and circular functions, composition of coordinates, rotary motion, inverse functions, a wide variety of triangle problems and trigonometric applications. Math Analysis is the focus for the remainder of the year. It covers such topics as two-dimensional vectors, conic sections, polar coordinates, parametric equations, complex numbers, rational functions and financial applications. Emphasis is placed on the development of critical thinking and problem solving as opposed to rote memorization. Suggested Course Preparation/Critical Skills: Enrolling students should have successful completion of prerequisite courses with a "C" or better in each course. Additionally, students should exhibit solid algebraic and reasoning skills Course Description: This course is designed to meet the mathematical needs of those students who have successfully completed Algebra 3-4 (with a "C" or better) and are interested in continuing their math education beyond Algebra, but not necessarily in Calculus (yet!). A variety of topics – some review, some new – will be covered, including graphing, conic sections, geometry, probability, graph theory, statistics, linear programming, finite differences, matrices, and consumer mathematics (compound interest, annuities, consumer loans, etc.) Finite Math qualifies as "advanced math" under the CSU and UC systems for entrance requirements. While this course does not substitute for Pre-calculus, it is a challenging course with high expectations. Major Projects/Assignments: Varies by instructor. Sample projects include the mock purchase and financing of a car, graphing project, video project This class focuses on the fundamental topics of calculus. It covers Limits, Derivatives and Integrals. The course covers the graphical, numerical, analytical and verbal components of functions and their application. Equal time is spent on the mechanics of these topics and on the applications of each. Some applications include optimization, net change, area under a curve and volume of solids generated by rotating curves The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: Exploring Data: Describing patterns and departures from patterns; Sampling and Experimentation: Planning and conducting a study; Anticipating Patterns: Exploring random phenomena using probability and simulation; Statistical Inference: Estimating population parameters and testing hypotheses. It is imperative to understand that this course is different from other math courses due to the heavy emphasis on mathematical concepts and theories. Suggested Course Preparation/Critical Skills: Enrolling students typically need additional practice/assistance in order to pass the California High School Exit Exam (CAHSEE). Course Description: CAHSEE English/Mathematics are courses designed to assist students in preparation for passing the exam. Students must pass this exam in order to graduate from high school. Regular attendance is required.
Courses in Mathematics (Division 428) Only open to designated summer half-term Bridge students. IIIb. (2 in the half-term). (Excl). Review of elementary algebra; rational and quadratic equations; properties of relations, functions, and their graphs; linear and quadratic functions; inequalities, logarithmic and exponential functions and equations. Equivalent to the first year of Math. 105/106. Students with credit for Math. 103 can elect Math. 105 for only 2 credits. No credit granted to those who have completed any Mathematics course numbered 110 or higher. (4). (MSA). (QR/1). ThisSee Elementary Courses above. Enrollment in Math. 110 is by recommendation of Math. 115 instructor and override only. No credit granted to those who already have 4 credits for pre-calculus mathematics courses. (2). (Excl). A condensed half-term version of Math 105. Offered as a self-study course through the Math Lab and directed toward students who are unable to complete a first calculus course successfully. Students study on their own and consult with tutors in the Math Lab whenever needed. Four years of high school mathematics. See Elementary Courses above. Credit usually is granted for only one course from among Math. 112, 115, 185, and 295. No credit granted to those who have completed Math. 175. (4). (MSA). (BS). (QR/1). This course presents calculus from three points of view: geometric (graphs); numerical (tables); and algebraic (formulas). Students develop their reading, writing, and questioning skill. Topics include functions and graphs, derivatives and their application to real-life problems in various fields, and definite integrals. Three years of high school mathematics including a geometry courseThis course introduces students to the ideas and some of the basic results in Euclidean and non-Euclidean geometry. The course begins with an historical perspective of how the ancient Greeks influenced the study of geometry prior to the 19th century. Then notions of non-Euclidean geometry and geometry in higher dimensions are introduced and studied. High school mathematics through at least Analytic GeometryDesigned for non-science concentrators and students with no intended concentration who want to learn how to think mathematically without having to take calculus first. Students are introduced to the ideas of Number Theory through lectures and experimentation by using software to investigate numerical phenomena, and to make conjectures that they try to prove. Math. 112 or 115. No credit granted to those who have completed a 200- (or higher) level mathematics course. (3). (MSA). (BS). An introduction to the mathematical concepts and techniques used by financial institutions. Topics include rates of simple and compound interest and present and accumulated values; annuity functions and applications to amortization, sinking funds and bond values; depreciation methods; introduction to life tables, life annuities and life insurance value. Permission of the Honors advisor. Credit is granted for only one course from among Math. 112, 113, 115, 185, and 295. No credit granted to those who have completed Math. 175. (4). (MSA). (BS). (QR/1). Topics covered include functions and graphs, derivatives, differentiation of algebraic and trigonometric functions and applications, definite and indefinite integrals and applications. Other topics are included at the discretion of the instructor. Permission of the Honors advisor. Credit is granted for only one course from among Math. 114, 116, 119, 156, 176, 186, and 296. (4). (MSA). (BS). (QR/1). Topics covered include transcendental functions, techniques of integration, introduction to differential equations, conic sections, and infinite sequences and series. Other topics included at the discretion of the instructor. Math. 115 and 116. Credit can be earned for only one of Math. 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in Math. 513. (4). (MSA). (BS). This course is an alternative to Math 216 (Differential Equations) in that it emphasizes linear algebra including the geometry of two, three and n-dimensional space, and has a lighter treatment of differential equations. It is particularly designed for students who are planning to take a course in linear programming. Math. 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of Math. 215, 255, or 285. (4). (MSA). (BS). (QR/1). Topics software. Math. 116, 119, 156, 176, 186, or 296. Credit can be earned for only one of Math. 216, 256, 286, or 316. (4). (MSA). (BS). MathFocuses on the development of mathematical problem-solving skills. Problems are taken from classical analysis, elementary number theory, and geometry. For students with outstanding problem-solving ability. Prior knowledge of first year calculus and permission of the Honors advisor. Credit is granted for only one course from among Math. 112, 113, 115, 185, and 295. (4). (MSA). (BS). (QR/1). Introduction to mathematical analysis with emphasis on proofs and theory. Covers such topics as set theory, construction of the real number field, limits of sequences and functions, continuity, elementary functions, derivatives and integrals. Additional topics may include countability, topology of real numbers, infinite series, uniform continuity. This course follows the historical evolution of three fundamental mathematical ideas, in geometry, analysis and algebra – Euclid's parallels postulate and the development of non-Euclidean geometries, the notion of limit and infinitesimals, and the development of the theory of equations culminating with Galois theory. Math. 385 and enrollment in the Elementary Program in the School of Education. (1-3). (Excl). (EXPERIENTIAL). May be repeated for a total of three credits. An experiential mathematics course for elementary teachers. Students would tutor elementary (Math. 102) or intermediate (Math. 104) algebra in the Math. Lab. They would also participate in a weekly seminar to discuss mathematical and methodological questions. Formulation and solution of some of the elementary initial- and boundary-value problems relevant to aerospace engineering. Application of Fourier series, separation of variables, and vector analysis to problems of forced oscillations, wave motion, diffusion, elasticity, and perfect-fluid theory. A survey course of the basic numerical methods which are used to solve scientific problems. In addition, concepts such as accuracy, stability and efficiency are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra as well as practice in computer programming. Math. 215, 255, or 285; and 217. No credit granted to those who have completed or are enrolled in 512. Students with credit for 312 should take 512 rather than 412. One credit granted to those who have completed 312. (3). (Excl). (BS). Sets, functions (mapping, relations, and the common number systems (integers to complex numbers). These are then applied to the study of groups and rings. These structures are presented as abstractions from many examples. Notions such as generator, subgroup, direct product, isomorphism and homomorphism. Not open to freshmen, sophomores or mathematics concentrators. (3). (Excl). (BS). Review of algebra, functions, and graphs followed by an intuitive introduction to the rudiments of calculus. Applications of differentiation and integration to problems in the social sciences. Designed especially for seniors and graduate students with minimal mathematics background. Four terms of college mathematics beyond Math. 110. Credit can be earned for only one of Math. 214, 217, 417, or 419. No credit granted to those who have completed or are enrolled in Math. 513. I and II. (3). (Excl). (BS). Finite dimensional linear spaces and matrix representation of linear transformations; bases, subspaces, determinants, eigenvectors, and canonical forms; and structure of solutions of systems of linear equations. Applications to differential and difference equations. The course provides more depth and content than Mathematics 417. Mathematics 513 is the proper election for students contemplating research in mathematics. We explore how much insurance affects the lives of students (automobile insurance, social security, health insurance, theft insurance) as well as the lives of other family members (retirements, life insurance, group insurance). While the mathematical models are important, an ability to articulate why the insurance options exist and how they satisfy the consumer's needs are equally important. In addition, there are different options available (e.g., in social insurance programs) that offer the opportunity of discussing alternative approaches. Rates used in compound interest theory; annuities-certain and their application to amortization, sinking funds, and bond values; and introduction to life annuities and life insurance. Both the discrete and the continuous approach are used. The development of employee benefit plans, both public and private. Particular emphasis is laid on modern pension plans and their relationships to current tax laws and regulations, benefits under the federal social security system, and group insurance. Investigation of Euclidean geometry based on the Birkhoff or SMSG metric axiom system and reference to contemporary high school texts. Comparison with synthetic Euclid-Hilbert foundations. Historical development of absolute and hyperbolic geometry. Other non-Euclidean geometries. New directions in high school geometry, transformation groups especially isometries of the Euclidean plane as generated by reflections, similarities, and affine transformations. In the first third of the course the notion of a formal language is introduced and propositional connectives, tautologies and tautological consequences are studied. The heart of the course is the study of 1st order predictive languages and their models. New elements here are quantifiers. Notions of truth, logical consequences and probability lead to completeness and compactness. Applications. One year of high school algebra. No credit granted to those who have completed or are enrolled in 385. I and IIIb. (3; 2 in the half-term). (Excl). (BS). May not be included in a concentration plan in mathematicsMath. 385 or 485. May not be used in any graduate program in mathematics. (3). (Excl). The second course in a two-course sequence required of elementary teaching certificate candidates. Topics covered include: the real-number system, probability, and statistics, geometry and measurement. Math. 489. (3). (Excl). (BS). May be repeated for a total of six credits. Selected topics in geometry, algebra, computer programming, logic, and combinatorics for prospective and in-service teachers of elementary, middle, or junior high school mathematics. Content may vary from term to term. At least two 300 or above level math courses, and graduate standing; Qualified undergraduates with permission of instructor only. (1). (Excl). (BS). Offered mandatory credit/no credit. May be repeated for a total of 6 credits. Math 501 is an introductory and overview seminar course in the methods and applications of modern mathematics. The seminar has two key components: (1) participation in the Applied & Interdisciplinary Math Research Seminar; and (2) preparatory and post-seminar discussions based on these presentations. Topics vary by term. Topics include utility theory, application to buying general insurance to reduce risk, compound distribution models for risk portfolios, application of stochastic processes to the ruin problem and to reinsurance. Isometries and congruences in the Euclidean plane as generated by reflections, translations, and half-turns. Tilings, affine and hyperbolic geometries, and Poincaré model of the hyperbolic plane. Selected applications to ornamental design, crystallography, and regular polytopes. The course covers topics in discrete and applied geometry which change from year to year. Possible topics include: crystals and quasi-crystals; best packing of spheres and applications; convex geometry and optimization problems; geometric combinatorics and applications in computer science. Centers on the construction and use of agent-based adaptive models. Course begins with classical differential equation and game theory approaches, and then focuses on the theory and application of particular models of adaptive systems such as models of neural systems, genetic algorithms, classifier systems, and cellular automata. Intended primarily for students of engineering and of other cognate subjects. Doctoral students in mathematics elect Mathematics 596. Complex numbers, continuity, derivative, conformal representation, integration, Cauchy theorems, power series, singularities, and applications to engineering and mathematical physics. A study of some of the differential equations of mathematical physics and methods for their solution. Separation of variables for heat, wave, Laplace's and Schrödinger's equations; special functions and their integral representations and asymptotic properties; and eigenvalues as solutions of variational problems. Elementary distributions, Green's functions and integral solutions for nonhomogeneous problems, Fourier and Hankel transforms, and Fredholm alternative and elementary methods of solution of integral equations, with additional topics as time permits. Formulation of problems from the private and public sectors using the mathematical model of linear programming. Development of the simplex algorithm; duality theory and economic interpretations. Postoptimality (sensitivity) analysis and applications and interpretations. Introduction to transportation and assignment problems and special purpose algorithms and advanced computational techniques. Students have an opportunity to formulate and solve models developed from more complex case studies and to use various computer programs. The main topics are set algebra (union, intersection), relations and functions, orderings (partial-, linear-, well-), the natural numbers, finite and denumberable sets, the Axiom of Choice, and ordinal and cardinal numbers.
Unfortunately, for much of this subject, there is no substitute for brute memorization. This course is often used as pre-calculus. "Algebra masters" will have a much smaller memorization load than other students. [I mean College Algebra, not the higher-math version.] Much of this subject is highly dependent on either calculators+ or tables [slide rules have been passé since the electronic calculator, but could be used.] Traditionally, this subject relies on some familiarity with "College Algebra", but not an intensive mastery. Note: in many places, I will mention algebraic identities. For serious students who are either algebra-deficient or have to use the material under time pressure, I highly recommend working through "all of the plausible forms" and memorizing them. This usually means algebraic isolation of various variables in the equations, and figuring out how to use multiple equations in one problem. Currently, I am not providing the homework that is required to learn the material. I would like to partially remedy this deficiency. [No timetables!] Note: There are several kludge notations lurking in this crash review: SQRT for "square root" (correctly notated for 2, 3, 5, and 6) pi for p (correctly notated outside of popup text for pictures) I will remove instances of these kludge notations, without advance warning, when it is convenient in my schedule to do so. These functions have a single argument, and take angles. By the heuristic of "wrapping the real number line around the unit circle," we can think of these functions as taking real numbers as arguments. Note that in "stratosphere" math, the above approach is very painful; other techniques are used to define these functions. These techniques are the ones which calculators are programmed with -- but they're not appropriate for this section. Incidentally, there are three angle units listed on my HP-48SX: degrees, radians, and gradients. [Gradients are not commonly used in the U.S.A.] To rebuild the conversion formulae, remember: 1 circle = 360 degrees = 2p radians = 400 gradients. We inherited degrees from Babylonia. There are 60 minutes in a degree, and 60 seconds in a minute. [When dealing with the Earth's rotation in astronomy, the Earth rotates "about" 1 angular degree in 4 solar-day minutes. The Earth rotates 1 degree in 4 sidereal-day minutes.] Also, a nautical mile is "about" 1 arc-minute on the Earth's surface. This would be exact if the Earth was a perfect sphere. A common notation for, say, 3 degrees 4 minutes 5 seconds is 3°4'5". Radians are the "natural" angle unit when dealing with "stratosphere" math. The defining formulae for sin and cos are much simpler then. Radians also behave better if you have to deal with calculus [deriviatives and integrals]. I don't know much about the history of gradients. A right angle is 1/4th of a circle; i.e. 90°, p/2 radians, or 100 gradients. I will use the common symbol for a right angle, in the rest of this crash review. An angle larger than 0, but smaller than a , is called an acute angle. An angle larger than a , but smaller than half a circle, is called an obtuse angle. is a standard symbol in the literature (although found more often in geometry texts than trigonometry texts). When it shows up in a diagram, it designates the labeled angle as a right angle. For the record: Triangles are constructed by picking three points, then joining each pair by a straight line segment. We assume we can neglect curvature of the surface. That is, we assume the geometry is Euclidean. [You will not get the same kind of triangles on a sphere as on a flat desk or piece of paper. The sphere is visibly curved, the desk and the flat piece of paper are not supposed to be curved.] I will occasionally use the fact the geometry is Euclidean. The sum of the three (interior) angles of a triangle is half a circle, i.e. 180° or p radians or 200 gradients. I will sometimes denote this by 2 in the rest of this crash review; this is not standard notation. An implicit exercise will be translating 2 to angular measure [degrees, radians, and/or gradients.]. If we pick a point on a straight line, the two parts of the straight line formed by taking out the point form an angle of half a circle, i.e. 180° i.e. p radians i.e. 200 gradients. In general, I will omit "interior" when talking about angles of a triangle. We say a triangle, that contains a right angle, is a right triangle. If a triangle has two sides of equal length and one side of different length, we call it an isosceles triangle. If a triangle has three equal sides, we say it is an equilateral triangle. Note: For an isosceles triangle, the two angles opposite the sides with equal length (i.e., the two angles whose bounding sides have one of the two sides of equal length, and the side with different length) are equal. For an equilateral triangle, all three angles are equal, and equal 60° i.e. p/3 radians i.e. 200/3 gradients. The angle measure in radians is simply arc length on a circle of radius 1. In general, for a circle with radius R and an arc with central angle X in radians, (arc length)=RX. There are two pictures to keep in mind here, the generic right triangle: First of all, all physical angles have some size. We cannot visualize an angle with negative physical size. They do not exist in anything sufficiently similar to the physical space we live in. However, (especially when dealing with the unit circle), it is often convenient to measure angles in a specific direction: counterclockwise. [I'm not going to digress into "stratosphere" math now, but that is dictating the convention here.] Then, a negative sign means we are measuring the angle "unconventionally", i.e. clockwise. This will simplify the use of some of the trigonometric identities we are going to look at. Why should I know the generic right triangle? Given a right triangle, the trig function values for the two acute angles [angles smaller than a right angle] can be computed without knowing the angles. I prefer to remember the formulae this way [X is an angle]: A mnemonic for the formulae for sin(X), cos(X), and tan(X) is the (fictitious) Indian Chief Soh-cah-toa, who had no problems with this part of trigonometry. [I got this from Mr. Coole, a long time ago -- I was in grade school then.] The way I wrote the formulae, above, emphasizes the following identities: sin(X)csc(X)=1 cos(X)sec(X)=1 tan(X)cot(X)=1 These identities do work hold when both functions involved are defined for the angle X, regardless of size. Another fact, of some use, is the Pythagorean theorem: H²=A²+O². If we relabel A as a, O as b, and H as c, we get the familiar form of the Pythagorean theorem: c²=a²+b². This only works for right triangles. The generalization of the Pythagorean theorem to non-right triangles is called the law of cosines. A common strategy is to memorize how to compute tan(X), cot(X), sec(X), and csc(X) in terms of sin(X) and cos(X), and then reduce everything to this. This is not necessarily the least painful way to do a trig problem, but it is often more important to start the problem, than figure out how to do it elegantly. [EXERCISE: derive this from the A, H, O formulation for acute angles. The formulae work for arbitrary angles.] The generic right triangle also motivates some terminology [which we inherited from twelfth century Arabian mathematics]. First of all, we say two angles are complementary if they add up to a right angle. That is, for an angle X, we say -X is complementary to X. For instance, the angle in the upper right-hand corner is complementary to, i.e. the complement of, the marked angle in the lower left-hand corner. A related piece of terminology is supplementary angles: two angles are said to be supplementary if they add up to half a circle, i.e. 180° i.e. p radians i.e. 200 gradients. That is, 2 - X is supplementary to the angle X. To get an intuition for this, draw a unit circle with the horizontal axis.. Draw an arbitrary radius from the center to somewhere on the unit circle. The two angles formed between the radius, and the horizontal axis, are supplementary. We say that sin and cos [sine and cosine], tan and cot [tangent and cotangent], and sec and csc [secant and cosecant] are cofunctions, and that the trig function of the complement of an angle X is equal to the trig cofunction of the angle. This is explicitly in the function names: cosine is the cofunction of sine, cotangent is the cofunction of tangent, and cosecant is the cofunction of secant. These identities do work for arbitrary angles. If one side is undefined, both sides are undefined. What are the reference triangles? The reference triangles are right triangles that are "easy to construct". They provide easily-memorized values for the angles with measure 30°, 45°, and 60°, i.e. p/6, p/4, and p/3 radians, i.e. 100/3, 50, and 200/3 gradients. There are two reference triangles. They [in the U.S.A.] are known by their degree names: The 45-45-90 (degree) right triangle can be constructed from a square with sides of length one. The hypotenuse is the line connecting two opposite vertices of the square; it has length by the Pythagorean Theorem. [Exercise: compute this!] The legs of the triangle are sides of the square. Note: 45° is its own complementary angle. The 30-60-90 triangle is constructed from an equilateral triangle with sides of length 2. We put one side on the horizontal axis, and bisect the angle opposite this side. [Note that an equilateral triangle has three vertex angles, all of which are 60°.] We now have a hypotenuse of length 2, one leg of length 1 [from bisecting the horizontal side], and one side with length [from the bisecting line]. We get: sin(30°)=cos(60°)=½ cos(30°)=sin(60°)=/2 tan(30°)=cot(60°)=1/=/3 cot(30°)=tan(60°)= sec(30°)=csc(60°)=2/=(2)/3 csc(30°)=sec(60°)=2 [Again, do it.] Why should I know the unit circle? The unit circle provides a picture on which to memorize reference values of the trig functions. Think of it as the set of possible endpoints for a length 1 hypotenuse H, with one endpoint of H fixed at the origin. We can construct generic right triangles with hypotenuse 1 in it. Pick a point on the circumference, draw a line segment from it to the origin, and then draw a perpendicular line segment down to the x-axis. Notice that the coordinates of the vertex, in Cartesian coordinates, is (cos(X), sin(X)), where X is the central angle. The horizontal side (on the x-axis) is A, and the vertical side (parallel to the y-axis) is O. The radius (length 1) is H. The slope of the hypotenuse H is tan(X). However, observe the four quadrants. Our example triangle has its hypotenuse in the upper-right quadrant [both coordinates positive]. Horizontal and vertical hypotenuses create line segments rather than triangles. Also, at least one of the coordinates go negative in the other three quadrants [upper-left, lower-left, lower-right]. We proceed by assuming that the coordinates of the vertex, in Cartesian coordinates, is (cos(X), sin(X)), regardless of where the vertex is on the unit circle. This immediately leads us to the Pythagorean identities: sin²(X)+cos²(X)=1 [standard; if you memorize only one, learn this one] tan²(X)+1=sec²(X) [divide by cos²(X)] 1+cot²(X)=csc²(X) [divide by sin²(X)] If we interpret undefined as equal to undefined, these identities hold for arbitrary angles. Incidentally, the computation of the slope of the hypotenuse H via tan(X) also works for arbitrary angles. [Recall that an undefined slope corresponds to a vertical line]. The next point is that the signs of the various trigonometric functions are controlled by the quadrant the function is evaluated in. We number the quadrants I through IV [Roman numerals] counterclockwise, as follows: Now, the trigonometric function signs are controlled by the quadrants as follows: As should be clear, the boundaries between the quadrants do not behave this way. In fact, they are reference values for the trigonometric functions. [For ease of memorization, I will put all of the reference values for the first quadrant and its boundaries in one place, elsewhere in this document.] Now, let's look at another way to reconstruct the cofunction identities i.e. the identities relating complementary angles. What happens if we reflect the unit circle about the line y=x? We are swapping the x and y coordinates. That is, (letting X be the central angle), we are swapping sin(X) and cos(X). We are also physically reflecting the central angle X to the angle -X. So, we find that (here are the cofunction identities again): It is no coincidence that the slope of the line y=x is 1. This gives a central angle between the line y=x, and the x-axis, of 45° i.e. p/4 i.e. 50 gradients [think of the 45-45-90 triangle]; note that this is exactly half of a right angle. Now, let us consider reflecting the unit circle about the x-axis: Note that the x-coordinate [cos(X)] is unaffected, while the y-coordinate [sin(X)] is negated. The resulting point is the point we get from rotating through the angle -X from the angle 0. This gives the following formulae: sin(-X)=-sin(X) "sin(X) is an odd function" cos(-X)=cos(X) "cos(X) is an even function" tan(-X)=-tan(X) "tan(X) is an odd function" cot(-X)=-cot(X) "cot(X) is an odd function" sec(-X)=sec(X) "sec(X) is an even function" csc(-X)=-csc(X) "csc(X) is an odd function" [Exercise: derive the last four [tan, cot, sec, and csc versions] from the first two [sin and cos versions.] These formulae classify the trigonometric functions into even functions and odd functions. As you may recall from College Algebra, even functions are those functions whose value is unchanged by negating the argument, and odd functions are those functions whose value is negated by negating the argument. It is no coincidence that the slope of the x-axis is 0. The central angle of the x-axis with the x-axis is clearly 0 [degrees, radians, gradients, it matters not which unit]. 0 is also exactly half of 0. Now, let us consider reflecting the unit circle about the y-axis: Note that the y-coordinate [sin(X)] is unaffected, while the x-coordinate [cos(X)] is negated. The resulting point is the point we get from rotating through the angle -X from the angle 0. This gives the following formulae: [Exercise: derive the last four (tan, cot, sec, and csc versions) from the first two (sin and cos versions.)] It is no coincidence that the slope of the y-axis is undefined. The central angle of the y-axis with the x-axis is clearly . This is also exactly half of 2 . Now, we can directly compute the reference values of cos and sin for 45° i.e. p/4 radians i.e. 50 gradients, i.e. ½ , without using the 45-45-90 reference triangle. 45° is the angle that is its own complementary angle. Thus, i.e. [solve for cos(45°); we know we need the positive root because 45° is in the first quadrant, so I can omit ±] cos(45°) = 1/ = /2 We can also directly compute the reference values of cos and sin for 60°, i.e. p/3 radians, i.e. 200/3 gradients, i.e. [2/3] . To do this, we first consider inscribing an equilateral hexagon in the unit circle: [Just like an equilateral triangle, an equilateral hexagon has equal lengths for all of its sides. In general, an equilateral polygon (regardless of how many sides it has) has equal lengths for all of its sides.] Note that the inscribed hexagon can be considered as the 'splicing together' of six equilateral triangles. [If we draw the line segments from the vertices to the center of the inscribed hexagon, since the sides have the same length, the angles as viewed from the center will have the same size. 360/6° = 60°. (The prior two sentences use Euclidean geometry). We know that the triangle we just created is isosceles, (two of its sides are radii), so the two angles opposite the radii have the same size, and add up to 120°: they are both 60°. All three angles are equal. Thus all three sides of the triangle have equal length. (The very last sentence also uses Euclidean geometry)] Now, observe that the horizontal side "above the x-axis" is bisected by the y-axis. Thus, the length of this side in the first quadrant of the unit circle is ½ [the triangle is equilateral, so the side being bisected has the length of the radius, i.e. is length 1]. That is, cos(60°)=½. [The y-axis has an angle of 90° i.e. p/2 radians i.e. 100 gradients. The angle created by drawing line segments from the vertices of this side, to the center, starts at 60° and ends at 120°. So, the y-axis is 90° - 60° = 30° into the above angle, which means the y-axis bisects this angle.] i.e. [solve for sin(60°); we know we need the positive root because 60° is in the first quadrant, so I can omit ±] sin(60°) = /2 Since 30° is the complementary angle to 60°, we also have computed sin(30°) and cos(30°). How does "wrapping the real number line around the unit circle" work? The unit circle has a circumference of 2p. "Thus", all trig functions will have the same value when evaluated 2p radians apart. We say that all trig functions have a period. [In "stratosphere" math, this period is arrived at in a very different way.] The trig function period identities are [X is an angle, n is a positive integer]: These identities hold even in the undefined case [if one side is undefined, they both are.] To formally demonstrate the n part, I would use natural induction, which should be buried somewhere in College Algebra. If you don't recall this term clearly, don't worry about it. However, I'm only going to explain it for n=1. We read these from the unit circle immediately: sin(X+[circle]) = sin(X) cos(X+[circle]) = cos(X) We use the rewrite of sec(X) and csc(X) in cos(X) and sin(X) to derive these: sec(X+[circle]) = sec(X) csc(X+[circle]) = csc(X) Now, to deal with tan(X) and cot(X), we have to be a little more clever. For tan(X), write: i.e. tan(X+[½][circle])=tan(X). The identity cot(X+[½][circle]) = cot(X) is similar, but works with the multiplicative reciprocals throughout. What are the triangle area formulae? There are two basic formulae, and one "impractical" one. "½ base times height" (Area)=(½)(length of base)(length of height) To use this formula, pick one side of the triangle as the "base". Note its length. Then, draw a perpendicular line segment from the vertex of the triangle not in the "base", to the "base", and note this line segment's length (this is the height). [This formula does work for obtuse triangles. Extend the base to where it would hit the perpendicular line.]. This formula is easily visualized for a right triangle [a rectangle with a line segment between two opposite vertices gives two right triangles, both clearly with half the original area since they are congruent]. It behaves reasonably for line segments [it gives zero area, which is correct for a line segment; either base or height is zero for a line segment.] EXERCISE: learn to use this formula by applying it to the reference triangles. The 45-45-90 triangle with hypotenuse should have area ½, and the 30-60-90 triangle with hypotenuse length 2 should have area . This formula has useful analogies in higher dimensions. The volume of either a pyramid or a cone, for instance, is given by: (Volume)=(1/3)(area of base)(length of height) The "obvious generalization" for n-dimensional Euclidean space (n a positive integer) is (n-d hypervolume)=(1/n)(n-1 hypervolume of base)(length of height) and for 4-d Euclidean space, English permits a simplification: (hypervolume)=(¼)(volume of base)(length of height) The n-dimensional formula is clearly dimensionally consistent: using a length unit, both sides have dimension (length)n. The n-dimensional formula can be directly computed if one is familiar with iterated integrals (say, from Calculus III or a decent physics course). "½ of the product of the lengths of two sides, and the sine of the included angle" (Area)=[½](length of side 1)(length of side 2)sin(angle between sides 1, 2) (Area)=[½]absin(C) (Area)=[½]acsin(B) (Area)=[½]bcsin(A) We can see this, from the immediately prior formula, by taking side 1 to be the base, side 2 to be the hypotenuse of the right triangle formed between the [extended, if necessary] base and the height, and then solving for the height in terms of side 2 and the angle between sides 1 and 2 [an acute angle of the right triangle we just constructed]. We get: (length of height)=(length of side 2)sin(angle between sides 1,2) EXERCISE: Learn to use this formula by applying it to the reference triangles. [The correct areas are the same as before.] EXERCISE: Now, learn to use this formula by applying it to the equilateral triangle with all sides length 2. This triangle is essentially two copies of the 30-60-90 triangle referred to earlier, so its area is twice as large -- 2. I do not know how to generalize the above formula to n-dimensional Euclidean geometry. Heron's area formula for a triangle: (Area)² = s(s-a)(s-b)(s-c) where s=a+b+c and a, b, c are the lengths of the sides. [Take the positive square root to get area.] This formula gives zero when the length of one side is the same as the length of the other two sides, but will malfunction when one side has length zero. The Heron referred to here is a Greek mathematician (B.C.), so the formula can (or should be able to, at least) be derived in straight Euclidean geometry without coordinates. However, I have not read this, so I cannot explain it. EXERCISE: Learn to use this formula by applying it to the reference triangles, and also to the equilateral triangle with all sides length 2. The mathematician Cartan generalized this formula to n-dimensional Euclidean geometry, using matrix determinants [this is the determinant of a certain 3x3 matrix]. Cartan's generalization is definitely beyond the scope of this crash review. What is the law of sines? sin(A)/a = sin(B)/b = sin(C)/c Note that the angles A, B, and C are strictly between 0 and 2 in angular measure. This means that solving for the sine of an angle by the law of sines does not strictly determine the angle, normally. [It does if the angle is a right angle; then sin(angle)=1]. If the solved-for sin(angle) is strictly between 0 and 1, then some work is required to determine the actual angles. The inverse sine function on a calculator, or spreadsheet, is programmed to give an acute angle [strictly between 0 and in angular measure]. However, since the sine of an angle X is equal to the sine of its supplementary angle 2-X [sin(X)=sin(2-X)], the supplementary angle is also a viable choice. [EXERCISE: Learn to use the sine law by explicitly writing out the equalities for the 45-45-90 triangle with hypotenuse , the 30-60-90 triangle with hypotenuse 2, and the equilateral triangle with all sides length 2.] What is the law of cosines? This is the generalization of the Pythagorean theorem to non-right triangles. I'm going to present it "deus ex machina". c²=a²+b²-2abcos(C) b²=a²+c²-2accos(B) a²=b²+c²-2bccos(A) However, this formula does behave correctly in the extreme cases [worked for C, others are similar]: The last equation is physically correct: if C=2, then the triangle is really a line segment, and the side c physically has length a+b. This is what the algebra states: c²=(a+b)² i.e. \|c\|=\|a+b\| i.e. [a, b, c are all guaranteed to be non-negative, since they represent physical lengths] c=a+b [EXERCISE: Learn to use the cosine law by explicitly writing out the equalities for the 45-45-90 triangle with hypotenuse , the 30-60-90 triangle with hypotenuse 2, and the equilateral triangle with all sides length 2.] [EXERCISES: Learn to use these formulae with the reference values we already have: 0°, 30°, 45°, 60°, and 90°. Namely: try A=0° [should reduce to trigonometric function of B or -B, respectively] and B=0° [trigonometric function of A]. Also, try 20°=0°, 245°=90°, 230°=60°, and 30°+60° = 90°. Ranging into the second quadrant: try 90°+(another reference angle), 260° = 120°, and 290° = 180°. The tangent identities should not be usable when one of the angles is a right angle.] Note: several entries in Trigonometry Survival 201 are/will be based on this. What are the angle-halving formulae? The angle-halving formulae are easily derived from the Pythagorean Identity and the formula for cos(2A). In general, we need to know which quadrant the angle A/2 is in to decide on the correct sign. All are trig(onometric) sum or difference formulae. The first four are also product formulae. EXERCISE: Derive these from the angle sum and difference formulae, as follows: Set X=A+B and Y=A-B Substitute in the angle sum and difference formulae for the affected functions, and simplify. Solve for A and B in terms of X and Y, and then replace A, B with their expressions in X, Y. EXERCISE: Numerically use the sum and difference identities for X=A+B, Y=A-B where A, B are reference angles. The tangent ones will break down when 90° is A, B, X, or Y. EXERCISE: Numerically use the product identities for A=(X+Y)/2, B=(X-Y)/2 where X, Y are reference angles. Wait! I'm not completely sure how to solve for A and B in terms of X and Y! Until I get a College Algebra page going, here's a quick summary on how to solve systems of linear equations. (This domain can use several.) [While not all systems of linear equations are solvable, the one we want to is solvable.] Substitution We hope that by cleverly adding multiples of pairs of equations, we can get equations with reasonably isolated variables. This works fairly well with two variables. How this works in practice: X=A+B, Y=A-B. To solve for A, eliminate B from the resulting sum and then solve. Since 1+(-1)=0, we simply add both equations: X+Y=2A. Dividing by 2 yields (X+Y)/2=A. To solve for B, eliminate A from the resulting sum and then solve. Since 1+(-1)1=0, we subtract Y=A-B from X=A+B: X-Y=2B. Dividing by 2 yields (X-Y)/2=B. Gaussian Elimination (named after Gauss, the mathematician) Taking variables from left to right (in our case, A, then B): Pick a linear equation using the "leading variable". If this variable's coefficient is not 1, divide the equation by this coefficient. This equation is now the "topmost equation". By adding a suitable multiple of the "topmost equation" to the other equations, remove A from the resulting equations. We are now done with the "topmost equation". Set it aside. When the only equations left have a multiple of a single variable equal to a constant, solve those variables. Then replace those variables in the equations that have been set aside. Repeat until all variables have been explicitly solved. How this works in practice: X=A+B, Y=A-B: A is "leading variable". Both X=A+B and Y=A-B have coefficient 1 for A. However, the multiple of the "topmost equation" I am subtracting is 1[=1/1; numerator is from the equation I am subtracting from, denominator is from the "topmost equation". I arbitrarily choose my topmost equation to be Y=A-B. We subtract Y=A-B (i.e. 1[Y=A-B]) from X=A+B to get X-Y=2B. We solve for B: B=(X-Y)/2. We then subsitute this into the "topmost equation" X=A+B, getting X=A+(X-Y)/2 Isolating A, we end up at (X+Y)/2=A. Cramer's Rule: This is theoretically interesting, since it directly informs you when the system of linear equations does not have a unique solution. However, it requires the introduction of even more terminology. I won't cover it in this refresher. Angle classifications Acute -- strictly between 0 and strictly between 0 and 90° strictly between 0 and p/2 radians strictly between 0 and 100 gradients Right -- exactly 90° exactly p/2 radians exactly 100 gradients Obtuse -- strictly between and 2 strictly between 90 and 180° strictly between p/2 and p radians strictly between 100 and 200 gradients Suggestions: Note that 15° is computable either with the half-angle or the difference-angle formula from the standard reference table. Use both of these methods. Also, 75° can be computed by the sum formula from the standard reference table; use this method. Once you are confident that these tables are correct, and if you want more practice with the angle sum, difference, halving, and doubling formulae, use these additional reference values in combination with the earlier ones [0°, 30°, 45°, 60°, and 90°, i.e. the standard table]. [EXERCISE: translate everything into radians. If you plan to use gradients, also translate everything into gradients.] Suggestions: First, let X be an angle such that 5X works out to be 0, 1, 2, 3, or 4 full circles. [That is, we are directly interested in 72°, 144°, 216°, or 288°. I also included 0°, but that is a standard reference value. We will recover: 18° from 72° and the cofunction identities 36° from 144° and the supplementary angle identities 54° from 36° and the cofunction identities It may provide some intuition about the following equations to subtract 1 circle off 216° [-144°] and 288° [-72°].] Next, use the angle addition formulae to rewrite in terms of sin(X) and cos(X) sin(5X)=0 cos(5X)-1=0 [a convenient rewrite of cos(5X)=1, for this problem] These are the equations that describe an inscribed equilateral pentagon. They are* solvable using nothing more than the quadratic formula(!), and what we already are supposed to know. This would occur to me from sin(X) being an (algebraically) odd function, combined with the angle comments above: sin(0°)=0, so we can factor sin(X) out of our expanded version of sin(5X)=0. Then, use the Pythagorean identity to replace cos²(X) with 1-sin²(X). Expand the results. This should give a quartic in sin(X) [oops], which is also a quadratic in sin²(X) [great]. Use the quadratic formula to solve for sin²(X). Then take square roots on the solutions we get for sin²(X); we need both the positive and negative roots. One of these root sets is for 72° and -72°, and the other one is for 144° and -144°. Geometrically, the larger positive root goes with 72°, and the smaller positive root goes with 144°. Solve for cosine of 72° and 144° with the Pythagorean identity [be sure to use the quadrants to force the correct sign]. Then fill in the table as summarized initially. Also: when completing the table, tan(18°) and tan(54°) [and their corresponding cofunction values, cot(72°) and cot(36°)] are technically difficult to algebraically compute directly from the sine and cosine values. [The denominator needs two stages to cancel out correctly.] I tried that three times in a row, and got three different answers, all of them wrong. The method I used for the table was to compute cot(18°) and cot(54°) respectively, and then take the multiplicative inverse algebraically to get tan(18°) and tan(54°). Instant numerical trigonometric tables for sin, cos, and tan near 0 This isn't really "fair", since it relies on the "stratosphere" math approach. The first mention of the basis for this, traditionally, is in the middle of a Calculus series [business or conventional]. However, it is very practical. (Especially if you plan to use trigonometry in an engineering course.) I'm going to present how the result is arrived at in just enough detail, that those readers who actually know the relevant material will be able to see that I'm doing it right. [If you know what a power series is, and the alternating series test for convergence, you will immediately recognize what I'm doing. If not -- well, I said this wasn't "fair". Put these equations and inequalities into a spreadsheet to see why the above is plausible. If you don't have access to a spreadsheet, then use a calculator. If you don't have even that, at least do it for the numbers 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9.] For three decimal place accuracy (the least we are interested in, for practical purposes), we need to control the error to less than 510-4 i.e. [½]10-3. This error term is: for sin(X), X³/6 for cos(X), (X4)/24 Now, let's solve for X: sin(X) X³/6<510-4 i.e. X³<3010-4 i.e. X³<310-3 i.e. X<[31/3]/10 which is between 0.144 and 0.145 cos(X) (X4)/24<510-4 i.e. X4<12010-4 i.e. [yes, there's a reason I'm not reducing here!] X<[1201/4]/10 which is between 0.330 and 0.331 That is, for X in radians: when 0<X<0.144, sin(X)=X to three decimal places when 0<X<0.330, cos(X)=1-X² to three decimal places What if you want the "instant trig table" to more decimal places? Just work the above bound calculations with 510-(number of decimal places+1) instead of 510-4. Note that at the final stage, I took the decimal my TI-36SX Solar calculator gave out, and found the three-decimal place numbers that bracketed it. For a different number of decimal places, bracket the result with decimals to as many places as you need precision. Computing tan(X) and sec(X) from the results of this "instant trig table" will give reasonably accurate numerical results. Computing cot(X) and csc(X) will not work reasonably "near 0"; in general, you cannot get more significant digits out than you put in, and sin(X) will lose significant digits as X ends up near 0. This means you are dividing a large number by a small, imprecise number, which will not give reasonable numerical results. [The zero decimal places between the decimal point and the first non-zero digit are "lost significant digits". For example, sin(0.021)=0.021 to three decimal places -- but there are only two significant digits.]
Algebra The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a... Algebra (in 'Group theory' article) Here, the basic idea is to associate a group (the so-called Galois group, named after the mathematician E. Galois) with algebraic equation (6) in 6 su Applications to algebra and geometry (in 'Lattice (mathematics)' article) Lattices, like groups and rings, can be defined as abstract algebras, that is, as systems of elements combined by universally defined operations. The Lie algebra (in 'Lie group' article) Let G be a Lie group. The identity component of G is an open subset of G and is a smooth manifold. Thus it makes sense to speak of tangent spaces. Multilinear algebra and tensors (in 'Linear algebra' article) Linear algebra is generally regarded as including also multilinear algebra, the basic notion of which is that of a bilinear mapping of the pair of vec
Software Categories Math software downloads by HydeSoft Computing Graphing software for scientists, engineers, and students. It features multiple scaling types, including linear, logarithmic, and probability scales, as well as several special purpose XY graphs and contour plots of 3D data. by Clay Pot Software Learn basic math with deep understanding easier and faster by simply practicing using tables (ex. New Multiplication Table with Pictures) that continually expose students to the big picture of how and why math works
Functional Skills in Mathematics Rob Apperley and Gill Colley Focus on key skills All current GCSE specifications now require a proportion of questions to have embedded 'functional elements', testing everyday mathematics skills. At foundation tier this applies to up to 40% of questions, and it remains a key concern even in higher tier papers. Functional Skills in Mathematics is specifically designed to develop the skills that all students will need, as applied to real life and workplace situations. It contains materials to test and then reinforce the following mathematical concepts: numbers calculations ratio and proportion fractions, decimals and percentages equations and formulae discrete and continuous data statistical methods probabilities area, perimeter and volume of common shapes 2D representations of 3D objects metric and imperial measures. Once they have taken their initial test, students then work on the areas where they need most reinforcement, using step-by-step worked examples and practice questions. Full teacher's guidance and useful Web links are also included. Essential grounding for later life Mathematics departments need to make sure that their students have a firm grounding in functional skills, both to comply with the requirements of the new GCSE and other examination syllabuses, and to give students the basic capabilities they will need in later life. Functional Skills in Mathematics gives you a bank of copiable resources designed for the purpose, which can be used to support a programme of study or as reinforcement or exam preparation for particular students. Convenient format Functional Skills in Mathematics is supplied on a CD-ROM and comes with a full site licence, meaning that it can be placed on a network for the whole department to use. Students needing reinforcement can access the materials independently, and teachers can find and use material whenever they need it.
The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics. The primary purpose of the book is to highlight approximations to the difficult isomorphism problem... more... The book introduces readers in the often-overlooked math-related fields to the ideas of writing-to-learn (WTL) and writing in the disciplines (WID). It offers a guide to the pedagogy of writing in the mathematical sciences, and gives theoretically grounded means by which writing can be used to help undergraduate students to understand mathematical... more...
Course Number and Title Number of Credits Minimum Number of Instructional Minutes Per Semester Prerequisites Corequisites None Other Pertinent Information At least four one-hour tests, quizzes, and a two-hour comprehensive departmental final examination will be given. Catalog Course Description This is the first course in the calculus sequence for physical science, business, computer science, mathematics, and engineering students. Topics include: limits, the rate of a function, derivatives of algebraic and basic trigonometric functions, applications of derivatives, integration, and applications of the definite integral. Required Course Content and Direction Learning Goals: Course Specific: The student will be able to: demonstrate understanding of the concept of limit. evaluate limits. demonstrate understanding of the concept of continuity. evaluate derivatives of algebraic and trigonometric function. demonstrate correct use of implicit differentiation to find a derivative. Category III: Critical Thinking/Problem Solving: The student will be able to: demonstrate an understanding of solving problems by: recognizing the problem reviewing information about the problem developing plausible solutions evaluating the results These skills are developed in VII.B.3 and VII.B.5. Planned Sequence of Topics and/or Learning Activities: The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lesions required to study the topic. Limits and Continuity (8 lessons) Geometric Interpretation of Limits Evaluating Limits Limit Theorems One-Sided Limits Continuity The Derivative (12 lessons) Geometric Interpretation - Tangent Line to a Curve Definition of Derivative Velocity, Acceleration, and Other Rates of Change Finding Derivatives, Using the Limit Definition Finding Derivatives, Using the Formulas Product and Quotient Rules Derivatives of Basic Trigonmetic Functions Chain Rule and Composite Functions Implicit Differentiation Higher Order Derivatives Applications of the Derivative (12 lessons) Straight Line Motion Related Rates Increasing and Decreasing Functions Relative and Absolute Extrema Concavity and Inflection Points 2nd Derivative Test Optimization Problems Differentials Integration (9 lessons) Indefinite Integrals Differential Equations Summation Notation Finding Areas and Definite Integrals by Definition Fundamental Theorem of Integral Calculus Properties of the Definite Integral Using Substitution to Evaluate Integrals Applications of Integration (7 lessons) Area Under a Curve Average Value of a Function Area Between Curves Volumes of Revolution - Disk and Shell Method Length of a Plane Curve open-ended questions reflecting theoretical and applied situations. Reference, Resource, or Learning Materials to be used by Students: Departmentally selected textbook and graphing calculator. Details provided by the instructor of each course section. See Course Format.
10. Gain competency in other areas of mathematics (which ones and how many depends on the selected option). 11. Demonstrate basic competency in both oral and written communication. MS Mathematics In the Mathematics MS program students choose one of two options: Option 1 (General Mathematics) and Option 2 (Applied Mathematics). The learning outcomes are somewhat different for each as seen below. Graduating students in both options will: 1. Have a broad exposure to advanced mathematics through electives chosen from a wide range of topics including abstract algebra, advanced calculus, geometry, differential equations, linear algebra, probability, number theory, and topology. 2. Understand and devise proofs of mathematical theorems. This includes understanding the role of definitions, axioms, logic, and particular proof techniques such as proof by induction, proof by contradiction, etc. 3. Be able to write a coherent, clear article on a mathematical theme, and to present this orally. 4. Be able to search the mathematical literature to research a topic of interest. 5. Understand and be able to apply basic results of complex analysis including: the relationship between complex analytic functions and harmonic functions, conformal mapping, and applications to Dirichlet problems; Cauchy's integral formulas and their consequences including the fundamental theorem of algebra; series expansions, classification of singularities, and the application of residue calculus to definite integrals and sums. Graduating students in Option 1 (General Math) will: 1. Have a broad understanding at the graduate level of the content of the required courses of the option. This includes the theory of groups, rings and fields, topology, complex analysis, and real or functional analysis. 2. Understand the basic theories of groups, rings and fields, including the structure of finite groups, polynomial rings and Galois theory. 3. Understand how the main topological concepts (connectedness, compactness, products and separation properties) are introduced and used in abstract spaces where the topological structure is not derived from an underlying metric. 4. Understand basic set theory including axiom of choice, basic topological properties of the real line; properties of real functions, sequences of real functions and various notions of convergence such as pointwise and uniform convergence. 1. Have a broad understanding at the graduate level of the content of the required courses of the option. This includes numerical analysis, linear analysis, mathematical modeling and complex analysis. 2. Be able to use a variety of mathematical tools (differential equations, linear algebra, etc) to formulate a mathematical model of real world problems. Understand the balance between the complexity of a model and its mathematical tractability. Understand the iterative process of modeling and the necessity to test a model against data. 3. Be able to apply numerical methods to solve problems, such as large systems of linear equations, eigenvalue/eigenvector problems, and understand the theoretical underpinnings of these methods. 4. Be able to solve partial differential equations numerically and be able to analyze the stability and convergence of these approximate solutions. This includes the understanding of the fundamental differences among parabolic, elliptic and hyperbolic partial differential equations, the Max/Min principle for certain elliptic partial differential equations and the method of characters for and second order hyperbolic partial differential equations. 5. Understand metrics, norms, and inner products on important spaces of functions, including Banach spaces and Hilbert spaces and be able to use important applications including Fourier series and solutions of integral equations by contraction. They will be familiar with basic properties of linear operators, especially on Hilbert spaces, invertiblity and spectrum, and be able to apply these to solution of integral equations and differential equations.
Exponential Functions In this lesson, Professor John Zhu gives an introduction of the exponential functions in the general form as well as the special exponential function. He goes through several example problems utilizing the exponential properties. This content requires Javascript to be available and enabled in your browser. Exponential Functions Useful identities: Sometimes helpful to think of numbers as exponents: , , etc
Algebra Algebra is helpful But also very boring. By the time the lesson's finished, Over half the class is snoring. Their alarm clock is the bell That signals the next class. They haven't learned a single thing, Except how to sleep through math. I know this poem's boring, But it's also very true. If you took the time to read this, You can learn math, too. It's not as easy as it seems, To stay awake in class. But with a little practice, You can make the grade and pass. -Megan, 12, Pensacola, FL
Beginning Algebra : Text / Workbook - 7th edition Summary: Pat McKeague's passion and dedication to teaching mathematics and his ongoing participation in mathematical organizations provides the most current and reliable textbook series for both instructors and students. When writing a textbook, Pat McKeague's main goal is to write a textbook that is user-friendly. Students develop a thorough understanding of the concepts essential to their success in mathematics with his attention to detail, exceptional writing style, and or...show moreganization of mathematical concepts. BEGINNING ALGEBRA: A TEXT/WORKBOOK, Seventh Edition offers a unique and effortless way to teach your course, whether it is a traditional lecture course or in a self-paced format. In a lecture-course format, each section can be taught in 45-to-50 minute class sessions, affording instructors a straightforward way to prepare and teach their course. In a self-paced format, Pat's proven EPAS approach (Example, Practice Problem, Answer and Solution) moves students through each new concept with ease and assists students in breaking up their problem-solving into manageable steps. The Seventh Edition of BEGINNING ALGEBRA: A TEXT/WORKBOOK has new features that will further enhance your students' learning, including boxed features entitled Improving Your Quantitative Literacy, Getting Ready for Chapter Problems, Section Objectives and Enhanced and Expanded Review Problems. These features are designed so your students can to practice and reinforce conceptual learning. Furthermore, iLrn/MathematicsNow, a new Brooks/Cole technology product, is an assignable assessment and homework system that consists of pre-tests, Personalized Learning Plans, and post-tests to gauge concept mastery. ...show less Paired Data and Graphing Ordered Pairs. Solutions to Linear Equations in Two Variables. Graphing Linear Equations in Two Variables. More on Graphing: Intercepts. The Slope of a Line. Finding the Equation of a Line. Linear Inequalities in Two Variables. Multiplication with Exponents. Division with Exponents. Operations with Monomials. Addition and Subtraction of Polynomials. Multiplication with Polynomials. Binomial Squares and Other Special Products. Dividing a Polynomial by a Monomial. Dividing a Polynomial by a Polynomial. 6. FACTORING. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials. More Trinomials to Factor. The Difference of Two Squares. Factoring: A General Review. Solving Equations by Factoring. Applications. Definitions and Common Roots. Properties of Radicals. Simplified Form for Radicals. Addition and Subtraction of Radical Expressions. Multiplication and Division of Radicals. Equations Involving Radicals. 0495108987 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!! $7495108986-5-0 $7.1741
Equation is a useful software that can let you study and solve the equations of the second degree, enter only the values of a, b, and c and this software will do the rest. Once all the values are entered, the application will display ... Equation Illustrator V has been designed to ease the ... graphics and complicated formatted text such as math equations in electronic and printed documents. A WYSIWYG interface ... what you want where you want it. Formatted equation macros can be stored and retrieved with a ... also included, over 50 drawing tools in all. Equation Illustrator V is designed for people who know ... The program allows you to solve algebraic equations in the automatic mode. You just enter an equation in any form without any preparatory operations. Step by step Equation Wizard reduces it to a canonical form performing ... After that it determines the order of the equation, which can be any - linear, square, cubicQuadratic equation has the form ax2 + bx + c ... two different values of x that make the equation true. It can happen that both solutions are the same number, and it is possible that the solutions will be complex or imaginary numbers. To use this software, type in values ... FX Equation software was designed to be an equation editor that takes the chore of formatting equations away from you. It is for people who love the output from the modern equation editors but hate using them. FX Equation automatically formats, with a minimum of input from you, just about all of the equations an average mathematics teacher uses everyday. FX ... AutoAbacus is a powerful equation solving library that finds solutions to equation sets with a snap. A set of equations can be passed in as text, while AutoAbacus ... find a solution that satisfies all constraints. The equations are not limited to be only linear, but ... include arbitrary functions. By profiling the types of equations in the system and their dependencies on each ... MathType is a powerful interactive equation editor for Windows and Macintosh that lets you ... MathML documents. More Ways to Create Equations * Entering Math by Hand: Enter equations as easily as you would write math with ... 7. * Point-and-Click Editing with Automatic Formatting: Create equations quickly by choosing templates from MathType's palettes and ... MathCast is an equation editor, an application that allows you to input mathematical equations. These equations can be used in written documents and webpages. The equations can be rendered graphically to the screen, to ... interface is suited for rapid development of mathematical equations. A part of this interface is called The ... user to create scientific mail messages with complex equations. This modern and beautiful scientific software makes the exchange of complex ideas simple. The scientific equation editor used in this software allows you to create complex letters, including complex scientific equations, at almost the same speed as typing standard ... Scientific Letter, will see the message text with equations included in it as graphical parts. The recipient ... DeadLine is a free program useful for solving equations, plotting graphs and obtaining an in-depth analysis of ... numerical calculus, in a very intuitive approach. Most equations are supported, including algebraic equations, trigonometric equations, exponential equations, parametric equations. DeadLine solves equations graphically and numerically. It displays the graph of ... a list of the real roots of the equation. You can evaluate the function and the first ... Basically an equation editor, however not focused over one single equation, but you can write your mathematical artwork over ... pages. You can easily move and copy your equations and expressions by mouse touch. Illustrate your equations using hand-drawing tools. Use symbolic calculator and function
Introduction to Topology Book Description: This text is intended for a one-semester undergraduate course in topology. The fundamental concepts of general topology are covered rigorously but at a gentle pace and an elementary level. It is accessible to students with only an elementary calculus background. In particular, abstract algebra is not a prerequisite. The first chapter develops the elementary concepts of sets and functions, and in Chapter 2 the general topological space is introduced. Subspaces, continuity, and homeomorphisms are covered in Chapter 3. The remaining chapters cover product spaces, connected spaces, separation properties, and metric spaces. Buyback (Sell directly to one of these merchants and get cash immediately) Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
Provides appendices with solutions to select exercises, a glossary, a list of notations, and a guide to the literature Summary From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, Maple™, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences. THE CAUCHY THEORY The Cauchy Integral Theorem Variants of the Cauchy Formula The Limitations of the Cauchy Formula APPLICATIONS OF THE CAUCHY THEORY The Derivatives of a Holomorphic Function The Zeros of a Holomorphic Function ISOLATED SINGULARITIES Behavior near an Isolated Singularity Expansion around Singular Points Examples of Laurent Expansions The Calculus of Residues Applications to the Calculation of Integrals Meromorphic Functions THE ARGUMENT PRINCIPLE Counting Zeros and Poles Local Geometry of Functions Further Results on Zeros The Maximum Principle The Schwarz Lemma THE GEOMETRIC THEORY The Idea of a Conformal Mapping Mappings of the Disc Linear Fractional Transformations The Riemann Mapping Theorem Conformal Mappings of Annuli A Compendium of Useful Conformal Mappings
Geolo Library Preface One of the purposes of the elementary working courses in mathematics of the freshman and sophomore years is to exhibit the bond that unites the experimental sciences. The bond of union among the physical sciences is the mathematical spirit and the mathematical method which pervade them. For this reason, the applications of mathematics, not to artificial problems, but to the more elementary of the classical problems of natural science, find a place in every working course in mathematics. This presents probably the most difficult task of the text-book writer, namely, to make clear to the student that mathematics has to do with the laws of actual phenomena, without at the same time undertaking to teach technology, or attempting to build upon ideas which the student does not possess. It is easy enough to give examples of the application of the processes of mathematics to scientific problems; it is more difficult to exhibit by these problems, how, in mathematics, the very language and methods of thought fit naturally into the expression and derivation of scientific laws and of natural concepts. It is in this spirit that the authors have endeavored to develop the fundamental processes of the calculus which play so important a part in the physical sciences; namely, to place the emphasis upon the mode of thought in the hope that, even though the student may forget the details of the subject, he will continue to apply these fundamental modes of thinking in his later scientific or technical career. It is with this purpose in mind that problems in geometry, physics, and mechanics have been freely used. The problems chosen will be readily comprehended by students ordinarily taking the first course in the calculus. A second purpose in an elementary working course in mathematics is to secure facility in using the rules of operation which must be applied in calculations. The first five show distinctly that the independent variable is ac, whereas the last three do not explicitly indicate the variable and should not be used unless there is no chance of a misunderstanding.2. The fundamental formulas of differential calculus are derived directly from the application of the dehnition (2)or (3)and from a few fundamental propositions in limits. First may be mentioned(5) D(u 31; 11) -- Du j;Dv, +vDu. (6) (7)It may be recalled that(4), which is the rule for differentiating a function of a function, follows from the application of the theorem that the limit of a product is the product of the limits to the fractional identity- -- ;whence Aa: Ay Aa: lim 55: limA 2 lim 534: limi lim 934, which is equivalent to(4). Similarly, if y= f(.1:)and if rc, as the inverse function of y, be written re :f-1(y) from analogy withy =-sins: and :c=- sin 1 y, the relation(5) follows from the fact that AxAy and AyAa: are reciprocals. The next three result from the immediate application of the theorems concerning limits of sums, products, and quotients( 21).The rule for differentiating a power is derived in case nis integral by the application of the binomial theorem. and the limit when A.r=0is clearly n:1: 1.The result may be extended to rational values of the index nby writing n= B, y :xii, 1 I ::xl and by differentiating both sides of the equation and reducing. To prove that(7) still holds when nis irrational, it would be necessary to have a workable definition of irrational numbers and to develop the properties of such numbers in greater detail than seems wise at this point. The formula is therefore assumed in accordance with the principle of permanence of form( 178), just as formulas like ama =a +of the theory of exponents, which may readily be proved for rational bases and exponents, are assumed without proof to hold also for irrational bases and exponents. See, however, 18-25 and the exercises thereunder. It is frequently better to regard the quotient as the product u- v-1and apply(6). TFor when Arn = 0, then Ay= 0 or AyAn: could not approach a limit. The present small volume is intended to form a sound introduction to a study of the Diflferential Calculus suitable for the beginner. It does not therefore aitn at completeness, but rather at the omission of all portions which are usually considered best left for a later reading. At the same time it has been constructed to include those parts of the subject prescribed in Schedule I. of the Regulations for the Mathematical Tripos Examination for the reading of students for Mathematical Honours in the University of Cambridge. Particular attention has been given to the examples which are freely interspersed throughout the text. For the most part they are of the simplest kind, requiring but little analytical skill. Yet it is hoped they will prove sufficient to give practice in the processes they are intended to illustrate. The topics in this book are arranged for primary courses in calculus in which the formal division into differential calculus and integral calculus is deemed necessary. The book is mainly made up of matter from my Infinitesimal Calculus. Changes, however, have been made in the treatment of several topics, and some additional matter has been introduced, in particular that relating to indeterminate forms, solid geometry, and motion. The articles on motion have been written in the belief that familiarity with the notions of velocity and acceleration, as treated by the calculus, is a great advantage to students who have to take mechanics. Part of the preface of my Infinitesimal Calculus applies equally well to this book. Its purpose is to provide an introductory course for those who are entering upon the study of calculus either to prepare themselves for elementary work in applied science or to gratify and develop their interest in mathematics. Little more has been discussed than what may be regarded as the essentials of a primary course. An attempt is made to describe and emphasise the fundamental principles of the subject in such a way that, as much as may reasonably be expected, they may be clearly understood, firmly grasped, and intelligently applied by young students. There has also been kept in view the development in them of the ability to read mathematics and to prosecute its study by themselves. With regard to simplicity and clearness in the exposition of the subject, it may be said that the aim has been to write a book that will be found helpful by those who begin the study of calculus without the guidance and aid of a teacher. Ox account of the present disturbed state of public afairs, the publication of the Mathematical Monthly will be discontinued until further notice. Electrotyped md Printed by Welch, Bigelow, md Company. This volume is intended to meet the demands of- Teachers and Students, who begin the study of the Calculus before Analytical Geometry. It assumes a knowledge of Elementary Algebra, and Trigonometry as far as the properties of plane triangles. The examples include all those on the subjects treated, set in the South Kensington Examinations of recent years. T.H. M.Borough Road Training College, Isleworth, May 1891. In preparing this second edition the earlier portions of the book have been partly re-written, while the chapters on recent mathematics are greatly enlarged and almost wholly new. The desirability of having a reliable one-volume history for the use of readers who cannot devote themselves to an intensive study of the history of mathematics is generally recognized. On the other hand, it is a difficult task to give an adequate bird s-eye-view of the development of mathematics from its earliest beginnings to the present time. In compiling this history the endeavor has been to use only the most reliable sources. Nevertheless, in covering such a wide territory, mistakes are sure to have crept in. References to the sources used in the revision are given as fully as the limitations of space would permit. These references will assist the reader in following into greater detail the history of any special subject. Frequent use without acknowledgment has been made of the following publications: Annuario Biografico del Circolo MaknuUico di Palermo 1914; Jakrhuch uber die Fortschritte der Mathematiky Berlin;. C.Poggendorffs Biographisch-Literarisckes Handworterbuch, Leipzig; Gedenkkigebuch fur McUhenuUikeTf von Felix Miiller, 3. Aufl., Leipzig und Berlin, i()i 2 Revue SemestrieUe des Publications MathinuUigues, Amsterdam. The author is indebted to Miss Falka M.Gibson of Oakland, Cal. for assistance in the reading of the proofs. Floman Cajori. University of California March, 1919. The treatment of tlie calculus that here follows is based on the courses which I have given in this subject in Harvard College for a number of years and corresponds in its main outlines to the course as given by Professor B.0. Peirce in the early eighties. The introduction of the integral as the limit of a sum at an early stage is due to Professor Byerly, who made this important change more than a dozen years ago. Professor Byerly, moreover, was a pioneer in this country in teaching the calculus by means of problems, his work in this direction dating from the seventies. The chief characteristics of the treatment are the close touch between the calculus and those problems of physics, including geometry, to which it owed its origin; and the simplicity and directness with which the principles of the calculus are set forth. It is important that the formal side of the calculus should be thoroughly taught in a first course, and great stress has been laid on this side. But nowhere do the ideas that underlie the calculus come out more clearly than in its applications to curve tracing and the study of curves and surfaces, in definite integrals with their varied applications to physics and geometry, and in mechanics. Por this reason these subjects have been taken up at an early stage and illustrated by many examples not usually found in American text-books. It is exceedingly difficult to cover in a first course in the calculus all the subjects that claim a place there. Some teachers will wish to see a fuller treatment of the geometry of special Professor Campbells book: The Elements of the Differential and Integral Calculus, Macmillan, 1904, in its excellent treatment of the integral as the limit of a sum, is a notable exception. The chief object of the present work is, as its title indicates, to ixumish to the student examples by which to illustrate the processes of the Differential and Intral Calculus. In this respect it will be seen to agree with frofessor Peacocks Collection of Examples; and indeed if a second edition of that excellent work had been published I should not have undertaken the task of making this compilation. But as Professor Peacock informed me that he had not leisure to superintend the publication of a second edition of his Examples which had been long out of print, I thought that I should do a service to students by preparing a work on a similar plan, but with such modifications as seemed called for by the increased cultivation of Analysis in this University. Accordingly I have not limited myself to the mere collection of Examples and Problems illustrative of Theorems given in Elementary Treatises on the subject, but I have also introduced demonstrations of propositions which, although important and interesting, do not usually find a place in works devoted to the exposition of the principles of the Calculus. In the differential calculus, we have to find the rates, or differentials, of given functions. In the integral calculus, having given any differential, we have to determine the function of which this is the rate; this function is called the integral of the given differential. The integral sign is i; it is always written before an expression for a rate, the rate being generally expressed by a single variable and its differential; as, a dx f:which means that function of xwhose rate is a dx. 2.A definite integral is written with a number or letter, denoting a special value of the independent variable, at the bottom, and another at the top of the integral sign (these letters or numbers being called limits); thus, 3 xdx and indicates the amount by which a quantity, varying with the rate under the integral sign, actually varies while the independent variable passes from the lower to the upper limitThus, the above expression denotes the increment received by any quantity which has the rate a dx while xincreases from 1 to 3.3. An indefinite integral is simply a variable which varies with the rate expressed under the integral sign, and is written without limits; thus, a dx pIt will be seen that the definite integral may, then, be defined as the increment received by the indefinite integral while Xpasses from the lower to the upper limit. An experience of more than fifteen years, in teaching large Classes in the U.S. Military Academy, has afforded the Author of the following pages unusual opportunities to become familiar with the difficulties encountered by most pupils, in the study of the Differential and Integral Calculus. The results of previous endeavours to remove these difficulties were given to the Public in a former edition. The favour with which that edition has been received, induces him to offer a new one, containing, not only such modifications as have been suggested by a thorough trial in the recitation room, but, in addition, an elementary treatise on the Calculus of Variations. That he has, in some degree, realized the hope of advancing a more general and thorough study of one of the most important auxiliaries to scientific research, is an ample reward for the labour which he has bestowed upon the work. The Author has in preparation, and expects soon to publish, an Elementary Treatise on Analytical Geometry. U.S. Military Academy, West Point, N.Y., Augtist 1, 1850. The significance of the Calculus, the possibility of applying it in other fields, its usefulness, ought to be kept constantly ind vividly before the student during his study of the subject, rather than be deferred to an uncertain future. Not only for students who intend to become engineers, but ilso for those planning a profound study of other sciences, the isefulness of the Calculus is universally recognized by teachers; tshould be consciously realized by the student himself. It is )bvious that students interested primarily in mathematics, particularly if they expect to instruct others, should recognize ;he same fact. To all these, and even to the student who expects only genjral culture, the use of certain types of applications tends to nake the subject more real and tangible, and offers a basis form interest that is not artificial. Such an interest is necessary ;osecure proper attention and to insure any real grasp of the essential ideas. For this reason, the attempt is made in this book to present Is many and as varied applications of the Calculus as it is possible to do without venturing into technical fields whose lubject matter is itself unknown and incomprehensible to the ;tudent, and Avithout abandoning an orderly presentation of fundamental principles. The same general tendency has led to the treatment of lOpics with a view toward bringing out their essential usefulless. Analytical, science, after having been long n-lected in these cbuntries as an elementary depart ment of edticaticHi, has, within a few years, been cultivated by the young aspirants for mathematical celebrity with an ardour; and prosecuted with a rapidity and success, whick its warmest admirers could scarcely have hoped for. This change would probably have taken place at an earlier period, but for the obstade opposed to it by the want of treatises on the subject, in our language, of a sufficiently elementary nature. The restless activity of the human mind In the pursuit of knowledge was not long to be checked by so trifling an impediment, and our students soon found in foreign works that which our own professors had failed to supply; and though the medium of these treatises, analytical science began, and has continued, to be cultivated at the universities with singular success. De Morgans Ele Amentary Illustrations of the Differential and Integral Calculus forms, quite independently of its interest to professional students of mathematics, an integral portion of the general educational plan which the Open Court Publishing Company has been systematically pursuing since its inception, which is the dissemination among the public at large of sound views of science and of an adequate and correct appreciation of the methods by which truth generally is reached. Of these methods, mathematics, by its simplicity, has always formed the type and ideal, and it is nothing less than imperative that its ways of procedure, both in the discovery of new truth and in the demonstration of the necessity and universality of old truth, should be laid at the foundation of every philosophical education. The greatest achievements in the history of thought Plato, Descartes, Kant are associated with the recognition of this principle. But it is precisely mathematics, and the pure sciences generally, from which the general educated public and independent students have been debarred, and into which they have only rarely attained more than a very meagre insight. The reason of this is twofold. In the first place, the ascendant and consecutive character of mathematical knowledge renders its results absolutely unsusceptible of presentation to persons who are unacquainted with what has gone before, and so necessitates on the part of its devotees a thorough and patient exploration of the field from the very beginning, as distinguished from those sciences which may, so to speak, be begun at the end, and which are consequently cultivated with the greatest zeal. Sn.,.:.:. 638522 : -- ; j.T)?2 Preface To The First Edition The significance of the Calculus, the possibility of applying it in other fields, its usefulness, ought to be kept constantly and vividly before the student during his study of the subject, rather than be deferred to an uncertain future. Not only for students who intend to become engineers, but also for those planning a profound study of other sciences, the usefulness of the Calculus is universally recognized by teachers; it should be consciously realized by the student himself. It is obvious that students interested primarily in matheo? matics, particularly if they expect to instruct others, should recognize the same fact. To all these, and even to the student who expects only gen eral culture, the use of certain types of applications tends to make the subject more real and tangible, and offers a basis for an interest that is not artificial. Such an interest is necessary to secure proper attention and to insure any real grasp of the essential ideas. For this reason, the attempt is made in this book to present as many and as varied applications of the Calculus as it is possible to do without venturing into technical fields whose subject matter is itself unknown and incomprehensible to the student, and without abandoning an orderly presentation of fundamental principles. The same general tendency has led to the treatment of topics with a view toward bringing out their essential usefulness. In this text on differential calculus I have continued the plan adopted for my Analytic Geometry, wherein a few central methods are expounded and appUed to a la, rge variety of examples to the end that the student may learn principles, and gain power. In this way the differential calculus makes only a brief text suitable for a terms work and leaves for the integral calculus, which in many respects is far more important, a greater proportion of time than is ordinarily devoted to it. As material for review and to provide problems for which answers are not given, a supplementary list, containing about haKas many exercises as occur in the text, is placed at the end of the book. I wish to acknowledge my indebtedness to Professor H.W. Tyler and Professor E.B. Wilson for advice and criticism and to Dr. Joseph Lipka for valuable assistance in preparing the manuscript and revising the proof. H.B. Phillips. Boston, Mass., August, 1916. This Primer has been written to meet the needs of the author, first, for a primary course in the calculus, and secondly, for an outline of topics in a more advanced course that is suitable for combined lecture and text book instruction. The authors method of development is essentially Newtons method of fluxions, as presented by Hamilton in his Elements of Quaternions, Bk. Ill, ch. II. This method is clear, logical, and scientific, and it deserves more recognition than it has received in general analysis, if for no other reason than that it is the method of the original discoverer of the calculus. Its failure to be adopted is due to want of early publication and defective notation, since it is remarkably perfect and general in principle. The subsequent discoverer, Leibintz, gained the field by publications in a desirable notation, although founded upon inferior infinitessimal principles. Lagrange attempted a modification of the infinitessimal into the idea of a principal part as determined by first terms of expansions, and made the differential coefficient the primary quantity. Modern text books have returned to Newtons method of limits as applied to Lagranges differential co-efficient; there is here offered a complete return to Newton, with the fluxion or difierential as the primary quantity. Sfcl Preface The favorable reception accorded the two volumes on the Calculus in this series shows that they have been serviceable in supplying a real need. A general demand has arisen for a similar treatment of the subjects in briefer form, suitable for use in shorter and more elementary courses. Accordingly, in response to numerous requests and suggestions, the present volume has been prepared. The part on the Differential Calculus is of essentially the same character as the former separate volume (which will be referred to in the text as D.C), but the range of topics is restricted; various theorems have been put in less abstract form, and fewer alternative proofs have been given. The chapter on the expansion of functions has been so arranged that the remainder theorem may be omitted without marring the continuity of the subject. In the treatment of functions of two independent variables no use is made of an auxiliary variable. The characteristic features of the larger book are retained. Some of these are as follows:1. The derivative is presented rigorously as a limit.2. The process of differentiation is so arranged as to give the a?-derivative of a function of uin which tis a function of X;the resulting type forms being printed in full-face letters in the text and collected for reference at the end of the chapter. Mo rTSo Thjs book presents a first course in the calculus substantially as the author has taught it at the University of Michigan ibr a number of years. The following points may be mentioned as more or less prominent features of the book. In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the students clear understanding of this principle, without distracting his attention by the discussion of a multitude of details. The accompanying exercises are intended to present the problem in hand in a great variety of forms and guises, and to train the student in adapting the general methods of the text to fit these various forms. The constant aim is to prevent the work from degenerating into mere mechanical routine, as it so often tends to do. Wherever possible, except in the purely formal parts of the course, the summarizing of the theory into rules or formulas which can be applied blindly has been avoided. For instance, in the chapter on geometric applications of the definite integral, stress is laid on the fact that the basic formulas are those of elementary geometry, and special formulas involving a coordinate system are omitted. Where the passage from theory to practice would be too difficult for the average student, worked examples are inserted. As this work contains a great number of Integrals fully worked out, the Author hopes that it will considerably facilitate the progress of those who are entering on this branch of study, by showing them almost all the artifices that are used in those branches that come within its scope. The works that have been consulted are those of Peacock, Gregory, Hall, De Morgan, Young, and various mathematical periodicals; also the excellent little work on the Calculus by Mr. Tate, which, like all the productions of that eminent writer, abounds with useful information, apart from the able manner in which he has treated the first principles. Where integration by parts is used, the whole process is put down, but the student should endeavour as soon as possible to acquire the facility of running off the quantities without writing down all the intermediate stepsEntered according to the Act of Congress, in the year one thousand eight hundred and thirty-six, by Charles Davies, in the Clerks Office of the District Court of the United States, for the Southern District of New YorkThe present pamphlet is intended to be used by mathematical students as supplementary to an ordinary treatise on the Integral Calcnlns. A method of Integration is proposed which makes this operation, always of a tentative nature, more systematic and certain; and in this method the hyperbolic functions are used freely in conjunction with the circular trigonometrical functions. Considering their importance in Applied Mathematics, the hyperbolic functions have not received adequate treatment in ordinary text-books; to illustrate this importance, a digression has been made on their principal properties, illustrated by examples of their application. The recent Cambridge examination papers have been consulted for examples, to exhibit the methods of integration explained in this pamphlet, which, it is hoped, will prove usefnl and interesting to the mathematical student.
Mammoth, AZ SAT Math modern Algebra we most frequently use "x" to represent "the thing". Start any word problem with labeling the unknown, "Let x = the number of ...." It is this great art that has so greatly advanced all the modern sciences. Think of it as the art that supports the sciences!
Welcome to Chapter Three of Math Planet Algebra Crash Course. In this chapter, we will talk about polynomials. Polynomials are the essentail parts of algebra, and they have many uses, and we will mainly talk about their basic concepts and the most common manipulations of polynomials. But before you continue, you should learn the terms below so that you can have a better understanding of the lesson afterward. Different parts of the lesson are also provided so that you can go to the section of your choice.
TI-Nspire Video Tutorials Sign up for a Webinar to get an Overview of Media4Math+! Need help with the TI-Nspire? Media4Math has a library of YouTube videos for the TI-Nspire, the TI-Nspire CAS, the TI-Nspire Touchpad, the TI-Nspire CX, and the TI-Nspire CX CAS. Learn to use the TI-Nspire with these byte-size segments. These video-based (which are embedded videos from our YouTube channel) tutorials can be used in multiple ways: Learn the basic keystrokes for using Nspire Explore key concepts in Algebra and Geometry using the Nspire Whether you use the Nspire Clickpad or the newer Touchpad and CX models, we have a video-based tutorial from our YouTube channel. Many of our video tutorials come with worksheets that show all the relevant keystrokes shown in the video. (Subscribe to our YouTube channel.) Are you looking to take your knowledge of the Nspire CX to the next level? Check out our DOWNLOADABLE VIDEO SERIES FOR ALGEBRA. Click here. TI-Nspire CX Tutorial: Slope Between Two Points TI-Nspire CX Tutorial: Slope for Randomly Generated Points In this Nspire CX tutorial, randomly create two points in a Spreadsheet Window. Graph them as a scatterplot. Connect the two points using the Line tool, then measure the slope of the line. Creating new random coordinates will yield a new line with a new slope. TI-Nspire CX Tutorial: Slope Formula 2 In this TI-Nspire CX tutorial, the Graph Window and Spreadsheet Window are used to calculate the slope of the line between two points. The coordinates of the points are linked to variables, which are then used in the Spreadsheet Window to calculate the slope. The split-screen, dynamically linked windows allow you to manipulate the points, while getting an updated value for the slope.
Costs Course Cost: $300.00 Materials Cost: None Total Cost: $300 Special Notes State Course Code 02052Algebra I provides a curriculum focused on the mastery of critical skills and the understanding of key algebraic concepts, preparing students to recognize and work with these concepts. Through a "Discovery-Confirmation-Practice" based exploration of algebraic concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include an Introductory Algebra review; measurement; an introduction to functions; problem solving with functions; graphing; linear equations and systems of linear equations; polynomials and factoring; and data analysis and probability. Within each Algebra I Algebra I assessments include a computer-scored test and a scaffolded, teacher-scored test. To assist students for whom language presents a barrier to learning or who are not reading at grade level, Algebra I includes audio resources in both Spanish and English. The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards.
Synopsis This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. By the author's design, no problems are included in the text, to allow the students to focus on their science course assignments. Found In eBook Information ISBN: 9780080559674
Scientific Calculators From basic calculations to sophisticated 2-variable statistics, conversions, regression analysis and scientific data plotting, TI's scientific calculators provide a range of functionality for general math, algebra, trigonometry and statistics. Compare the features of various scientific calculators by selecting the boxes below.
College Algebra Essentials CourseSmart eTextbook, 4th Edition Description Bob Blitzer has inspired thousands of students with his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations. Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical. With the Fourth Edition, Blitzer takes student engagement to a whole new level. In addition to the multitude of exciting updates to the text and MyMathLab® course, new application-based MathTalk videos allow students to think about and understand the mathematical world in a fun, yet practical way. Assessment exercises allow instructors to assign the videos and check for understanding of the mathematical concepts presented. Table of Contents P. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials Mid-Chapter Check Point P.5 Factoring Polynomials P.6 Rational Expressions SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER P TEST 1. Equations and Inequalities 1.1 Graphs and Graphing Utilities 1.2 Linear Equations and Rational Equations 1.3 Models and Applications 1.4 Complex Numbers 1.5 Quadratic Equations Mid-Chapter Check Point 1.6 Other Types of Equations 1.7 Linear Inequalities and Absolute Value Inequalities SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 1 TEST 2. Functions and Graphs 2.1 Basics of Functions and Their Graphs 2.2 More on Functions and Their Graphs 2.3 Linear Functions and Slope 2.4 More on Slope Mid-Chapter Check Point 2.5 Transformations of Functions 2.6 Combinations of Functions; Composite Functions 2.7 Inverse Functions 2.8 Distance and Midpoint Formulas; Circles SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 2 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2) 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions and Their Graphs 3.3 Dividing Polynomials; Remainder and Factor Theorems 3.4 Zeros of Polynomial Functions Mid-Chapter Check Point 3.5 Rational Functions and Their Graphs 3.6 Polynomial and Rational Inequalities 3.7 Modeling Using Variation SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 3 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms Mid-Chapter Check Point 4.4 Exponential and Logarithmic Equations 4.5 Exponential Growth and Decay; Modeling Data SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 4 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4) 5. Systems of Equations and Inequalities 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations in Three Variables 5.3 Partial Fractions 5.4 Systems of Nonlinear Equations in Two Variables Mid-Chapter Check Point 5.5 Systems of Inequalities 5.6 Linear Programming SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 5 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5) Appendix: Where Did That Come From? Selected Proofs Answers to Selected Exercises Subject Index Photo Credits
This would be a problem if it was a history book like lenoat's school, as schools should be getting new history textbooks every five or so years in my opinion (unless no new edition of the book they're using has come out and there's no better textbook that they can find), as companies like to publish new editions of history books every few years to keep up-to-date with modern events and to rewrite history a bit in accordance with those events. An Algebra II book, however, isn't going to be affected by that, so the school doesn't really need to replace them that often. Sure, the problem may include something that doesn't exist, but will that affect your answers to the problem or the concept they're teaching you? If it does, then I think there might be a problem. Our math textbooks in our school are the first to be replaced and last is our history books. For the most part the required classes don't need history that comes up to present day. My sophomore US history class finished the year with the Vietnam War which is over 30 years old. Even books that deal with older history need to be replaced. Vietnam is actually more recent history (especially in comparison to something like ancient Greece or Rome), and is especially something that would be updated and cause a new textbook to be needed. Authors of history books like to often produce new editions so that they can update history to be more accurate and more in-line with what is accepted to have happened in modern times. This can change a lot, which some people find surprising, but shouldn't. My AP US History textbook for this year (America: A Narrative History by George Brown Tindall and David Emory Shi) is on its 8th edition, and it was first published in 1984. History changes quickly, and the world should not be lagging behind it. True but most history is also just that history, set in stone, fact. You are right that the opinion on that does change a little because we don't exactly know everything that went on then but I know that math like his Algebra book is changing in the same way as national organizations are always trying to find what is the best way to do math or whatever topic you are in. I have also heard many good arguments for why math textbooks are and should be updated more than history books (most from math teachers but still good reasons). The hard thing I think for most schools is the cost of updating 100 books is a couple 100 dollars a piece so you could spend 2000-3000 dollars on one class not even the entire history section but just government or just algebra I I find that it's the opposite way around. There is rarely any piece of history that can be set in stone, whereas almost the entirety of mathematics will never change because most of the theorems and axioms taught are generally accepted as fact. This is the same reason I prefer math over history - it's far more static, so when you learn something, you almost never need to go back and revise your knowledge on it. We're always uncovering new things about history, though, and we're always changing the way we interpret it. For example, consider a theoretical textbook that has a chapter detailing US involvement in the Middle East in the late 20th century. The first edition of this book was published before the September 11th attacks, and praises the theocratic rebel leaders in the area for standing up against the Soviets, and for being leaders of a new democracy in the area. Obviously, after the September 11th attacks, such leaders were no longer seen that way. So what do the authors do? They create a new edition of the textbook detailing the history as the United States fighting the Soviet Union but failing to predict the outcome of letting the rebel groups take power in the area. Math, on the other hand, does not face such changes that often. Algebra II and Geometry are especially areas that do not need to be revised - much of those classes are based around concepts will likely never change, and the methods to solve problems involving those concepts are also unlikely to change. I'm not sure what level of math you've taken, so I'll assume at least Algebra II. Consider a problem involving the properties of logarithms. Say you're asked to simplify log(2x3 )+log(6x). Using the properties of logarithms, you would get log(12x4 ), and then 4log(12x). There really are no alternate ways to solve such a problem, so such a concept will never be change. Nor would properties of exponents, matrices, or polynomials. Math teachers often want new books because math students for some reason are very good at destroying the books. However, I've not met a math teacher that is always complaining for a new edition, just new books to replace the 8 year old books that are missing 20 pages and half a cover. I agree. However, I do find it odd that the publisher didn't bother changing a few words when they reprinted the textbook to avoid offending 9/11 victims. Math textbooks aren't the only problem. My freshman year world history book said "Egyptian president Hosni Mubarak is working to implement democratic reforms in the country." I laughed at that. It's the same in my district, and even within my school. In my school, the entire foreign language department has iPads. In my district's middle school, there's a Kindle for every student and they do all their textbooks through that. However, that was only something done after I got into high school (in fact, they did that last year, and I'm a junior now) because the tech department was given a huge budget that it didn't need that year.
Register for Math Assessment On behalf of the Department of Mathematics at Hamline University I would like to welcome you to Hamline University. Whether you are just beginning your university studies, continuing your studies after a break or continuing your studies having begun them at a different institution, W E L C O M E. I hope that you find Hamline everything that you hoped for in a university. Soon you will be registering for your first classes at Hamline University and we in the Department of Mathematics want to help you so that you register for the appropriate mathematics course and for the correct course in any area which requires quantitative reasoning. We would like you to help us help you by going through an evaluation of your mathematical and quantitative skills. We have prepared a placement assessment which you must complete before you register for any mathematics course. The assessment covers six areas of mathematics, each addressing different concepts of mathematics: If you have not taken courses which deal with some of these topics, that is OK. We just want to understand your current level of mathematical knowledge. You only need to complete the sections on material to which you have been exposed. If you didn't take mathematics in high school or at your current institution past Algebra II, for instance, you can skip the Calculus portion of the test. If you register for a mathematics course, we want your experience in that course to be both satisfying and successful and so it is important that you get this advice on where you should start your college level mathematics. It is important that you take the placement examination whether or not you plan on taking a mathematics course during your first year at Hamline. When you finish the placement examination, you will be advised on the appropriate mathematics course for you at Hamline University. It is also important that you are prepared when you take this assessment. We suggest that you review the mathematics that you have learned in the past. We have found a good collection of resources at West Texas A & M and suggest that you visit those pages before you begin. Remember that this assessment is not a test for which you will get a grade. Before you start answering questions, you will be asked about your mathematical background and your attitude about mathematics. You will be presented with one question at a time. Please answer as many questions as you can. There is no time limit. Wojciech Komornicki Chair, Department of Mathematics The goal of collegiate mathematics is the understanding of mathematical ideas per se. The role of applications is to enhance that understanding and not vice versa. Saunders Mac Lane In order to use the Assessment Tool you must register with your user name and user id. Please use the user name and user id you have been provided. If you have not been given one or you do not know it, click on the first letter of your last name in the alphabet listing below. In the list of names which appears, click on your name. User name: ID: If you do not remember your user name or are unsure of how we have recorded your name, or have problems in accessing your records click on the first letter of your last name below. Your name will appear in the listing below. Choose it and then supply your ID.
The purpose of this reddit is to help each other understand the course materials, not to share solutions to assignments. Please follow the Stanford Honor Code, and don't post any links to pirated versions of the textbook. Dr. Ng not only makes the class LOOK EASY, he did MAKE the class much EASIER to understand. I can do calculus fairly well, but he helped me understand a lot of things I didn't really understand before. I greatly appreciate his effort to walk you through those "daunting" calculations and see how all makes sense. I have no complaints about AI class -- it feels like a normal class I had in the college; but I love ML class. I mean, I had no interest in Linear Algebra or Differential Calculus before taking the class. Now, those subjects may be ones I'll look into as a result of the interest sparked by the class. Because now I have a use for them. Just as a result of vectorizing the homework for the ML class, I've learned a bit of Linear Algebra. (And my answers were vectorized in the first homework.) If I were a great student, perhaps I'd have the interest in pure maths, even without an application. But as an imperfect student, Dr. Ng's class reaches me. Ok, the math is over-simplified. Big deal. Heck, I'm glad he's not trying to explain gradients and partial derivatives. I don't need the explanation. And the people who don't know don't know their calculus are getting enough of an idea of what's going on to use these techniques he's teaching. It's not like even a tiny portion of the people who don't know vector calculus will get up to speed in 2-3 weeks. Well, this is still personal opinion, of course, but I find that the danger of just applying without understanding the underlying concepts upon which the technique is built has two major pitfalls: increased probability of misuse (i.e.: in statistics, such as in this study) and/or decreased flexibility (it's harder to adapt a technique to a new situation if one doesn't fully understand it). Just my experience; I understand it's a matter of personal preference:P I think I agree. I've been digging away at the AI class and getting good marks, but truthfully I must not understand anything about the class because I find myself disagreeing with the questions a lot. On ML, which zBard is using as troll material, I do get 100% on every test. But you know what? I get it first time. When I am told the answers in AI class, I would still answer the same question differently. Not particularly .. I am a huge fan of Prof Andrew since a long time. Not so much a fan of useless comparisons between the two. For example, you just compared getting all the questions right the first time in ML class to getting questions right in AI. Apples and oranges. The questions in ML are straight forward variants of what has been covered in class; you are expected to get (mostly) all correct in the first attempt, especially if you followed the lecture. And that's exactly how "Review questions" should be. The AI questions on the other hand, are "Homework" - totally different mindset. Ok, fair enough - but I think you're making the mistake that people are preferring ML because they get 100%. Granted, I can only speak for myself, but the 100% is not the important part. If I may be so bold, the AI homework has never been particularly hard - all the work comes from trying to decipher what exactly they're trying to ask you - that's why people get annoyed. If you manage to decipher the questions correctly, they're straight-forward. In ML, the questions are well forumlated but you do need to have watched the lectures to answer them. For the last AI homework I only watched one of the two lecture sets because of heavy commitments and the stuff I got right was the stuff I didn't watch, the stuff I got wrong was the stuff I watched. Something is not right there, in my humble opinion. I must stress i'm not knocking the professors - I particularly like Thrun's style. I just feel the homework is rushed and too open-ended in interpretation to be suited to checkbox marking. The ML class is not about getting 100%. They make that clear by allowing you to re-take each set of questions till you reach 100%. You also have infinite tries for the programming questions. If you want to complete the course, you will get 100%, it is as simple as that. I wish they made the AI-class like that too. These courses are about learning, and they are not beauty contests. The competitive element HAS to exist. It's from human nature (read Darwin). Saying "first place doesn't really matter" or "let everyone get 100%) is the speech of a loser. Watch "Senna" the movie. Always go for the top ! You didn't get my point. I am not arguing whether or not competitiveness has to exist in learning (that is a separate argument), but stating that this particular course is meant to be completely free of that. You are not proving anything to anyone by scoring more than them (scores can easily be gamed). But getting a 100% on review questions and programming indicates that you took the trouble to complete and understand the course.
second semester of algebra 1 course covers: solving systems of equalities and inequalities, exponents and polynomials, factoring polynomials, quadratic equations and functions, exponential equations and functions, radical expressions and equations, as well as rational expressions and equations. Because high school students have unique needs and experiences, CompassLearning ensures that students know where they are, while challenging them to grow. Odyssey High School Math focuses on foundational skills to support learners, emphasizes repetition and practice of key skills, reinforces study habits, including note-taking, to sharpen studentsí comprehension, and covers National Mathematics Advisory Panelís concepts for success in algebra.
Mathematics in our world by Robert E Eicholz( Book ) 64 editions published between 1976 and 1983 in English and held by 160 libraries worldwide Elementary school mathematics by Robert E Eicholz( Book ) 13 editions published between 1963 and 1971 in English and held by 108 libraries worldwide This series of braille mathematics textbooks for primary and intermediate grades uses the Nemeth Code and provides material for mastering the basic math facts and computation techniques. Basic strands extending throughout the series stress the structure of mathematics. Attention is focused upon the fact that a few fundamental concepts compose the foundation from which the entire structure rises in logical sequence.
Join MyAlgebraBook.com and have the first truly interactive and personalized learning experience on the web. With our FREE online book, you'll find algebra to be both fun and rewarding (No, we're NOT kidding!). With a typical math book, you're left out of an important part of the learning process — actively discovering new ideas. But, with MyAlgebraBook.com, you become part of the process through hundreds of interactive questions and , giving you the chance to truly own your new knowledge. Premium Homeschool Members And, our premium homeschool members, get the additional benefits of a completely personalized learning experience. Perfect for the homeschooled student or the adult who would like some algebra review, we'll take care of creating the syllabus, assigning homework problems and we'll even automatically grade them! And, once an assignment is graded, you'll have the chance to retry the challenging problems, until you understand the concept. With the chance to learn from your mistakes in a non-pressured environment, you'll see just how quickly you gain mastery of concepts that might have initially seemed baffling. Premium Instructor Members Signing up as a premium instructor member gives you complete flexibility and control in designing your algebra course. In creating your assignments, you have access to over 1,000 thought-provoking questions and solutions in our database and can choose among free-response, numerical, multiple-choice, and true/false questions. You can have us grade assignments automatically or have your students hand in traditional assignments so that you can check their work — or create a course that's a mix of the two. And, for added flexibility, you can easily supplement pages in the text with your own material, and quickly create your own homework questions for any assignment.
MATH 050 - Provincial Algebra and Trigonometry Course Details Course Code: MATH 050 Calendar Description: In Provincial Level Mathematics, students study the following types of functions: polynomial, quadratic, logarithmic, exponential, exponential, and trigonometric. This course prepares the adult learners with the necessary skills and knowledge for entry into technical, vocational, and career programs that require Math 12 equivalency as a prerequisite and for future study in higher-level math course at College/University. Functions and Graphs - two points in a plane and midpoint of a segment - distance and midpoint formulas - graphs of common functions: linear, constant, quadratic, cubic, square root, absolute value, reciprocal - vertical line test - domain, range, intervals of increase, decrease, constant for graphs and graph functions - real life applications formulas and functions - symmetry of x- and y-axes, odd or even functions - translation, reflection, stretching, and shrinking of graph transformation of functions - sum, difference, product, and quotient of two functions - two functions, f and g finding formulas for f(g(x)) and g(f(x)), domain of and composite function - equation defining a relation and equation of the reverse relation - graph of a relation and graph of the reverse - horizontal line test to determine if function is one-to-one and therefore has a reverse - formula for the reverse of a function - f-1(f(x)) and f(f-1(x))for any number x in the domains of the functions when the reverse of a function is also a function Sequences and Series - terms of sequences given the general term or nth term - formula for the general or nth term given a sequence - summation notation and series evaluation - terms of a sequence defined by a recursive formula - arithmetic and geometric sequences - nth term formulas to find a specified term - the sum of first n terms - sum of an infinite geometric series - sequences and series to solve real-life problems, Learning Outcomes: Upon successful completion of this course, students will be able to: Functions and Graphs - find the distance between two points in the plane and the midpoint of a segment - apply the distance and midpoint formula to solve problems - recognize graphs of common functions: linear, constant, quadratic, cubic, square root, absolute value, reciprocal - use the vertical line test to identify functions - graph and analyze functions, identifying: domain, range, intervals on which the function is decreasing, increasing or constant - write formulas or functions to model real-life applications - determine graph or function symmetry with respect to the x-axis, y-axis, and origin - identify even or odd functions and recognize their symmetry - graph transformations, translations, reflections, stretchings, and shrinkings of functions - graph functions defined piecewise - find the sum of, difference, product, quotient of two functions and determine their domains - find the composition of two functions f and g finding formulas for f(g(x)) and g(f(x)) - write an equation of the inverse relation given an equation defining the relation - sketch a graph of its reverse given the graph of the relation or function - use the horizontal line test to determine if a function is one-to-one and therefore has an inverse - find a formula for the inverse of a function - evaluate composite functions Polynomial and Rational Functions - graph and analyze quadratic functions identifying the vertex, line of symmetry, minimum/maximum values and intercepts. - solve applied problems involving minimum and maximum function values - determine the behaviour of graphs of polynomial functions of higher degree using the leading coefficient test - determine whether a function has a real zero between two real numbers - write and manipulate complex numbers - divide polynomials using long and synthetic division - demonstrate the use of remainder and factor theorems - factor polynomial expressions and solve polynomial functions and find the zeros - find a polynomial equation given its roots Exponential and Logarithmic Functions - understand the relationship between exponential and logarithmic functions - recognize the inverse relationships - graph and analyze exponential and logarithmic functions - use the laws of exponents and the laws of logarithms to simplify expressions and solve equations - use exponential and logarithmic equations to solve real-life applications including exponential growth and decay Trigonometric Functions - identify angles in standard position, positive and negative angles, co-terminal and reference angles - identify special angles and use the unit circle and convert between radians and degrees - determine the trig function values of an angle in standard position given a point on a terminal arm - use trig identities and algebra to simply expressions and solve trig equations - graph and analyze the sine, cosine, and tangent functions -use a calculator to evaluate inverse trig relations - use trig functions to model and solve real-life problems Series and Sequences - distinguish between and solve problems involving arithmetic and geometric sequences and series - use the formulas to find terms, positions of terms, arithmetic and geometric means, differences or ratios, sums of series , and sums of series and sums of infinite series. - use sequences and series to model and solve real-life problems Knowledge: Learners will acquire the knowledge, skills and strategies required to analyze, manipulate, graph and interpret a variety of mathematical functions Grading System: Letters Passing Grade: D Grading Weight: Final Exam: 30 % Other: 70 % Percentage of Individual Work: 100 Course Offered in Other Programs: No Supplies: Please note that textbooks and resources may vary by campus and/or to meet the needs of individual learners. Please contact the instructor at campus of attendance for list of required books.
+ By CYZ SOFT Smart Math Calculator is a powerful tool to calculate mathematical expression and/or solve unknown variables from the expressions. It supports complex number, array (matrix), higher order integral, unit conversion and chart plotting. It is a powerful tool for students and/or professionals to analyze mathematical problems. Because it also support normal calculation, it can also be used as normal calculator for all Android users. This calculator has provided more than 40 diffused mathematical functions covering trigonometric calculation, complex number, matrix, integration, polynomial and chart plotting. It is also able to handle mathematical operators like +, -, , /, , ', %, etc. And these operators fully support matrix and complex numbers. In this way user is able to evaluate complicated expressions, which are either not supported or hard to input in most traditional calculators. Moreover, the 4x*2 + x == 3, or a group of expressions like y13+4y2-3y3==7 y2/2-3y3+y1==9 y3/3-6An input expression is made up of operands, operators, variables, functions and parameters. An operand or a parameter may not be a number, it can be an expression. Blank characters between expression elements do not affect calculation result. Capitalized and uncapitalized characters are both supported. Examples of expression includes pow(4.01,3.1) (0.0731 + 9i) + sin(toRAD(sum(17, 21, avg(3.71, log(198.2), -9.99,112.7)))), abs(-11.2)/(2!) + exp(i+0.7) + x1 2 == 12 - 6 x1 ** 3 or [[2, 3+7i], [3-4.07i, 4.11i], [2, 6]]' * [[2],[7-3i],[6.88 * stdev(2, 3, 4)]]. This calculator provides a calculator assistant tool which has two functions. One is inserting a constant into input. The other is converting value from one unit to another unit. If text in the input box is a valid real value, units conversion tab will use the value in the input box as initial value to-be-converted. Otherwise, units conversion tab does not place an initial value. If conversion is successful, user is able to insert the converted value into input. In order to help user input and evaluate (higher level) integration and plot 2D charts, this calculator includes built-in integration and chart-plotting utilities. User needs not
A revision of the market leader, Kreyszig is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, helpful worked examples, and self-contained subject-matter ... A revision of the market leader, Kreyszig is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, helpful worked examples, and self-contained subject-matter ...
Curves and Surfaces for Geometric Design offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work-whether you're a graduate student, scientist, or practitionerCreate high-quality and professional-looking texts, articles, and books for Business and Science using LaTeX Overview Use LaTeX's powerful features to produce professionally designed texts Install LaTeX; download, set up, and use additional styles, templates, and tools Typeset math formulas and scientific expressions to the highest standards Include graphics and work with figures and tables Benefit from professional fonts and modern PDF features In Detail LaTeX is high-quality Open Source typesetting software that produces professional prints and PDF files. However, as LaTeX is a powerful and complex tool, getting started can be intimidating. There is no official support and certain aspects such as layout modifications can seem rather complicated. It may seem more straightforward to use Word or other WYSIWG programs, but once you've become acquainted, LaTeX's capabilities far outweigh any initial difficulties. This book guides you through these challenges and makes beginning with LaTeX easy. If you are writing Mathematical, Scientific, or Business papers, or have a thesis to write, then this is the perfect book for you. LaTeX Beginner's Guide offers you a practical introduction to LaTeX with plenty of step-by-step examples. Beginning with the installation and basic usage, you will learn to typeset documents containing tables, figures, formulas, and common book elements like bibliographies, glossaries, and indexes and go on to managing complex documents and using modern PDF features. It's easy to use LaTeX, when you have LaTeX Beginner's Guide to hand. This practical book will guide you through the essential steps of LaTeX, from installing LaTeX, formatting, and justification to page design. Right from the beginning, you will learn to use macros and styles to maintain a consistent document structure while saving typing work. You will learn to fine-tune text and page layout, create professional looking tables as well as include figures and write complex mathematical formulas. You will see how to generate bibliographies and indexes with ease. Finally you will learn how to manage complex documents and how to benefit from modern PDF features. Detailed information about online resources like software archives, web forums, and online compilers completes this introductory guide. It's easy to use LaTeX, when you have LaTeX Beginner's Guide to hand. Create professional-looking texts, articles, and books for Business and Science Load fonts and vary their shape and style; choose between thousands of LaTeX symbols from specialized fonts Use macros to save time and effort; load packages to extend LaTeX's capabilities Generate an index, cite books, and create bibliographies Use external pictures, color, PDF bookmarks, and hyperlinks Structure and manage large documents by splitting the input Manage large documents containing lists, index, and bibliography Approach Packed with fully explained examples, LaTeX Beginner's Guide is a hands-on introduction quickly leading a novice user to professional-quality results. Who this book is written for If you are about to write mathematical or scientific papers, seminar handouts, or even plan to write a thesis, then this book offers you a fast-paced and practical introduction. Particularly during studying in school and university you will benefit much, as a mathematician or physicist as well as an engineer or a humanist. Everybody with high expectations who plans to write a paper or a book will be delighted by this stable software. By exploring the recipes in this book, you will learn how to use each of the various blocks and content areas including the resume sections, Journals, and plans. You will learn how to archive a portfolio, and set access levels. We will build an art gallery, a newspaper, use groups for collaboration and assessment, and use the Collections feature to build complex layered portfolios. You will also find recipes for building templates for standards-based report cards and teacher certification. The book is packed with ideas from the simple to the extremely advanced, but each idea is supported with step-by-step instructions that will make all of them seem easy. Meer info This hands-on guide cuts short the preamble and gets straight to the point – actually creating graphics, instead of just theoretical learning. Each recipe is specifically tailored to satisfy your appetite for producing real-time 3-D graphics using GLSL 4.0. If you are an OpenGL programmer looking to use the modern features of GLSL 4.0 to create real-time, three-dimensional graphics, then this book is for you. Familiarity with OpenGL programming, along with the typical 3D coordinate systems, projections, and transformations is assumed. It can also be useful for experienced GLSL programmers who are looking to implement the techniques that are presented here. Meer info This is the second edition of The Visual Display of Quantitative Information. This new edition provides excellent color reproductions of the many graphics of William Playfair, adds color to other images, and includes all the changes and corrections accumulated during 17 printings of the first edition. Meer info This book is more a tool than a book - an idea-generating, horizon-expanding, knowledge-broadening power tool that can be used to boost the creative output of designers, illustrators and anyone else who uses type. If you seek new ways to employ type in your works of art and design (or new twists to apply to your current typographic techniques), use this book. You will find yourself face-to-face with 650+ custom-created examples of typography and type-intensive design. Meer info - Complete Details on language support in the SAP System - Best practices for efficient upgrade planning and successful conversion projects - Instructions on Unicode tools, ABAP enabling, interfaces, printer solutions, translations, and much more Meer info
Foundations of Geometry, CourseSmart eTextbook, 2nd Edition Description Foundations of Geometry, Second Edition implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers– text is ideal for an undergraduate course in axiomatic geometry and assumes calculus and linear algebra as prerequisites. Table of Contents 1. Prologue: Euclid's Elements 1.1 Geometry before Euclid 1.2 The logical structure of Euclid's Elements 1.3 The historical significance of Euclid's Elements 1.4 A look at Book I of the Elements 1.5 A critique of Euclid's Elements 1.6 Final observations about the Elements 2. Axiomatic Systems and Incidence Geometry 2.1 The structure of an axiomatic system 2.2 An example: Incidence geometry 2.3 The parallel postulates in incidence geometry 2.4 Axiomatic systems and the real world 2.5 Theorems, proofs, and logic 2.6 Some theorems from incidence geometry 3. Axioms for Plane Geometry 3.1 The undefined terms and two fundamental axioms 3.2 Distance and the Ruler Postulate 3.3 Plane separation 3.4 Angle measure and the Protractor Postulate 3.5 The Crossbar Theorem and the Linear Pair Theorem 3.6 The Side-Angle-Side Postulate 3.7 The parallel postulates and models 4. Neutral Geometry 4.1 The Exterior Angle Theorem and perpendiculars 4.2 Triangle congruence conditions 4.3 Three inequalities for triangles 4.4 The Alternate Interior Angles Theorem 4.5 The Saccheri-Legendre Theorem 4.6 Quadrilaterals 4.7 Statements equivalent to the Euclidean Parallel Postulate 4.8 Rectangles and defect 4.9 The Universal Hyperbolic Theorem 5. Euclidean Geometry 5.1 Basic theorems of Euclidean geometry 5.2 The Parallel Projection Theorem 5.3 Similar triangles 5.4 The Pythagorean Theorem 5.5 Trigonometry 5.6 Exploring the Euclidean geometry of the triangle 6. Hyperbolic Geometry 6.1 The discovery of hyperbolic geometry 6.2 Basic theorems of hyperbolic geometry 6.3 Common perpendiculars 6.4 Limiting parallel rays and asymptotically parallel lines 6.5 Properties of the critical function 6.6 The defect of a triangle 6.7 Is the real world hyperbolic? 7. Area 7.1 The Neutral Area Postulate 7.2 Area in Euclidean geometry 7.3 Dissection theory in neutral geometry 7.4 Dissection theory in Euclidean geometry 7.5 Area and defect in hyperbolic geometry 8. Circles 8.1 Basic definitions 8.2 Circles and lines 8.3 Circles and triangles 8.4 Circles in Euclidean geometry 8.5 Circular continuity 8.6 Circumference and area of Euclidean circles 8.7 Exploring Euclidean circles 9. Constructions 9.1 Compass and straightedge constructions 9.2 Neutral constructions 9.3 Euclidean constructions 9.4 Construction of regular polygons 9.5 Area constructions 9.6 Three impossible constructions 10. Transformations 10.1 The transformational perspective 10.2 Properties of isometries 10.3 Rotations, translations, and glide reflections 10.4 Classification of Euclidean motions 10.5 Classification of hyperbolic motions 10.6 Similarity transformations in Euclidean geometry 10.7 A transformational approach to the foundations 10.8 Euclidean inversions in circles 11. Models 11.1 The significance of models for hyperbolic geometry 11.2 The Cartesian model for Euclidean geometry 11.3 The Poincaré disk model for hyperbolic geometry 11.4 Other models for hyperbolic geometry 11.5 Models for elliptic geometry 11.6 Regular Tessellations 12. Polygonal Models and the Geometry of Space 12.1 Curved surfaces 12.2 Approximate models for the hyperbolic plane 12.3 Geometric surfaces 12.4 The geometry of the universe 12.5 Conclusion 12.6 Further study 12.7 Templates APPENDICES A. Euclid's Book I A.1 Definitions A.2 Postulates A.3 Common Notions A.4 Propositions B. Systems of Axioms for Geometry B.1 Filling in Euclid's gaps B.2 Hilbert's axioms B.3 Birkhoff's axioms B.4 MacLane's axioms B.5 SMSG axioms B.6 UCSMP axioms C. The Postulates Used in this Book C.1 The undefined terms C.2 Neutral postulates C.3 Parallel postulates C.4 Area postulates C.5 The reflection postulate C.6 Logical relationships D. Set Notation and the Real Numbers D.1 Some elementary set theory D.2 Properties of the real numbers D.3 Functions E. The van Hiele Model F. Hints for Selected Exercises Bibliography
Stewartstown ACT also learn about rational numbers, polynomials, roots, quadratic and exponential functions. Algebra II is a continuation of Algebra I, and will cover many of the same topics, but with more depth. Equations and inequalities become standard, and are used regularly in other topics
How I Teach Calculus: A Comedy (Optimization) This post is a part a larger series documenting the changes I am making to my calculus course. My goals are to implement standards-based grading and to introduce genuine applications of the concepts being taught. I'm not suffering any delusions that any of this is all that ground-breaking, I just want to log the comedy that ensues: What does this map of Middle-Earth do for me? Other than indulging my current obsessions with Tolkien, it gets at the inherent inelegance and drudgery of guess and check. At this point my kids have been working with related rates. They've been doing things with water jugs, as well as working the traditional book style problems. Kids tend to be frustrated by "word" problems. This is because they can't memorize and repeat a process. Most people love to be told exactly what to do — whether they'll admit that or not — if the process has enough complicated steps, but not too many, then they'll feel like they're getting something done, but it was easy because the task had already been planned out with an explicit end in mind. Word problems piss kids off because they have to try and piece together information and frame it mathematically in a form that will allow them to apply the appropriate technique. That is not a fun process for someone who has no idea what that technique actual does or means. This is why you must generate context before content. The changes to my calculus class have brought me a lot of work, but they've also brought on a whole lot more student conceptual understanding. Cornally is happier. So, in a pretty large breach of calculus etiquette, I skip most of the material about critical points, extrema, 1st and 2nd derivative tests, and what have you, and I move straight to optimization. How can they do optimization, if they don't know all that other stuff?! Easily, optimization is really only about using your noggin and finding critical points. So, what better way to introduce a whole chapter of "Applications of the Derivative," as Larson so deftly puts it, than by starting with the most useful application itself! A word about text book structure. Why, oh WHY, do we always put "applications" after abstract content? Don't you get it? The only thing I'm trying to do here is switch that order. You have to be very very judicious in how you do this so as not to burn the children, but why would anyone give two shakes about critical points until they know why they'd want to find them? So, optimization we must do first. Aside of an aside: do not pretend that the "real world applications" your book gives you are sufficient. They just put those in there as a buzz word to sell more books. I blame Texas. So, I spent a lot of this winter reading Tolkien's Lord of the Rings. I've never gotten through all three in a row, and I felt it was about time. I didn't anticipate how engrossing they would be, and when they started showing up in my lessons, I knew I had a problem. See above. I presented the kids this map, and asked them what's the shortest distance to Mordor? I accompanied this question with a little set-up from the book. I won't reproduce it here, but I read an excerpt from Two Towers Book 4 Chapter 3. I also showed the complementary part from the movie (Two Towers DVD Chapter 15 The Black Gate is Closed). The story is that Gollum leads Sam and Frodo to the gates of Mordor, but they are shut. Gollum then leads the two hobbits on a crazy hike through the mountains north of the gate. This is an exercise in implicit differentiation, orthogonal trajectories, and — nominally — optimization; however, the task becomes very daunting very quickly. The kids start drawing lines. Some quickly realize that each step down requires use of the Pythagorean theorem to find the actual distances covered. Many students eventually raise the important question, "Aren't there an infinite number of ways to check?" Yes. They become sad at the thought that I might make them do this. Of course, we don't. The point has been made; we need to develop some mathematics that gets at optimization.1 So where from here? We now need to learn how to optimize. A discussion of critical points occurs. I don't say those words; vocab always comes last. We draw some graphs, what's common about all the highest points? My slope-minded students easily point out that the slope there is nothing. So, if only we could get a function, find its derivative, and then set it to zero, perhaps then we've built a process here? Yup. We then launch into the very classic open-topped-box-from-sheet-of-paper example. I tell a story about camping and chili and having limited tin foil with which to make a chili holding vessel. This kind of contrived problem really rubs me the wrong way, but I'm OK with it now that the kids have context, we're using it to learn process. I have the kids build boxes the boxes by cutting out the edges and taping them up. They then measure the length, width, and height of the box and find its volume. Many students realize that there was really no point in making the box, but hey a lot don't. Fold on the grey lines! They then graph their data on the board making a graph of Volume vs. Cut-out length. It comes out a little shaky but pretty much looks like this plot: (from 0 up to 4.25 anyway…) f(x) = x(8.5-2x)^2 The 8.5 is the dimension of our paper. A great discussion of domain ensues, I'm sure you already see it. In fact, I am suffering absolutely no delusions that this is at all unique. In fact this is about as traditional as I get. Sometimes you just do what works best, even if it smacks of pretense. All that's left to do is develop the math for this model. We get to work out a fairly simple example to show how to combine two equations that relate the same idea: An equation in one variable for single-variable calculus, it must be Christmas! Derivatives ensue, zeroes get thrown around, and optimum values get found. In case you're trying to learn from this:2 we need to use the product then chain rule (or you could distribute first) Again, my goal is always to motivate the necessity for a new technique. I am not Mr. Wizard. 1. I don't usually give impossible/extremely difficult tasks, but I planned this map bit in response to a conversation about the method of guess and check: A student told me that he prefers guess and check because he can usually get the right answer to a problem, and sometimes it's even faster. He likes the method mostly because he doesn't have to learn anything new. This should strike some of you, I know it hit me hard. He recognized the inherent ridiculousness of many math lessons; the techniques taught aren't always the best way to do it. SO WHY ARE YOU TEACHING IT? What does this map of Middle-Earth do for me? Other than indulging my current obsessions with Tolkien, it gets at the inherent inelegance and drudgery of guess and check. 2. I never intended for this blog to teach content, but I've noticed a that a lot of the Google searches that lead to my site are from students looking for help. If you want to learn calculus, you can attend my high school and take my course. Otherwise there are about six trillion other sites that attempt to teach you calculus. I didn't at all get the impression that you don't do math. I just want for math people to consider the benefits or ramifications of stressing "real-world" applications before context and theory. The more we examine this topic in our own classrooms, the better our knowledge will be about it. I know certainly that I've had lots of supervisory "help" that essentially said that "real-life" is the only thing I should teach and that students will be able to construct the theory to match. I'd really like to be able to point to more than one set of research on it. One reason to put abstract teaching before real world applications is that students may learn better that way. I had always felt that it was easier to learn a simplified version before trying to analyze a complicated real-world situation but I didn't really have more than an anecdotal sense of this until I found this article. I read this article when it was published in 2008. As much as I'd love to argue the merits of the study, I guess I don't feel that the article is clear enough about what was taught, how, and then how the assessments were given. For me, it's not about "real-world" it's about context. I've seen the data in my own students that show that concise context building scaffolds the rigorous symbolic math. I hope I haven't given the impression that I don't do hard math. I definitely spend my fair share of time at the board working examples. Hopefully my posts haven't obfuscated that. I think you may be contesting my use of a complicated introduction, which, as I footnoted, I rarely do. I actually try to be as clear and to the point as possible with any non-direct instruction. Do you think I should be clearer about that when I write? Thanks for the comment
More About This Textbook Overview Solid Shape gives engineers and applied scientists access to the extensive mathematical literature on three dimensional shapes. Drawing on the author's deep and personal understanding of three-dimensional space, it adopts an intuitive visual approach designed to develop heuristic tools of real use in applied contexts.Increasing activity in such areas as computer aided design and robotics calls for sophisticated methods to characterize solid objects. A wealth of mathematical research exists that can greatly facilitate this work yet engineers have continued to"reinvent the wheel" as they grapple with problems in three dimensional geometry. Solid Shape bridges the gap that now exists between technical and modern geometry and shape theory or computer vision, offering engineers a new way to develop the intuitive feel for behavior of a system under varying situations without learning the mathematicians' formal proofs. Reliance on descriptive geometry rather than analysis and on representations most easily implemented on microcomputers reinforces this emphasis on transforming the theoretical to the practical.Chapters cover shape and space, Euclidean space, curved submanifolds, curves, local patches, global patches, applications in ecological optics, morphogenesis, shape in flux, and flux models. A final chapter on literature research and an appendix on how to draw and use diagrams invite readers to follow their own pursuits in threedimensional shape.Jan J. Koenderinck is Professor in the Department of Physics and Astronomy at Utrecht University. Solid Shape is included in the Artificial Intelligence series, edited byPatrick Winston, Michael Brady, and Daniel Bobrow Editorial Reviews Booknews A book like no other. The author who is attached to the Department of Physics and Astronomy at the University of Utrecht writes from a deep knowledge of those diverse branches of classical/modern mathematics which have to do with the representation and analysis of three- dimensional surfaces. But his objective has by no means been to produce a "poor man's guide to differential geometry, to topology, to catastrophy theory" but--by borrowing luminously from those fields and others--to expose to engineers concerned with robotics, with computer-aided design, the rich variety of concepts and organizing principles which are available to them as ready-made imagination- expanding tools. This he does in a wonderfully fresh way, with breezy text and heavy reliance upon a very large number of beautifully executed figures. This is, for technical people of many sorts, bedtime reading of the highest order, as unique and pleasure-filled as was d'Arcy Thompson's On Growth and Form. NW Annotation c. Book News, Inc., Portland, OR booknews.com Related Subjects Meet the Author Jan Koenderink was Professor of Physics at Utrecht University for many years. He is currently a Research Fellow at Delft University of Technology and Visiting Professor at MIT and École NationalSupérieure Paris. He is the author of Solid Shape (MIT Press, 1990
This site links students to a vast collection of educational online materials directly related to chapter content for Algebra 1, Geometry, and Algebra 2. Use a "GO" keyword from your textbook to access these resources. The National Library of Virtual Manipulatives (NLVM) is an NSF supported project that began in 1999 to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction. The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students.
Mathematics MATH 545 Probability & Statistics I for Secondary Teachers Description: This course presents the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. Topics also include basic ideas and techniques of statistical analysis. More Info MATH 551 Analysis II for Secondary Teachers Description: This course is the second semester of a two-semester sequence which provides a rigorous introduction to real analysis focusing on structures and problems relevant to the secondary mathematics curriculum. Math 551 continues this introduction with differentiation, properties of the exponential and logarithmic functions, Riemann integration, infinite series, improper integrals, sequences and series of functions, and integration in two variables. More Info Offered in: TBA MATH 570 History of Mathematics for Secondary Teachers Description: This course traces the development of mathematics from ancient times up to and including 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problems solving. Attention will also be paid to the relevance of history to mathematics teaching as well as investigation into the origins of non-Euclidean geometry even though this comes well after Newton and Leibniz, because of its relatively elementary character and fascinating nature. More Info
West Bengal Board Syllabus for Class 8 8th class is the class in which students are said to be in high school. This is a class where students start their self learning process. So they need West Bengal Board class 8 syllabus to do practice so that they can prepare for the chapters in advance so that it will help them to understand it more efficiently in the class. To start their studies since from the vacations, they need the books based on syllabus for class 8th West Bengal Board. When they prepare their topics according to the given syllabus then they know the time which is given to each topic. Students will study nearly 5 main subjects in this class. class 8 West Bengal Board syllabus covers all the subjects, which are Maths, Science, Social Science etc. Student can get well organized and disciplined West Bengal Board class 8 syllabus for all the subjects. Syllabus is something that guides students and helps in preparing their schedule, even on the basis of this syllabus for class 8th West Bengal Board, students can decided on which subject they need to pay more attention and how to manage time accordingly. Syllabus is very necessary for teachers as otherwise they will face difficulty to coordinate with students and they also need to prepare their monthly Plan showing the topic they will going to teach on a particular day so for that they need syllabus for class 8th West Bengal Board. If institutions do not know the syllabus than what they will follow to teach their students as they have to complete the whole course much before the exam date so that students can get sufficient time for revision, so for them also this class 8 West Bengal Board syllabus is necessary. Students can get other relevant materials to prepare for their class 8 West Bengal Board syllabus like the information about the books, reference book, previous year question papers and much more from our edurite portal. West Bengal Board Syllabus for Class 8 by Subject West Bengal Board Best Sellers In order to keep pace with technological advancement and to cope up with West Bengal Board examinations, Pearson group has launched Edurite to help students by offering Books and CDs of different courses online.
1 (800) 321-7511 Math Pathways: Trigonometry Grade Levels: 9 to 12 Mac/Windows List Price: $799.95 $799.95 Qty Cannot discount due to contractual obligations. Jump to: Description Guided by NCTM, a teacher-guided, self-paced, curriculum and standard-based trigonometry learning tool that creates a learning environment in which students can explore, visualize, and appreciate mathematics. +more Introduces and instructs students in major mathematic concepts utilizing a pathways methodology in which students are explained core mathematic concepts and then build on these concepts in their understanding of more complex mathematical problem solving. Guided by NCTM and designed as a teacher-guided, self-paced, curriculum and standard-based learning tool, Math Pathways creates a learning environment in which students can explore, visualize and appreciate mathematics. The unique combination of 3D animation and exercises will ensure all math students acquire necessary conceptual understanding and computational skills to achieve high school standards. With Math Pathways students will: Learn concepts and then build upon these concepts using various pathways that converge and build upon each other such that retention will be far greater than the traditional rote memorization method of teaching mathematics
Because of the visual nature of these courses, this set is available only in video formats. It contains thousands of visual elements to enhance your learning experience, including images, 3-D animations, animated graphics and models of the human brain, in-studio demonstrations, step-by-step walkthroughs of mental math problems, and on-screen text. COURSE DESCRIPTION Course 1 of 4: Improve and expand your math potential—whether you're a corporate executive or a high-school student—in the company of Professor Arthur T. Benjamin, one of the most entertaining members of The Great Courses faculty. The Secrets of Mental Math, his exciting 12-lecture course, guides you through all the essential skills, tips, and tricks for enhancing your ability to solve a range of mathematical problems right in your head. Along the way, you'll discover how mental mathematics is the gateway to success in understanding and mastering higher fields, including algebra and statistics. Course Lecture Titles 12 Lectures 30 minutes/lecture 1. Math in Your Head! Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the keys to rapidly solving basic multiplication problems and finding squares. 7. Intermediate Multiplication Take mental multiplication to an even higher level. Professor Benjamin shows you five methods for accurately multiplying any two-digit numbers. Among these: the squaring method (when both numbers are equal), the "close together" method (when both numbers are near each other), and the subtraction method (when one number ends in 6, 7, 8, or 9). 2. Mental Addition and Subtraction Professor Benjamin demonstrates how easily you can mentally add and subtract one-, two-, and three-digit numbers. He also shows you shortcuts using the complement of a number (its distance from 100 or 1000) and demonstrates the uses of mental addition and subtraction for quickly counting calories and making change. 8. The Speed of Vedic Division Vedic mathematics, which has been around for centuries, is extremely helpful for solving division problems—much more efficiently than the methods you learned in school. Learn how Vedic division works for dividing numbers of any length by any two-digit numbers. 3. Go Forth and Multiply Delve into the secrets of easy mental multiplication—Professor Benjamin's favorite mathematical operation. Once you've mastered how to quickly multiply any two-digit or three-digit number by a one-digit number, you've mastered the most fundamental operations of mental multiplication and added a vital tool to your mental math tool kit. 9. Memorizing Numbers Think that memorizing long numbers sounds impossible? Think again. Investigate a fun—and effective—way to memorize numbers using a phonetic code in which every digit is given a consonant sound. Then practice your knowledge by trying to memorize the first 24 digits of pi, all of your credit card numbers, and more. 4. Divide and Conquer Turn now to the last fundamental operation of arithmetic: division. Explore a variety of shortcuts for dividing by one- and two-digit numbers; learn how to convert fractions such as 1/7 and 3/16 into decimals; and discover methods for determining when a large number is divisible by numbers such as 3, 7, and 11. 10. Calendar Calculating The fun continues in this lecture with determining the day of the week of any date in the past or in the future. What day of the week was July 4, 2000? How about February 12, 1809? You'd be surprised at how easy it is for you to grasp the simple mathematics behind this handy skill. 5. The Art of Guesstimation In most real-world situations—such as figuring out sales tax or how much to tip—you don't need an exact answer but just a reasonable approximation. Here, develop skills for effectively estimating addition, subtraction, multiplication, division, and square roots. 11. Advanced Multiplication Professor Benjamin shows you how to do enormous multiplication problems in your head, such as squaring three-digit and four-digit numbers; cubing two-digit numbers, and multiplying two-digit and three-digit numbers. While you may not frequently encounter these large problems, knowing how to mentally solve them cements your knowledge of basic mental math skills. 6. Mental Math and Paper Sometimes we encounter math problems on paper in our daily lives. Even so, there are some rarely taught techniques to help speed up your calculations and check your answers when you are adding tall columns of numbers, multiplying numbers of any length, and more. 12. Masters of Mental Math Professor Benjamin concludes his exciting course by showing how you can use different methods to solve the same problem; how you can find the cube root of large perfect cubes; how you can use the techniques you've learned and mastered in the last 11 lectures; and more. Course 2 of 4: Embark on a startling voyage into the human mind and discover how the various aspects of your memory operate and the impact memory has on your daily experience of life with Memory and the Human Lifespan. Award-winning Professor Steve Joordens's 24 riveting lectures carefully explain the different systems that make memory possible; how these systems work together to build and access memories, solve problems, and learn skills; how memory systems develop throughout your lifespan; how and why memory deficits occur; and so much more. Course Lecture Titles 24 Lectures 30 minutes/lecture 1. Memory Is a Party Using the metaphor of a party whose "guests" include the different components of the complex interactions that make up memory, Professor Joordens introduces you to several kinds of memory—including episodic, semantic, and procedural—to arrive at an initial understanding of the variety of processes at work in human "memory." 13. Animal Cognition and Memory Does an elephant really never forget? Expand your study of memory to investigate the extent to which the mysterious abilities of humans may also exist in animals and, if so, how they might differ from our own. 2. The Ancient "Art of Memory" Techniques to embed and retrieve memories more easily—so-called mnemonic strategies—date back at least to classical Greece. See how one such technique—the Method of Loci—can help improve the episodic memory you depend on to recall a group of items such as grocery or to-do lists. 14. Mapping Memory in the Brain Almost two decades since its revolutionary appearance, fMRI—functional magnetic resonance imaging—is allowing researchers to watch the living human brain at work, with no harm or discomfort to the subject. Explore what happens in several areas of the brain as memories are created or retrieved. 3. Rote Memorization and a Science of Forgetting Is a mnemonic strategy always the most useful? Examine rote memorization and how it differs from mnemonics. Also, get an introduction to the work of Hermann Ebbinghaus, whose 19th-century experiments in remembering and forgetting marked the first scientific examination of memory. 15. Neural Network Models Can computer models mimic the operations of the human brain? Examine the use of neural network modeling, in which biologically inspired models posited by researchers in cognitive neuroscience are advancing our understanding of just how those operations take place. 4. Sensory Memory—Brief Traces of the Past Begin a deeper discussion of the different kinds of memory, beginning with sensory memory and how its brief retentive power lets you switch from one stimulus to another—and even gives you your sense of "the present moment." Here, the focus is on iconic (or visual) memory and its auditory counterpart, echoic memory. 16. Learning from Brain Damage and Amnesias Leave the world of computers for that of neuropsychology as you focus on the life situations of several patients who have suffered some form of brain injury. You learn how damage to different areas of the brain can have dramatically different impacts on memory and how these patients experience the world. 5. The Conveyor Belt of Working Memory Plunge into the mental processes that allow you to work with information, often with the goal of solving a problem. You learn that these processes can also be used to keep information briefly "in mind," though they require effort and are prone to interference. 17. The Many Challenges of Alzheimer's Disease In a lecture that explores one of our most frightening diseases from both the caregiver's and sufferer's perspectives, learn how Alzheimer's progresses, how that progression may be forestalled, and ways in which technology may be able to help through the emerging field of "cognitive prosthetics." 6. Encoding—Our Gateway into Long-Term Memory How does information make its way from your temporary working memory into long-term memory so you can access it again when you need it? This introduction to encoding explains the process and offers useful tips for improving your own recall. 18. That Powerful Glow of Warm Familiarity Why does something familiar to us actually feel that way? Discover the sources of familiarity as you are introduced to the concepts of perceptual fluency and prototypes, and explore some surprising ways that those feelings of familiarity can trump other considerations. 7. Episodic and Semantic Long-Term Memory Strengthen your grasp of how these two key memory systems function. You explore the relationship between them with analogies that range from the job requirements of London taxi drivers to the famed "holo-deck" of the Star Trek television series. 19. Déjà Vu and the Illusion of Memory Is déjà vu simply an illusion of memory? If so, can we learn more about memory by trying to understand how this common phenomenon comes about? Examine some of the theories that have been put forth to explain this uncanny experience. 8. The Secret Passage—Implicit Memory Encounter still another category of memory—a way in which your experiences can enter long-term memory without the kind of "effortful encoding" discussed earlier. You learn why this sort of memory creation is vitally important, yet also unreliable as a substitute for conscious effort. 20. Recovered Memories or False Memories? Is episodic memory subject to the same pitfalls as misattributed feelings of familiarity? Can we "remember" things that never took place with the same intensity and certainty as those that did? Gain new insights into what is at stake when long-forgotten "memories" resurface. 9. From Procedural Memory to Habit In this lecture, you see that your memory for procedures is useful not only in the "muscle memory" of physical skills, but also in cognitive processes. Also, learn about constructivist learning, in which the explicit structure of a procedure—which is usually taught verbally—instead is learned implicitly during exploratory practice. 21. Mind the Gaps! Memory as Reconstruction Metaphors for memory usually reference information storehouses of some kind, such as library stacks or computer hard drives, from which episodic memories are "retrieved." Learn about the extent to which we actually construct our memories anew each time we summon them and how this explains common memory errors. 10. When Memory Systems Battle—Habits vs. Goals What happens when implicit or procedural memories become so powerful they seize control? In this examination of the tenacity of habits, learn how and why habits are formed and what steps might be useful in changing them, or at least regaining control. 22. How We Choose What's Important to Remember Does our brain always make decisions for us about which aspects of our experience to encode for later recall, or can we influence that process ourselves? Learn potentially powerful techniques for influencing the shape of future memories. 11. Sleep and the Consolidation of Memories Does sleep play a role in strengthening memories of your experiences during the day? Gain a sense of the latest research about a subject that is difficult to study as you explore the relationship between sleep and memory, including the possible link between specific sleep stages and specific kinds of memory. 23. Aging, Memory, and Cognitive Transition Apply a reality check to the popularly held belief that memory naturally declines as we age. Learn what happened when a researcher corrected for the age-related variables long-ignored by traditional testers—and what conclusions we can draw about what lies ahead for us as we grow older. 12. Infant and Early Childhood Memory How does the maturation of memory fit into a child's overall brain development? Gain invaluable and surprising insights into the month-by-month and year-by-year development of a child's capacity for memory, beginning in the womb and continuing on with its dramatic development after entry into the world. 24. The Monster at the End of the Book Contemplate the significance of what you've learned, with special attention to the common question of whether you can improve your episodic memory—remembering what you want to recall, forgetting what you'd rather not, and making choices about how to achieve a balance. Course 3 of 4: Memory is, without a doubt, the most powerful (and practical) tool of everyday life. By linking both your past and your future, memory gives you the power to plan, to reason, to perceive, and to understand. Yet while all of us have an amazing capacity for memory, there are plenty of times when it seems to fail us. Why does this happen? And how can you fix it? In Scientific Secrets for a Powerful Memory, you'll explore the real research on how memory functions—and then apply these findings to help you make better use of the memory abilities you have. By tapping into a series of scientifically proven strategies, tricks, and techniques, and by practicing them through dynamic exercises, you'll emerge from the end of this short course with the ability to process information more effectively and to increase your chance of remembering almost anything you want. Course Lecture Titles 6 Lectures 30 minutes/lecture 1. Your Amazing Prehistoric Memory Discover how remarkable your memory ability can be and get an introduction to some of the fascinating ways you can transform your average memory into an excellent one. After a quick memory test to set the stage, Professor Vishton introduces you to one of the most basic ways your memory can encode information: the Major System. With this strategy, you'll learn how to encode numbers into words and then into distinct images that can help you recall the numerical information whenever you like. You'll also explore the prehistoric roots of why we think the way we do. 4. Why and When We Forget Forgetting happens to the best of us—but it can be mitigated through the use of several key techniques. Among the topics you'll investigate are the "Ebbinghaus forgetting function," which offers insights into the relationship between time, amount of studying, and the likelihood of memory recall; the most effective way to remember a new set of information (hint: it doesn't involve cramming); and how to access that pesky piece of information that's "on the tip of your tongue." 2. Encoding Information with Images Focus on one of the simplest tricks for memorizing information: the Method of Loci. Like the Major System, this strategy encodes information into a format your brain is especially good at using; in this case, it ties information to a physical location. Gain familiarity with this method through several engaging exercises. Also, peek inside the mind of mental athletes to see how their seemingly superhuman feats of memory are rooted in nothing more than innate brain power we all have. 5. Keeping Your Whole Brain in Peak Condition To have a good memory that functions at the peak of its powers, you need to keep your entire brain healthy. Professor Vishton shows you how to do just that. You'll learn how not just a part of your brain, but the entire organ, is involved in remembering things. You'll also investigate the science behind studies of exercise, sleep, and nutrition—and the curious ways that a balanced diet, daily activity, and a good night's sleep relate to optimal mental functioning. 3. Maximizing Short- and Long-Term Memory In this insightful lecture, Professor Vishton walks you through the three steps of successful memory: a perception to short-term memory, encoding short-term memory to your long-term memory, and retrieving information from your long-term memory. In addition, you'll explore how amnesia and other hippocampus-related damages can disrupt this normal memory process; you'll examine some intriguing ways (such as "chunking") to get around the limitations of your short-term memory; and much more. 6. Human Memory Is Reconstruction, Not Replay Why should you bother enhancing your memory when there are computers that can do it for you? In what ways is information stored on a computer different from information stored in the recesses of your brain? What are the limits of how memory functions? What are some important roles that technology can—and should—play in backing up our memories? Why are "source memories" and "flashbulb memories" so problematic, and how can you recognize them? Find the answers in this final lecture Course 4 of 4: How We LearnTaught by: Professor Monisha Pasupathi University of Utah Ph.D. \| Stanford University Shed some much-needed light on what's going on when you learn, and dispel some pervasive myths about an activity so central to your daily life. With Professor Monisha Pasupathi's 24-lecture course, How We Learn, you'll examine interesting theories about learning; explore the ways we master tasks such as speaking a new language, learning a musical instrument, or navigating through a new city; and gain vital strategies for excelling in a range of different learning situations. Course Lecture Titles 24 Lectures 30 minutes/lecture 1. Myths about Learning Explore what it means to learn, and consider 10 myths about learning—for example, that learning must be purposeful or that emotions get in the way of learning. None of these or eight other widely held views is accurate, as you discover in depth in this course. 13. Learning as Theory Testing Scientists engage in theory testing to evaluate their own work and that of their colleagues. But is it realistic to expect nonscientists to develop similar habits of mind? Examine the problems people have in overcoming natural biases that inhibit scientifically rigorous thinking and learning. 2. Why No Single Learning Theory Works Take a historical tour of early work on learning, which was deeply influenced by classical conditioning, made famous by Ivan Pavlov. Learn that in the effort to avoid anything that wasn't directly observable, researchers left out key unobservable factors, such as the attitudes of the subjects. 14. Integrating Different Domains of Learning Survey some common factors that apply to many learning situations, focusing on both intuitive and conscious processes. Tips for learning include spacing your rehearsals, varying the context, drawing on connections to things you know, learning the same way you'll use your learning, and sleeping on it! 3. Learning as Information Processing Investigate the information processing approach to learning, which holds that learning occurs as people encounter information, connect it to what they already know, and as a result, see changes in their knowledge or ability to do specific tasks. 15. Cognitive Constraints on Learning Delve into three constraints on learning: attention, working memory, and executive function. Consider the evidence for the importance of these capacities in supporting or limiting learning. Close by investigating how they can be improved to enhance learning abilities over your lifespan. 4. Creating Representations How do you create representations of categories and events in your mind? Explore two aspects of this process. First, you seldom, if ever, learn passively; instead, learning occurs in the context of purposeful action. Second, what you already know changes your experiences in learning. 16. Choosing Learning Strategies Monitoring progress in learning can help develop a more effective learning strategy. Examine research showing how easy it is to misjudge success or lack of success at learning a skill or subject. Then look at approaches that let you increase retrieval and retention of learning. 5. Categories, Rules, and Scripts Whether you realize it, you acquire new knowledge by organizing experiences into categories, searching for rules within those categories, and establishing scripts—or patterns—that serve as guides for predicting what happens next in an unfamiliar activity or interaction. Find out how in this lecture. 17. Source Knowledge and Learning Often it's important to know not only a piece of information but also its source, especially in today's information-rich culture with many different sources to be weighed for accuracy. Learn how to combat the common tendency to forget the source before anything else. 6. What Babies Know Newborns are not a blank slate on which parents can dictate whatever they want their children to know. Instead, babies come prepackaged to develop in certain ways. Investigate how babies manage an overwhelming amount of learning and what this tells us about how grownups learn. 18. The Role of Emotion in Learning How does it affect learning when you feel happy or sad? Examine the role of emotions in learning, discovering that some moods are better for some tasks. For example, mild anxiety in studying for a test might actually enhance performance by focusing attention. 7. Learning Your Native Tongue Developing humans progress from no words to about 60,000 words by adulthood, while also mastering complex syntax and grammar. Probe the mechanisms that permit babies to absorb the language they hear around them and make it their native tongue. 19. Cultivating a Desire to Learn Consider how to foster the kinds of motivation that will help support learning rather than undermine it. Rewards such as good grades can backfire by reducing a student's desire to learn about a topic and willingness to persist on that topic. But what is a more effective motivation? 8. Learning a Second Language If learning a native language occurs almost without effort, why is it so hard to learn a second language, particularly after childhood? Examine this question in light of experiments to teach human language to other species, which provide intriguing clues for the difficulties adult language learners face. 20. Intelligence and Learning Do IQ scores predict the ability to learn? Or are they simply a measure of what has previously been learned, giving a person a leg up on subsequent learning? Use the statistical concept of correlation to shed light on the long-running debate over the nature of intelligence and its role in learning. 9. Learning How to Move Focus on four questions central to learning a new motor skill: What should you pay attention to while learning the skill? Can verbalizing the skill help with mastering it? What about learning by watching versus learning by doing? Does imagining the movement provide any benefits? 21. Are Learning Styles Real? An influential contemporary view holds that we're all good at some things but not others, and that we may each differ in the way we like to learn. Probe the arguments for and against these ideas of multiple intelligences and differing learning styles. 10. Learning Our Way Around Investigate how you learn to navigate through the world, a skill we share with all other mobile creatures. Find that while spatial learning has a conscious component, we often don't know that we have a cognitive map of a particular place until we have to use it. 22. Different People, Different Interests Trace the origins and growth of the different interests that people naturally have. Interest stimulates the development of initially higher knowledge, which then facilitates further learning and further interest. Then consider an interest-related personality trait that is likely to be shared by the audience for this course. 11. Learning to Tell Stories Storytelling is a crucial way that you connect with other people and also learn about yourself. Discover how you learn to narrate your experiences in a way that is ordered in time, communicates the essential details of what happened, and makes clear to the audience why they should listen. 23. Learning across the Lifespan Focus on the role of age in learning by reviewing four principles presented earlier in the course and exploring how they relate to different age groups. Close by examining a variety of strategies for preserving information-processing abilities into late life. 12. Learning Approaches in Math and Science Math and science require learning both facts about the world and a special process—the "how" used to identify and solve new problems. Survey different approaches to teaching math and science. Some work for building a knowledge of facts, others for instilling an understanding of process. 24. Making the Most of How We Learn Conclude your exploration of how we learn with a look at today's frontiers of learning research. Then revisit the myths of learning from Lecture 1, review optimal approaches to learning, and consider what educators can do to make best use of our new understanding of this vital process.
Math IIC covers a variety of mathematical topics. ETS, the company that writes the SAT IIs, provides the following breakdown of the topics covered on the test: Topic Percent of Test Usual Number of Questions Algebra 18% 9 Plane Geometry — — Solid Geometry 8% 4 Coordinate Geometry 12% 6 Trigonometry 20% 10 Functions 24% 12 Statistics and Sets 6% 3 Miscellaneous 12% 6 While accurate, this breakdown is too broad to really help you direct your studying toward the meaningful areas of the test. We've created the following detailed breakdown based on careful examination of the test: Topic Percent of Test Usual Number of Questions Algebra 18% 9 Arithmetic 2% 1 Equation solving 5% 2.5 Binomials, polynomials, quadratics 14% 7 Solid Geometry 8% 4 Solids (cubes, cylinders, cones, etc.) 4% 2 Inscribed solids, solids by rotation 1% 0.5 Coordinate Geometry 12% 6 Lines and distance 6% 3 Conic sections (parabolas, circles) 5% 2.5 Coordinate space 2% 1 Graphing 2% 1 Vectors 1% 0.5 Trigonometry 20% 10 Basic functions (sine, cosine, tangent) 12% 6 Trigonometric identities 4% 2 Inverse trigonometric functions 2% 1 Trigonometry in non-right triangles 1% 0.5 Graphing trigonometric functions 1% 0.5 Functions 24% 12 Basic, compound, inverse functions 8% 4 Graphing functions 6% 3 Domain and range of functions 8% 4 Statistics and Sets 6% 3 Mean, median, mode 2% 1 Probability 2% 1 Permutations and combinations 4% 2 Group questions, sets 1% 0.5 Miscellaneous 12% 6 Arithmetic and geometric series 4% 2 Logic 1% 0.5 Limits 1% 0.5 Imaginary numbers 1% 0.5 This book is organized according to the categories in the above breakdown, allowing you to focus on each topic to the degree you feel necessary. In addition, each question in the practice tests at the back of this book has been categorized according to these topics so that when you study your practice tests, you can very precisely identify your weaknesses and then use this book to address them.
Few would argue that, through its development of science and technology, the human species has been more successful than any other in taking control of the environment and using the resources of the earth to its own advantage. It is probably equally clear that this dramatic development of science and technology is only possible because of our ability to think creatively, consistently and logically. Indeed, there seems to be a parallelism, a consistency, between the rules that govern logical thought and the rules that govern the functions of the physical universe. The physical universe is quite logical and consistent. It reveals its secrets to those who study it using creative, consistent and logical thought. And for the development of one's ability to exercise this very useful way of thinking there is probably no better approach than through the study of mathematics. So welcome to the Department of Mathematics where you will have the opportunity to hone your thinking skills by taking some of our twenty four courses in algebra, statistics, trigonometry, calculus and differential equations. In addition to improving your ability to think clearly, you will also learn about many of the astounding mathematical discoveries that have been made throughout the centuries and how they can be used for practical applications in science, engineering, business and the health fields. I encourage you to humbly and enthusiastically place yourself in the hands of our experienced and capable faculty who are fully devoted to teaching you mathematics. If you do this, you will be taken on an intellectual journey to fascinating places that you cannot easily imagine. You will come away not only well prepared with the technical knowledge you need for your chosen career or field of study, but with an enhanced ability to think more clearly, more deeply, more rigorously, more analytically and more precisely about yourself and everything you encounter. Welcome to the world of mathematics!
Mathematics for the Trades, CourseSmart eTextbook, 8th Edition Description For Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses servicing trade or technical programs at the undergraduate/graduate level. THE leader in trades and occupational mathematics, Mathematics for the Trades: A Guided Approach focuses on fundamental concepts of arithmetic, algebra, geometry, and trigonometry. It supports these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HVAC, and many other fields. The workbook format of this text makes it appropriate for use in the traditional classroom as well as in self-paced or lab settings. For this revision, the authors have added over 150 new applications, new chapter summaries for quick review, and a new chapter on basic statistics. Student will find success in this clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention. Table of Contents Chapter 1 Arithmetic of Whole Numbers Chapter 2 Fractions Chapter 3 Decimal Numbers Chapter 4 Ration, Proportion, and Percent Chapter 5 Measurement Chapter 6 Pre-Algebra Chapter 7 Basic Algebra Chapter 8 Pratical Plane Geometry Chapter 9 Solid Figures Chapter 10 Triangle Trigonometry Chapter 11 Advanced Algebra Chapter 12 Statistics Answers to Previews Answers
A Look Ahead A look ahead is a short weaving guide from the Nuffield Mathematics Project intended mainly for teachers of older students in upper primary and lower secondary. The object of the guide was to re-state the aims and methods of the project in the light of experience so far, and to consider some of the problems which were then arising. It attempts to answer the question of 'where is it going?'. Other questions discussed are 'How does this fit in with CSE?' or even the 11-plus. Others have wondered 'Why new mathematics?' and whether what we've already written has any relevance to the outside world of today. The contents list may help the reader to find where their own particular problems are discussed
CAT in Mathematics The CUNY Assessment Test in Mathematics (also known as the CAT in Mathematics, or the COMPASS Math test) is an untimed, multiple-choice, computer-based test designed to measure students' knowledge of a number of topics in mathematics. The test draws questions from four sections: numerical skills / pre-algebra, algebra, college algebra, and trigonometry. Numerical skills / pre-algebra questions range from basic math concepts and skills (integers, fractions, and decimals) to the knowledge and skills that are required in an entry-level algebra course (absolute values, percentages, and exponents). The algebra items are questions from elementary and intermediate algebra (equations, polynomials, formula manipulations, and algebraic expressions). The college algebra section includes questions that measure skills required to perform operations with functions, exponents, matrices, and factorials. The trigonometry section addresses topics such as trigonometric functions and identities, right-triangle trigonometry, and graphs of trigonometric functions. No two tests are the same; questions are assigned randomly from the four sections, adapting to your test-taking experience. Placement into CUNY's required basic math courses is based on results of the numerical skills/pre-algebra and algebra sections. The test covers progressively advanced topics with placement into more advanced mathematics or mathematics-related courses based on results of the last three sections of the test. Students are permitted to use only the Microsoft Windows calculator while taking the test. CAT in Mathematics Practice Materials Below are some sample tests and websites containing more samples and information about the CAT in Mathematics and related materials. Special software may be needed to view some of these files; check under our Software section to get them. Emmy Noether, the German algebraist that Albert Einstein called the most important woman in mathematics.
Shmoop Launches Calculus Guide for Students and Teachers Shmoop's new calculus guide breaks down the important concepts in engaging ways in a portable digital medium. Calculus Exercises Mountain View, CA (PRWEB) September 20, 2012 One of the most common questions that flits across a math student's mind is, "Why does this matter?" Understandably, it may be difficult to see at a glance how finding a solution to the derivative of an expression might directly correlate to one being able to tie their shoelaces. Thank goodness for calculus. Admittedly, some of the concepts are tough, but along the way you begin to see its wicked practical applications. Rather than simply juggling numbers and variables, you are beginning to apply the mathematical concepts you have picked up along the way to solve real-world problems. Suddenly, math has a purpose! Huzzah! Shmoop, a publisher of digital curriculum and online test prep, is proud to announce the launch of its new Calculus Guide. Here, students can learn that "dy is over dx." (Or is it in denial? It does still keep dx's photo in a frame on its desk…) Hundreds of examples, exercises, and sample problems. The best way to learn is by example. Which is how Jack Osbourne got to be such a phenomenal singer. 3 quizzes per chapter. Students master the skills, train with Newton's weapons, and climb towards that black belt of calculus. Shmoop's "In the Real World" section will fill students in on how calculus is used in STEM fields. These are not meadows where the tops of wildflowers have been chopped off. Graphs galore to help visualize calculus terms and functions. Let these axes be students' allies. Check out Shmoop's Calculus Guide and start making sense of the world. About Shmoop Shmoop is a digital curriculum and test prep company that makes fun, rigorous learning and teaching materials. Shmoop content is written by master teachers and Ph.D. students from Stanford, Harvard, UC Berkeley, and other top universities. Shmoop Learning Guides, SAT Prep, and Teacher's Editions balance a teen-friendly, approachable style with academically rigorous materials to help students understand how subjects relate to their daily lives. Shmoop offers more than 7,000 titles across the Web, iPhone, Android devices, iPad, Kindle, Nook, and Sony Reader. The company has been honored twice by the Webby Awards and was named "Best in Tech" for 2010 and 2011 by Scholastic Administrator. Launched in 2008, Shmoop is headquartered in a labradoodle-patrolled office in Mountain View, California.
MERLOT Search - materialType=Development%20Tool&category=2514 A search of MERLOT materialsCopyright 1997-2013 MERLOT. All rights reserved.Fri, 24 May 2013 21:31:14 PDTFri, 24 May 2013 21:31:14 PDTMERLOT Search - materialType=Development%20Tool&category=2514 4434GeoGebra Algebra and Geometry shape and graph maker. Multi-use.Description by developer:GeoGebra is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. It offers multiple representations of objects in its graphics, algebra, and spreadsheet views that are all dynamically linked. Grid and Percent It In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.Math 6 Spy Guys Interactive lessons that cover multiple Grade 6 standards from the Mathematics Framework for California Public Schools.Quadratic Transformer This Java applet demonstrates visually how changing the coefficients in a quadratic function changes the graph, and shows the relationship between roots and x-intercepts. An included activity handout guides students to develop rules for how changes to the quadratic and constant coefficients of a quadratic function change its graph, and to briefly explore the "polynomial," "root" and "vertex" forms of a quadratic function. Budgeting with Percents This is a full lesson plan for applying percents in a real life application
The curriculum offers students the opportunity to experience real-world applications, hands-on labs and interdisciplinary investigations. All students will be actively engaged in developing mathematical understandings in real and relevant contexts. By the end of 7th grade, students will be able to: Understand and use rational numbers, including signed numbers Solve linear equations in one variable Sketch and construct plane figures Describe and sketch solid figures, including their cross sections, and examine properties of similarity Represent and describe relationships between variables in tables, graphs, and formulas Analyze the characteristics of linear relationships Represent and analyze data using graphical display, measures of central tendency, and measures of variation. Solve problems, communicate mathematically, reason and evaluate mathematical arguments, make connections among mathematical ideas and in other contexts, and represent mathematics in multiple ways Textbook: Pearson/Prentice Hall Connected Mathematics2 – Grade 7 (Cost: Replacement Fee). If the textbook is lost, stolen, or damaged (missing barcode), it is the student's responsibility to pay for the book before a replacement book is issued. In the event that the lost book is found, please retain all receipts. The textbook is also available online. However, in the event that students cannot access the online text book for homework, this will not be accepted as an excuse for late work. . Standardized Test Requirements: Standards are embedded throughout the curriculum, which would aid students on the Criterion-Referenced Competency Test (CRCT). Students must earn a minimum score of 800. Final: 10%(i.e. Cumulative Semester Exam, all objectives will be assessed) Homework- Homework is expected to be completed as assigned. Assignments will also be posted on website. Homework is generally assigned daily Monday-Thursday. Make-up work: Announced work, such as homework, quizzes, tests, and other major assessments are due the day the student returns. For eachexcused absence, student will have one day per number of days absent to make up missed work. If a student is absent under extenuating circumstances, special arrangements can be made to make up work. IT IS THE STUDENT'S RESPONSIBILITY TO REQUEST/SUBMIT MISSED WORK. Academic honesty: Copying another person's work and submitting it as one's own is cheating. Allowing another person to copy is also considered cheating. When caught in the act, students will not receive credit nor receive the opportunity for a chance for make up. Plagiarism is not acceptable. If a student takes information from the Internet or any printed resource without a citation, it is considered plagiarism and will result in a reduction in grade. A referral to the appropriate assistant principal will be forwarded. Late Work: For the first day the starting grade will be 70%. 10 points will be deducted each subsequent day. Grades will not be changed after posting deadlines for progress reports. Opportunities, such as detention, academic lunch, morning tutorials etc. will be given to assist students with completing assignments for reduced credit. Supplies List: Math Binder with dividers ( as a portfolio) #2 Pencils Hand held pencil sharper Ruler Compass Graph Paper Classroom Expectations: Student must adhere to the DCSS Student Code of Conduct, the school Behavior contract, as well as specific team/classroom rules. Be on time and seated before the bell. HMS tardy policies will be enforced. Be respectful to everyone. Bullying will not be tolerated. Always bring materials and assignments. Be responsible for personal business and possessions. NO GUM! (Repeat offenders will receive detention) Dress appropriately according to DCSS and school guidelines. Cell phones must be turned off when in class. If there is a violation, the cell phone will be confiscated and must be picked up by a parent before or after the school day. Electronic devices are a student's responsibility. The school will not be responsible for loss or theft. Communications: Phone calls will be returned as soon as possible after instructional periods. Emails are the preferred method of communication. Websites will be updated frequently for current information. The agenda planner is also used as a tool for school-home communication. Grades can be accessed through Parent Assistant (eSIS). Conferences can be scheduled through the team leader, Mrs. Hallabi. Dates to Remember: ( Subject to change by DCSS/HMS) January 9-Report cards for Fall Semester January 16-MLK Holiday-no school February 13-22 Benchmark Tests February 9- 4.5 week progress reports February 16- Conference Night 4:15-6:15 February 20 –President's Day -no school March 15- 9 week progress reports March 26-30 Benchmark Tests March 29-Conference Night 4:15-6:15 April 2-6 Spring Break April 23-May 3 CRCT testing window April 25- 13.5 week progress reports May 25- End of Spring semester * We reserve the right to adjust the course work and/or differentiate instruction as needed to meet the needs of students and ensure academic success. We look forward to working with you and your child in 2013! Please print and/or complete the form below verifying that you have reviewed this syllabus.
CR offers Math Jam College of the Redwoods' math department will present Math Jam, three one-unit math review courses this summer on the college's main Eureka campus. The courses will run from July 9 to July 19, and consist of 2 hours of class Mondays through Thursdays. The three courses offered will be Math 301 Pre-algebra Review from 2 p.m. to 4:05 p.m., Math 302 Elementary Algebra Review from 8:30 a.m. to 10:35 a.m., and Math 303 Intermediate Algebra Review from 11:15 a.m. to 1:20 p.m. These review courses will be useful for preparing for a math placement test, preparing to challenge a current math placement or reviewing for the next math course a student plans to take. Another option offered during Math Jam is to take a free, self-paced review. These reviews are useful for preparing to take a math placement test, personal development of math knowledge, or anyone who is in need of math review including parents and students. For course descriptions, go to CR's website at and look at the webadvisor link for the course number. One can also find the classes on the college's main website, and look under "Hot Topics" for Open Summer 2012 Courses. See the math department website for more information at this link:
Description This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books à la Carte also offer a great value–this format costs significantly less than a new textbook. Mathematics for Elementary Teachers, Third Edition offers an inquiry-based approach to this course, which helps students reach a deeper understanding of mathematics. Sy mathematics. The new Active Teachers, Active Learners DVD (not included) Table of Contents 1. Numbers and the Decimal System 2. Fractions 3. Addition and Subtraction 4. Multiplication 5. Multiplication of Fractions, Decimals, and Negative Numbers 6. Division 7. Combining Multiplication and Division: Proportional Reasoning 8. Number Theory 9. Algebra 10. Geometry 11. Measurement 12. Area of Shapes 13. Solid Shapes and Their Volume and Surface Area 14. Geometry of Motion and Change 15. Statistics 16. Probability This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.
Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations. [via] More editions of Numerical Linear Algebra for Applications in Statistics:
Additional Mathematics Our Aims In Nature's infinite book of secrecy A little I can read. Antony and Cleopatra I.2.10 The world we live in is the way it is because of Mathematics. Whether we get our techno-fun from a WAP mobile phone, a Playstation 3 or an MP3 player, it is ultimately the Mathematics behind the micro-technology that we have to thank for our 21st century toys. Our aim in the Mathematics Department is to pass on to our pupils the power and beauty of Mathematics as it appears in their world. We aim to give much more than a functional ability to deal with numbers. Pupils learn to think critically, analytically and tangentially in their problem solving and gain the ability to apply their Mathematical skills in unfamiliar contexts. Our hope is that pupils will find their Mathematics enjoyable as they surmount its challenges and (like the Soothsayer) unravel some its secrets. Staff Mr S Graham Head of Department Ms S Ardis Teacher Dr G Brown Teacher Mrs L Cowan Teacher Mr N Irwin Teacher Ms S McIlhatton Teacher Mrs K McIntyre Teacher Miss A McMillen Teacher Mrs A Reynolds Teacher Dr C Scully Teacher Mr M Shields Teacher Dr S Springer Teacher Curriculum Key Stage 3 The Junior school curriculum covers the four statuary attainment targets namely Number, Algebra, Shape Space and Measure and Processes. Pupils are taught the basic Mathematical skills which provide them with a solid foundation for GCSE study. GCSE Pupils follow the linear AQA specification which entails 100% written examination taken at the end of form V. This is comprised of a calculator paper (60%) and a non-calculator paper (40%). The Collins text for AQA Modular Mathematics is used to support the students' learning. (It has the same content as the linear course!) Each student should have access to an electronic copy of book 1 & 2 to use throughout the year. AS/A2 The great themes introduced in Additional Mathematics are developed. Pupils cover a wide range of topics in Pure Mathematics, Mechanics and Statistics and begin for the first time to get a feel for how the various branches of Mathematics fit together. The CEA specification is followed. Facilities & Resources Mathematics is taught in the William Sillery building, one of the newest in the school. We have data projection and audio-visual facilities, and 15 departmental laptops for student use. Each year pupils have the opportunity to use ICT in a Mathematical context, for example statistics in the Fourth Form and projectile motion in the Sixth Form. Additional Information Pupils are encouraged to broaden their Mathematics horizons and have various opportunities to do so as they pass through the school. Many of our pupils enter for the Mathematical Association's Maths Challenges at junior, intermediate and senior level. A number of pupils each year are selected for participation in the Villiers' Park scheme. Potential Oxbridge candidates are given extra tuition in the department both to increase their Mathematical compass and to hone their interview skills.
is a comprehensive Personal Finance text which includes a wide range of pedagogical aids to keep students engaged and instructors on track. This book is arranged by learning objectives. The headings, summaries, reviews, and problems all link together via the learning objectives. This helps instructors to teach what they want, and to assign the problems that correspond to the learning objectives covered in class.Personal Finance includes personal finance planning problems with links to solutions, and personal application exercises, with links to their associated worksheet(s) or spreadsheet(s). In addition, the text boasts a large number of links to videos, podcasts, experts' tips or blogs, and magazine articles to illustrate the practical applications for concepts covered in the text This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing. Debt These resources are a selection of audio and video podcasts from a first year Dynamics class MAM1044H at the University of Cape Town. The lectures cover a wide range of topics. Systematic introduction to the elements of mechanics kinematics in three dimensions Newtons laws of motion models of forces friction elastic springs fluid resistance Conservation of energy and momentum Simple systems of particles including brief introduction to rigid systems Orbital Mechanics with applications to the planning of space missions to the outer planets " This course is about mathematical analysis of continuum models of various natural phenomena. Such models are generally described by partial differential equations (PDE) and for this reason much of the course is devoted to the analysis of PDE. Examples of applications come from physics, chemistry, biology, complex systems: traffic flows, shock waves, hydraulic jumps, bio-fluid flows, chemical reactions, diffusion, heat transfer, population dynamics, and pattern formation." health agriculture
MA4A5 Term 1 Course Description Algebraic geometry studies the geometry of spaces defined by polynomial equations. This module will study affine and projective varieties, focusing on examples and the dictionary between algebra and geometry. See also the description in the PYDC booklet. Announcements Assessment There will be homework assignments every two weeks. Homework assignments and due dates will be posted on the schedule webpage, which will also have the reading for the following week. You are encouraged to work on homework together, but you should write up the solutions yourself. No late homework will be accepted. The lowest homework score will be dropped, however, when calculating your homework mark. Homework will be due at 12pm on the Fridays indicated on the schedule page. In addition there will be a miniproject which will be due at the start of Term 2 (at 12pm on Tuesday, 10th January). Your final mark for this module will depend 20% on your homework, 10% on the mini-project, and 70% on the examination in Term 3. Mini-project There are many possible first courses in algebraic geometry, and we cannot cover everything that might belong in such a course. In the mini-project you will learn one of these topics, and write a five page description of the topic at a level suitable for reading by your classmates. The five page page-limit will be strictly enforced, and the font must be at least 11pt. Deadlines:
This module is about matrices that are rectangular tables of numbers, like this: . Matrices, in many ways, act like numbers, as you can add, subtract, multiply and sometimes invert them. They play central role in algebra, in numerical methods, in advanced engineering calculations, and in physics. Lessons under this topic discuss matrix operations and solution of systems of linear equations using Cramer's rule. One very nice tool for playing with matrix arithmetic is my linear algebra workbench
Home Page GEOMETRY AND ALGEBRA II CLASS RULES AND PROCEDURES Attendance: Mathematics is a challenging subject. One topic builds on another. Daily participation is a must. Do not get behind in your course work. Attendance is mandatory. The school has accepted rules and procedures for dealing with unexcused absences. Grades and Homework: Grades are determined by chapter tests, quizzes, and homework. Chapter tests count twice, quizzes count once, and you will receive two homework grades, one for the in-term as well as the term. For example: if there were 9 homework assignments in the first half of the term and 8 in the second half of the term, and you did 8 in the 1st half and 8 in the 2nd half, then you would receive an 8/9 or 89% on the in-term grade and an additional 8/8 or 100% on the term grade. Geometry and Algebra II are demanding college preparatory math courses and require at least 30 minutes of homework each night. If you find you have made an error, rework the problem until you get the correct answer. By doing so, you will discover errors before they become bad habits. Homework is the place for you to learn from your mistakes. There is no partial credit for homework. All or none! If a quiz or a test is missed because of an excused absence, it is your responsibility to see me and set a date for a make-up test within one week of your return to class. If the test is not made up during that time, you will receive a failing grade for that test or quiz. Classroom Materials: You must have a textbook, notebook, and a graphing calculator. Divide the notebook into two sections: Notes and Homework. Each entrance into your notebook should be dated and titled by both topic and textbook page number. All classes are to bring their textbook, notebook, graphic calculator and a pencil to class every day unless told otherwise. All homework, quizzes, and tests must be done in pencil. Classroom Management: You are not to enter the classroom unless I or another faculty member is in the classroom. If you enter the room without an adult present you will receive a detention. As soon as you are seated, open your textbook and take out your homework unless told otherwise. While other students or I are speaking during class, I expect you to show total respect. Extra Help: I am available before and after school for extra help, by appointment, in room 218. Also, during your resource period there will be a math teacher on duty in room 111 to answer any of your math questions.
Canon Press Logic Curriculum Introductory Logic and Intermediate Logic from Canon Press has recently been expanded and revised. With instructional DVDs available for both levels, it should be easy for homeschool parents to teach this fundamental course to their children. The tests for both levels of logic have been revised and expanded. The old coil binding has been replaced with the sturdier perfect binding. Introductory Logic DVD By Douglas Wilson and James Nance, Publisher: Canon Press The completely updated Introductory Logic DVD 8th grade logic course is taught by Jim Nance. It is easy to navigate, durable, and offers great instruction. The lessons on this DVD cover definitions, logical statements, fallacies, syllogisms, and many other elements. This course is a thorough introduction to logic and serves as both a self-contained course and a preparatory course for more advanced studies. The set includes two DVDs. In the new expanded and revised fourth edition of Introductory Logic Student Guide, review questions and review exercises have been added to each unit for every lesson in the text and some especially challenging problems have been included in the review exercises. The new edition is perfect-bound, with all exercise pages perforated for easy removal. There are 39 lessons and it is consumable for junior high. Grades 7-12 ISBN-13: 9781591280330 List $29.00 Sale Price $25.95 Introductory Logic Answer Key By Douglas Wilson and James Nance, Publisher: Canon Press The Introductory Logic Answer Key provides answers to all of the standard student text exercises and also includes answers and examples for the 'Additional Exercises' section found at the end of each lesson. You need this for the Logic course. ISBN-13: 9781591280347 List $20.00 Sale Price $18.00 Introductory Logic Test and Quiz Booklet By Douglas Wilson and James Nance, Publisher: Canon Press The nine tests in the expanded and revised Introductory Logic Test and Quiz Booklet will help test your understanding of Introductory Logic concepts. Answers are included and it is reproducible. ISBN-13: 9781930443990 Price $10.00 Intermediate Logic Intermediate Logic Bundle By James Nance, Publisher: Canon Press The Intermediate Logic Bundle includes one of each of the following: Intermediate Logic DVD Intermediate Logic Student Guide, Second Edition Intermediate Logic Answer Key Intermediate Logic Test Booklet Grades 8-12 ISBN-13: 9781591280354B List $114.00 Sale Price $98.95 Intermediate Logic DVD By James Nance, Publisher: Canon Press The new Intermediate Logic DVD set has clear and concise explanations by Jim Nance who teaches each lesson in the Intermediate Logic Student Text. Running time is over 6 hours. Intermediate Logic, together with Introductory Logic by James Nance and Douglas Wilson, provides students with a rigorous course in logic. Newly revised and updated, with additional review questions and exercises for each unit, Intermediate Logic has 27 lessons and is consumable. The Introductory Logic Student Guide has perfect-binding and all of the exercise pages are perforated for easy removal. It is consumable. Grades 8-12 ISBN-13: 9781591280354 List $27.00 Sale Price $24.49 Intermediate Logic Answer Key By James Nance, Publisher: Canon Press The Intermediate Logic Answer Key provides answers to the regular student text exercises and answers and examples for selected exercises in the Additional Exercises section found at the end of each lesson. Grades 8-12 ISBN-13: 9781591280361 Sale $20.00 Sale Price $18.00 Intermediate Logic Test and Quiz Booklet By James Nance, Publisher: Canon Press Recently expanded and completely redesigned New Edition! The tests contained in the Introductory Logic Test and Quiz Booklet will help test your understanding of Intermediate Logic concepts. Answers are included and it is reproducible.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education. Math 403:01Student informationPlease print! Name Major(s) E-mail address I would like to make a course webpage with the information above displayed. This should increase the ability of students to work together in this course. Do you agree to havi January 28, 2001 Math 403, section 1Locate some complex numbersAt least 2 students and no more than 4 students must work on this problem. Please print the names of those working on this problem:z1Suppose z is the complex number pictured. Dra 403:01How to locate some complex numbers1/29/2002I asked the following: Suppose z is the complex number pictured. Draw and label the following complex numbers as well as you can: 1 B = z C = iz D=z E= z A = 1z 2 Here are the answers.CFA Math 403, section 1 NameDraw some picturesFebruary 4, 2001Carefully sketch each of the collections of complex numbers. For each of them, answer the following questions (use Y for yes and N for No): Is this set open? A: zs so that Re z < 0. Is t 403:01How to draw some picturesFebruary 6, 2001I asked: Carefully sketch each of the collections of complex numbers. For each of them, answer the following questions (use Y for yes and N for No): Is this set open? Is this set closed? Is this se Math 403, section 1Questions about exp and logFebruary 11, 2002Exactly 2 students should work on this. Their names should be printed below.expWrite all values of exp(1 + i) :105Show all complex zs having a value of exp z which is real o Math 403, section 1Answers about exp and log expFebruary 12, 2002Since exp z = eRe z (cos(Im z) + i sin(Im z), we see that exp(1+i) must be e1 (cos 1)+i(sin 1). Numerical approximations of the numbers are not expected. The complex zs which have Math 403:01 course expectationsHeres what I expect from you in this course, beginning with an observation about myself. The statements below may help you make a reasonable judgment about the time and eort needed for success in this course. 0. I will Digital Camera Buyers Guide: As we are approaching Christmas you might be thinking of buying digital camera! Well if you are here are a few things to consider! The Digital Camera marketplace contains over a dozen key manufacturers and several other l As Class Convenes Get your Name Tag, Scantron, Team Folder REMOVE EVERYTHING from Team Folder Supply "Burning Questions" Find a seat at least 1 space apart Prepare SCANTRON FORM Bubble in your form like last time (Instructions will be shown n As Class Convenes If you have questions, jot them on a post-it, and stick it on my monitor Arrange the tables for Team Meetings Get out the work that will be used in today's class (i.e., Assignment #L2, Design Notebooks and checklists)Burning Qu Econ 456 - Law and Economics Instructor: David Givens Spring 2009 Solutions to Practice midtermProblem 1 - True/FalseLabel the following statements either true or false. Provide an explanation of at most a few sentences for each answer. Your expla CPSC313 / Spring 2008Machine Problem 1Machine Problem 1: A Simple Memory Allocator 100 points Due date: To Be AnnouncedIntroduction In this machine problem, you are to develop a simple memory allocator that implements the functions my malloc() a . you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part I: playing with arithmetic on Maple9/15/2002What I'd . you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part II: playing with algebra on Maple9/15/2002Maple's mos . you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part III: playing with calculus on Maple9/15/2002The basic . you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part IV: playing with graphs on Maple9/15/2002The graphing
Dacula ...Mathematics is fundamental to most physical sciences. As a geologist, I have taken courses in advanced math up to differential equations, and have used math extensively in my research modeling carbon dioxide diffusion through the soil. Algebra is fundamental to all advanced mathematics
Mathematics A Discrete Introduction 9780534398989 ISBN: 0534398987 Edition: 2 Pub Date: 2005 Publisher: Thomson Learning Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective
Geometry with Geometry Explorer Book Description: Geometry with Geometry Explorer combines a discovery-based geometry text with powerful integrated geometry software. This combination allows for the deep exploration of topics that would be impossible without well-integrated technology, such as hyperbolic geometry, and encourages the kind of experimentation and self-discovery needed for students to develop a natural intuition for various topics in geometry. Buyback (Sell directly to one of these merchants and get cash immediately) Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
As you begin doing advance math and statistics calculations, graphs help display simple and complex relationships. The Texas Instruments TI-Nspire CX Graphing Calculator is a real-world calculator that every aspiring math and science student or professional needs to keep ahead. Research evidence shows that when students are engaged and actively participate in their own learning, they progress faster and further in understanding mathematics and science. Graphing handhelds such as the TI-Nspire handhelds have been shown to foster student engagement and encourage participation in their own learning. The TI-Nspire CX handheld offers a set of fully integrated tools that allow dynamic links among multiple representations of a problem. The color display enables students to better observe patterns and make connections between math and science concepts and real-world learning. Features: Visualize in full color - Color-code equations, objects, points and lines on the full-color, backlit display. Make faster, stronger connections between equations, graphs and geometric representations on screen. Recharge with ease - The TI-Nspire Rechargeable Battery, installed with the handheld, is expected to last up to two weeks of normal use on a single charge. No alkaline batteries needed. Calculate in style - The sleek TI-Nspire CX handheld is the thinnest and lightest TI graphing calculator model to date. It's also the brightest with a high-resolution, full-color display that makes it easy to see every exponent, variable and line. TI also offers the Math Nspired resource center, a collection of free, online lessons and tools that enable teachers to leverage TI-Nspire technology with ready-to-use lessons that cover tough-to-teach, tough-to-learn topics. TI will launch the Science Nspired resource center for Physics and Chemistry in time for back to school 2011
Mathematics Grade 8 [2011] 4.Distance-Time Graphs This tutorial is designed to help students understand the concept of slope and how distance-time graphs represent the relationship of collected data. Functions - Standards 4 and 5 Curriculum Guide The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Cluster "Use Functions to Model Relationships Between Quantities." / Standards 4 and 5 Graphit With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane. Graphs and Functions This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas. Introduction to Functions This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables. Linear Function Machine By putting different values into the linear function machine students will explore simple linear functions. Proportional Reasoning In this lesson students explore proportions by examining proportional relationships, absolute and relative comparisons, and looking at graphs to learn about these relationships. Slope Slider This website's applet lets the student manipulate a linear function in order to better understand the relationship between slope and intercept in the Cartesian coordinate system
In this brief introduction to probability, emphasis is on the conceptual development of the subject as each successive step is presented as the natural outgrowth of the preceding material. The book requires minimal mathematical background, yet its modern notation and style primes the reader for advanced and supplementary material. It provides core curriculum material in probability, and reinforces the calculus course. You may copy this unique Krieger Book Number into the Quote and Information Form, for quick processing, if you're interested in this book
Solve real problems by finding out how they are transformed into mathematical models and learning the methods of solution. This course covers classical mechanical models as well as some non-mechanical models such as population dynamics; and methods including vector algebra, differential equations, calculus (including several variables and vector calculus), matrices, methods for three-dimensional problems, and numerical methods. Teaching is supported and enhanced by use of a computer algebra package. To study this course you should have a sound knowledge of relevant mathematics as provided by the appropriate Level 1 study will be of particular interest to you if you use mathematics or mathematical reasoning in your work and feel that you need a firmer grounding in it, or if you think you might find it useful to extend your application of mathematics to a wider range of problems. The course should also be suitable if you are teaching A-level applied mathematics, or if you intend to do so; the material on mechanics, in particular, gives a very careful treatment of the basic concepts of this subject. The teaching is supported and enhanced by the computer algebra package Mathcad. Around half of this course is about using mathematical models to represent suitable aspects of the real world; the other half is about mathematical methods that are useful in working with such models. The work on models is devoted mainly to the study of classical mechanics, although non-mechanical models – such as those used in heat transfer and population dynamics – are also studied. The work on methods comprises topics chosen for their usefulness in dealing with the models; the main emphasis is on solving the problems arising in the real world, rather than on axiom systems or rigorous proofs. These methods include differential equations, linear algebra, advanced calculus and numerical methods. Many are implemented in Mathcad, so you can use the computer to solve more difficult problems and to investigate case studies. The mechanics part of the course begins with statics, where there are forces but no motion, and then introduces the fundamental laws governing the motions of bodies acted on by forces – Newton's laws of motion. These are first applied to model the motion of a particle moving in a straight line under the influence of known forces. Undamped oscillations are discussed next. Newton's laws are then extended to the motion of a particle in space. The motions of systems of particles are modelled. Next we look at the damped and forced vibrations of a single particle. Then we look at the motion (and vibrations) of several particles. Finally, we investigate the motion of rigid bodies. The methods part of the course covers both analytic and numerical methods. The analytical (as opposed to numerical) solution of first-order and of linear, constant-coefficient, second-order ordinary differential equations is discussed, followed by systems of linear and non-linear differential equations and an introduction to methods for solving partial differential equations. The topics in algebra are vector algebra, the theory of matrices and determinants, and eigenvalues and eigenvectors. We develop the elements of the calculus of functions of several variables, including vector calculus and multiple integrals, and make a start on the study of Fourier analysis. Finally, the study of numerical techniques covers the solution of systems of linear algebraic equations, methods for finding eigenvalues and eigenvectors of matrices, and methods for approximating the solution of differential equations. You will learn Successful study of this course should improve your skills in being able to think logically, express ideas and problems in mathematical language, communicate mathematical arguments clearly, interpret mathematical results in real-world terms and find solutions to problems. Entry This is a Level 2 course and you need a good knowledge of the subject area, obtained either from Level 1 study with the OU or from equivalent work at another university. It is designed to follow both Using mathematics (MST121) and Exploring mathematics (MS221). You are more likely to successfully complete this Level 2 course if you have acquired your prerequisite knowledge through passing these courses. You are advised to obtain a good pass in both courses first, or to make sure that you have reached an equivalent standard. If you have only passed MST121 we can provide some study material to help you bridge the gap to MST209. The bridging material is available on the MST209 course website. Knowledge of mechanics is not needed, but we do not recommend the course if you have little mathematical experience. You need a good basic working knowledge of: algebra – you must be able to solve linear and quadratic equations with one unknown, to multiply and add polynomials, to factorise quadratic polynomials and to work with complex numbers geometry – you must know Pythagoras's theorem and how to use Cartesian coordinates, e.g. the equations of straight lines and circles trigonometry – you need to know the basic properties of the three trigonometric ratios sine, cosine and tangent, and the definitions of the corresponding inverse functions calculus – you must be able to differentiate and integrate a variety of functions, though great facility in integration is not necessary. Preparatory work The course starts with an introductory unit that enables you to revise the necessary topics (see Entry), but it is not suitable for learning them for the first time. You will need to familiarise yourself with the course software and Mathcad by studying a computer booklet and associated files that come in the first mailing. The time that takes will vary according to your experience with Mathcad. Regulations As a student of The Open University, you should be aware of the content of the Module Regulations and the Student Regulations which are available on our Essential documents website. If you have a disability Transcripts for the DVD-video are available on the website and the multi-media material on the DVD includes embedded transcripts. The printed study material is available in comb-bound format. Adobe Portable Document Format (PDF) versions of printed material are also available. However, some Adobe PDF components may not be available or fully accessible using a screen reader and formula, diagrams and certain mathematical elements may be particularly difficult to read in this way. The study materials are available on audio in DAISY Digital Talking Book format. Other formats may be available in the future. Our Services for disabled students website has the latest information about availability. It is important to note that use of the course software, which includes on-screen graphs and mathematical notation, will be an integral part of your study. YouCourse books, other printed materials, DVD, Mathcad, website. You will need You require internet access at least once a week during the course to download course resources and assignments, keep up to date with course news and submit the computer-marked assignments (CMAs). DVD player (optional - you can watch the DVD video on your computer if you have a DVD drive and appropriate software). A calculator. You may wish to use this during the course, but you are not allowed to take a calculator into the examination. Computing requirements-schools in your locality that you are encouraged, but not obliged, to attend, and there is an online forum You will need to submit CMAs electronically, using the eCMA system. Future availability The details given here are for the course that starts in October 2013 when it will be available for the last time. A new course, Mathematical methods, models and modelling (MST210), is available from October 2014. Students also studied How to register To register a place on this course return to the top of the page and use the Click to register button. Student Reviews "Wow! I thought S207 the previous year was an intense course (and it was) but MST209 is on another level ..." Read more "After passing MS221 and MST121 , the natural progression for a mathematical methods addict like me was MST209. I especially
Factoring Polynomials MatchingManiaFactoring Polynomials MatchingMania contains 3 different factoring activities - GCF and trinomial factoring. Cooperative Learning is involved in finding the factors of give polynomials. This activity is also available in the Algebra I MatchingMania Book, which includes 10 other similar activities. PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 250.74
AMC Archives Your browser does not appear to support JavaScript, or you have turned JavaScript off. You may use unl.edu without enabling JavaScript, but certain functions may not be available. The American Mathematics Competitions (AMC) The American Mathematics Competitions (AMC) is dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. We believe that one way to meet this goal is to identify, recognize and reward excellence in mathematics through a serics of national contests called the: American Mathematics Contest 8 (AMC 8), American Mathematics Contest 10 (AMC 10), American Mathematics Contest 12 (AMC 12), American Invitational Mathematics Examination (AIME), and United States of America Mathematical Olympiad (USAMO). In addition to the 5 contests listed above, we also have an invitation-only summer program, at which we choose the final six contestants for an international competition: Mathematical Olympiad Summer program (MOSP), and the International Mathematical Olympiad (IMO) For over 50 years many excellent exams have been prepared by individuals throughout our mathematical community in the hope that all secondary students will have an opportunity to participate in these problem solving and enriching mathematics experiences. The AMC contests are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most specialized school. To ensure this mission is served, each year the AMC solicits enrollment by mailing an Invitation Brochure to all schools in the United States teaching grades six through twelve. HISTORICAL BEGINNING On Thursday, May 11, 1950 the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematics Association of America (MAA) took place. It was given in approximately 238 schools to around 6,000 students in the New York area only. The following exerpt is taken from the Report of the Committee addressed to that year's participating teachers: "The first mathematics contest sponsored by the New York Metropolitan Section of the MAA is now history. It was a lot of work getting the contest organized and finally holding it. Like all new projects, we worried about it. Would the High Schools participate? Would they like the test? Is it worth while? Will any good be produced by it? Will it be a success?" Today, over fifty years and three generations later we can answer all of the Committee's questions with a resounding Yes! Yes! Yes! The overall success of this program can be viewed by simply looking at our growth in numbers. This last year over 413,000 students in over 5,100 schools participated in the AMC Contests. Of these 10,000 students qualify each year to participate in the AIME scheduled for late March / early April. From this group approximately 500 students will be invited to take the prestigous USAMO in early May. TODAY The AMC year begins in the fall with the American Mathematics Contest 8 (AMC 8, originally called the AJHSME - American Junior High School Mathematics Examination), held in November of each year. The AMC 8 is for students in the sixth, seventh or eighth grade; accelerated fourth and fifth grade students also take part. It is a 25-question, 40-minute multiple-choice contest, given the Tuesday before Thanksgiving week. A student's score is the number of problems correctly solved, there is no penalty for guessing. The material covered is the middle school mathematics curriculum. No problem requires the use of algebra or a calculator. AMC 8 eligibility extends to any student 14.5 years of age or younger on the day of the contest, and not enrolled in grades 9, 10, 11 or 12 or equivalent Students who score 20 or better on the AMC 8 are invited to take the next set of contests, the AMC 10/AMC 12. The American Mathematics Contest 12 (AMC 12, originally called the AHSME - Annual High School Mathematics Examination), is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. The AMC 12 is designed for students in a program leading to a high school diploma, and under 19.5 years of age on the day of the contest. The American Mathematics Contest 10 (AMC 10, added in 2000, when the names of the AMC 8 and AMC 12 were updated) is also a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. The AMC 10 is designed for students in a program leading to a high school diploma, under 17.5 years of age on the day of the contest, and not enrolled in grades 11 or 12 or equivalent. The AMC 12 and AMC 10Contests are given on two different dates, (designated by the use of the "A" and "B" suffix on the contest names - AMC 12A, AMC 10A, AMC 12B or AMC 10B) about two weeks apart, in February. A student may choose to take one contest on both dates. In other words, an 11th or 12th grader may take the AMC 12 on both dates. A student in 10th grade or below may choose whether he will take the AMC 10 or the AMC 12 on each date , so a 10th grader can take the AMC 10 A and the AMC 12B, the AMC 12A and the AMC 10B, the AMC 12A and the AMC 12B or the AMC 10A and the AMC 10B American Invitational Mathematics Examination (AIME), is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. It is given on two different dates, (designated by the use of the "I" and "II" suffix on the contest names - AIME-I and AIME -II) about two weeks apart, in late March. The questions on the AIME are much more difficult than the AMC 10 and the AMC 12 and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. Unlike on the AMC 10 and the AMC 12 a student can only take the AIME once, and are encouraged to take the AIME-I on the first date offered. Please see the Teachers' Manual for more information on situations where a student may take the AIME-II on the alternate date. Again, after United States of America Mathematical Olympiad (USAMO) and the United States of America Junior Mathematical Olympiad (USAJMO), are each a six question, two day, 9 hour essay/proof examination. All problems can be solved with pre-calculus methods. Approximately 270 of the top scoring AMC 12 participants (based on a weighted average) will be invited to take the USAMO. Approximately 230 of the top scoring AMC 10 participants (based on a weighted average) will be invited to take the USAJMO. U.S. citizens and students legally residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO. This is given on two consecutive days (usually a Tuesday and Wednesday) in late April. The twelve top scoring USAMO students are invited to an Olympiad Awards Ceremony in Washington, DC sponsored by the MAA. Six students will comprise the United States team that competes in the International Mathematical Olympiad (IMO). The IMO began in 1959; the USA has participated since 1974. The Mathematical Olympiad Summer Program (MOSP) is a 3-4 week, intensive training program in the summer. This program gives all participants, including the six IMO team members and two alternates, extensive practice in solving mathematical problems which require deeper analysis than those solved by students in even the best American high schools. Full days of classes and extensive problem sets give students thorough preparation in several important areas of mathematics which are traditionally emphasized more in other countries than in the United States. Traditionally there are 25 openings for the IMO team, alternates, and a select group of younger students. For the past several years The Akamai Foundation has sponsored an additional 25 openings for students just finishing ninth grade. The AMC year culminates with the International Mathematical Olympiad (IMO) which is a 10-14 day trip and contest for the top 6 students, who comprise the United States IMO team and represent the U.S. at the IMO.
Book Description: The essential guide to MATLAB as a problem solving toolThis text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. Stressing the importance of a structured approach to problem solving, the text gives a step-by-step method for program design and algorithm development. The fundamentals of MATLAB are illustrated throughout with many examples from a wide range of familiar scientific and engineering areas, as well as from everyday life.Features:. Numerous simple exercises provide hands-on learning of MATLAB's functions. A new chapter on dynamical systems shows how a structured approach is used to solve more complex problems.. Common errors and pitfalls highlighted. Concise introduction to useful topics for solving problems in later engineering and science courses: vectors as arrays, arrays of characters, GUIs, advanced graphics, simulation and numerical methods. Text and graphics in four colour. Extensive instructor supportEssential MATLAB for Engineers and Scientists is an ideal textbook for a first course on MATLAB or an engineering problem solving course using MATLAB, as well as a self-learning tutorial for students and professionals expected to learn and apply MATLAB for themselves.Additional material is available for lecturers only at This website provides lecturers with:A series of Powerpoint presentations to assist lecture preparationExtra quiz questions and problemsAdditional topic materialM-files for the exercises and examples in the text (also available to students at the book's companion site)Solutions to exercisesAn interview with the revising author, Daniel Valentine · Numerous simple exercises give hands-on learning· A chapter on algorithm development and program design · Common errors and pitfalls highlighted· Concise introduction to useful topics for solving problems in later engineering and science courses: vectors as arrays, arrays of characters, GUIs, advanced graphics, simulation and numerical methods· A new chapter on dynamical systems shows how a structured approach is used to solve more complex problems.· Text and graphics in four colour· Extensive teacher support on solutions manual, extra problems, multiple choice questions, PowerPoint slides· Companion website for students providing M-files used within the book
Unlike most engineering maths texts, this book does not assume a firm grasp of GCSE maths, and unlike low-level general maths texts, the content is tailored specifically to the needs of engineers. The result is a unique book written for engineering students that takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, especially for those who find the theoretical side of mathematics difficult. Now in its fifth edition, Basic Engineering Mathematics is an established textbook, with the previous edition selling nearly 7500 copies. All students that require a fundamental knowledge of mathematics for engineering will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering, the Diploma, and the BTEC First specifications. Level 3 students will also find this text to be a useful resource for getting to grips with essential mathematics concepts, because the compulsory topics in BTEC National and A Level Engineering courses are also addressed. less
Interactive Algebra II tutorial and testing package for individual e-learning and home schooling with emphasis on building problem-solving skills. Interactive Algebra II tutorial and testing package for individual e-learning and home schooling with emphasis on building problem-solving skills. Java- and web-based math course includes theoretical concepts, hands-on examples featuring animated... A program deals with formulas. A program deals with formulas. Formulas are not only important in math but also in science including physics, chemistry, etc. It includes how to construct formulas and its usage in algebra. It includes how to manipulate fomulas by changing itsWith 50 challenging puzzle levels, your objective is to help Jungle Jean reach the trapped chimpanzee. Use the various objects in each level, along with your ingenuity and problem solving skills to rescue the chimpanzee in all 50 levels of this puzzle game. A demonstration puzzle is included to get you started or you can see the solution for yourself with a click of a button. Jungle Jean is animated puzzle solving fun for the whole family! The Flop game is for those whom like to find precise algorithms of problem solving. The Flop game is for those whom like to find precise algorithms of problem solving. Before the beginning of game all game field is filled in with units. Each unit can be in three states, which can sequentially pass from one in other. Your task to... Tiny Go is a MIDlet (cell phone application using MIDP 2. Tiny... SCIRun is a modular dataflow programming Problem Solving Environment (PSE). SCIRun is a modular dataflow programming Problem Solving Environment (PSE). SCIRun has a set of Modules that perform specific functions on a data stream. Each module reads data from its input ports, calculates the data, and sends new data from...Well, now your wish has come true. FlexPDE is a scripted finite element partial differential equations problem solving environment.FlexPDE reads your partial differential equation system...
Math freeware? Math freeware? I'm sorta budgeted at the moment.. So freeware would be nice, but feel free to list what ever resources. I want some program that can help me learn math or atleast give me extra practice. Saying upper level of algebra and geometry and trig and calculas For problems, I agree with socrunningman. Just get some books from the library and do the exercises. Try to find ones with a good answer key so you can understand how they got the solution. For calc, something like Stewart has a good range of questions and a decent answer key book. It is also easy to find an older version (like the 5th edition) for about $5.
Test authoring mathematics software offers 35126 algebraic problems with answers and solutions and easy-to-use test authoring options. Algebra problems from basic to advanced are arranged by complexity and solution methods and correspond to linear, quadratic, cubic, reciprocal, biquadratic and fractional expressions, identities, equations and inequalities. The software enables users to prepare math tests, homeworks, quizzes and exams of varied complexity literally in a minute, and generates three variants around each prepared test. Tests with or without the solutions can be printed out. A number of variant tests are ready for students to review and reinforce their math skills. The software supports bilingual interface and a number of interface styles. Free fully functional trial software version is available ... Test authoring mathematics software offers 54806 solved algebraic inequalities - from basic to advanced - with answers, solutions and easy-to-use authoring options. Problems are arranged by complexity, solution methods and types of tasks. Linear, quadratic, biquadratic, reciprocal, cubic and fractional expressions. Applied solution methods include substitution, grouping, factoring, method of intervals and more. The program enables users to select problems by complexity and solution methods and create math tests, homeworks, quizzes and exams of varied complexity in a minute. The program generates 30 variant tests around a constructed example. A number of variant tests are ready for students to review and reinforce their skills. Free fully functional demo version of this program is available. .... ... ... Mavscript allows the user to do calculations in a text document. Plain text and OpenOffice Writer files (odt,sxw) are supported. The calculation is done by the algebra system Yacas or by the Java interpreter BeanShell.... algebra, text, openoffice, odt, beanshell, gpl, java, free, calculate, Having trouble doing your Math homework? This program can help you master basic skills like reducing, factorising, simplifying and solving equations. A step by step explanation of problems concerning fractions,binomials, trinomials etc. ... Have fun learning math with Algebra One On One. It combines the fun of a quiz show with the learning seen in Algebra classrooms. Over 21 levels and six ways of playing ensure continued challenge. Advance through the levels sequentially or jump right to the Einstein level to find challenges that might stump the experts. Algebra One on One combines fun and education in one complete ... Karnaugh Analyzer is a light and fast program that can analyze Karnaugh Map and not only this!!!! You can input your data in many form (Karnaugh Map, True Table, Function form - Boolean algebra, and in sets of Term) and you can take the function in sum of product (SOP) or in product of sum (POS).... Smooth Operators is a complete solution for learning, practicing, and testing the order of operations. An interactive lesson teaches the math concepts thoroughly with explanations and example problems, including an optional section on exponents. Popular memory aids are introduced, but users also learn a logical approach to truly understand the order of operations. In practice mode, students click on operators in the correct order, giving their complete attention to which operations come first. In test mode, the user performs all calculations and types in the answers. Score is always displayed. Problems can include parentheses and exponents, and the learner or supervisor can select the number of operations per problem and the size of operands. In the course of solving problems, users have an excellent review of basic math skills as they add, subtract, multiply, and divide positive and negative numbers. Smooth Operators helps students master crucial skills and prepare for algebra and higher math, while providing ample opportunity for arithmetic practice. This educational software is ideal for school or home, in class or independent study.... Free biquadratic, reciprocal, cubic and fractional algebraic identities, equations and inequalities, solutions of trigonometric and hyperbolic equations and more. The program is a trial version of the EMTeachline mathematics software...ESBPDF Analysis provides everything needed for using Discrete Continuous Probability Distributions in a single application. Most Tables and supplied functions (such as in MS Excel) give P(X = A) and using algebra other results can be found whereas ESBPDF Analysis handles all the Probability combinations for you.Features include Binomial, Poisson, Normal, Exponential, Student t, Chi Squared, F, Beta and Lognormal Distributions; Inverses of Normal, Student t, Chi Squared, F, Beta and Lognormal Distributions; Lists of Binomial Coefficients, Factorials and Permutations; Calculations of Gamma and Beta Functions; Printing of Standard Normal Tables Critical t Values; Fully Customisable; Integrated Help System which includes a Tutorial. We also plan on adding many more Distributions and features.Also includes Graphing of Distributions, addition Info on Distributions and registered users also get Electronic Documentation and a PDF version of the docs designed for printing.Ideal for the Maths/Stats Student who wishes to understand Probability Distributions better, as well as the Maths Buff who wants a well designed calculating tool.Designed for Win32 and optimised for Windows XP... Algematics can help you do your high school algebra, one step at a time You can finish your work without waiting to ask your teacher. Enter equations and expressions straight out of your book or from your homework sheet. Simply point and click to factori... Download Free Measure Converter: inch, feet, yard, rod, furlong, mile, league, chain. Length and Distance Conversions. The program interface is quite simple so even if you are a beginner you can use it without any trouble players, different, questions, dragon, numbers, ....Included areas: Arithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry and miscellaneous. Visual Mathematics, a member of the Virtual Dynamics Mathematics Virtual Laboratory, is an Intuitively-Easy-To-Use software. Visual Mathematics modules include the theory necessary to understand every theme, they include very many solved examples. Every student should have this powerful tool at home. Teachers use Visual Mathematics to prepare homeworks and tests in a short time. With Visual Mathematics the student solves homework problems while he/she really learns and enjoys mathematics. Visual Mathematics may be used (1) in the classroom, to very easily make clear the topics the teacher covers, (2) in the school library, as reference to review themes covered in classes (3) at home, for the student to study at his own pace and understand while solving and visualizing hundreds of problems. Teachers may use Visual Mathematics to prepare classes. <>... mathematics, visual, student, problems, this program very useful as well opportunities
More About This Textbook Overview This new adaptation of Arfken and Weber's bestselling Mathematical Methods for Physicists, Fifth Edition, is the most comprehensive, modern, and accessible text for using mathematics to solve physics problems. Additional explanations and examples make it student-friendly and more adaptable to a course syllabus. KEY FEATURES: · This is a more accessible version of Arfken and Weber's blockbuster reference, Mathematical Methods for Physicists, 5th Edition · Many more detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems · More frequent and thorough explanations help readers understand, recall, and apply the theory · New introductions and review material provide context and extra support for key ideas · Many more routine problems reinforce basic concepts and computations Editorial Reviews From the Publisher "...achieves a comprehensive coverage of the 'essential' topics in mathematical physics at the undergraduate level...filled with enlightening examples..." - David Hwang, University of California at Davis "The book contains many worked out problems some of which are solved in more than one way to accommodate different learning needs and styles..." - Amit Chakrabati, Kansas
These web pages are provided to help high school and college/university students learn important algebra facts. In much the same way that you are assumed to know your basic multiplication facts, so also you need to know certain facts in algebra. Without having that knowledge memorized it is difficult to successfully solve many problems that involve algebra, whether that algebra is used in an algebra class, a trigonometry class, or a calculus class (or beyond). My hope is that the flashcards and learning center examples can help you learn these algebra facts, and together with what you learn from your teacher and textbook, help you become more successful in your use of algebra. If you are a student who makes more algebra mistakes than you would like, use the flashcards to check your knowledge of algebra facts. Use the learning center pages to further explore algebra facts through examples and explanations. If something does not make sense, write to me at the email address below. If you have suggestions for improving these pages, you may send them to the email address below. I don't guarantee to use any suggestions or material sent to me. Please note: If you send me any material, you agree that I will provide you no compensation or sharing of any revenue generated by the web site in exchange for using that material. If you notice any serious errors on these web pages, I would appreciate hearing from you so that I may correct the problem. Please realize that reasonable people will disagree about how to explain certain concepts. In certain cases, therefore, I may not act on your advice. I may in certain cases receive or have a conflicting opinion on some aspects of these pages and will choose the approach that makes the most sense to me. Therefore, please resist the temptation to nit-pick the content of these pages.
0321652797 9780321652799 Using and Understanding Mathematics: Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make better decisions every day. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts. Note: This is the standalone book, if you want the book with the Access Card please order the ISBN below: 0321727746 / 9780321727749 Using and Understanding Mathematics: A Quantitative Reasoning Approach with MathXL (12-month access) * Package consists of 0201716305 / 9780201716306 MathXL -- Valuepack Access Card (12-month access) 0321652797 / 9780321652799 Using and Understanding Mathematics: A Quantitative Reasoning Approach «Show less Using and Understanding Mathematics: Using and Understanding Mathematics: A Quantitative Reasoning Approach, Fifth Edition increases readers' mathematical literacy so that they better understand the mathematics used in their daily lives, and can use math effectively to make... Show more» Preface xi Acknowledgments xviii Prologue: Literacy for the Modern World PART ONE Logic and Problem Solving Thinking Critically Activity Bursting Bubble Recognizing Fallacies Propositions and Truth Values Sets and Venn Diagrams A Brief Review: Sets of Numbers Analyzing Arguments Critical Thinking in Everyday Life Approaches to Problem Solving Activity Global Melting The Problem-Solving Power of Units A Brief Review: Working with Fractions Using Technology: Currency Exchange Rates Standardized Units: More Problem-Solving Power A Brief Review: Powers of 10 Using Technology: Metric Conversions Problem-Solving Guidelines and Hints PART TWO Quantitative Information in Everyday Life Numbers in the Real World Activity Big Numbers Uses and Abuses of Percentages A Brief Review: Percentages A Brief Review: What Is a Ratio? Putting Numbers in Perspective A Brief Review: Working with Scientific Notation Using Technology: Scientific Notation Dealing with Uncertainty A Brief Review: Rounding Using Technology: Rounding in Excel Index Numbers: The CP1 and Beyond Using Technology: The Inflation Calculator How Numbers Deceive: Polygraphs, Mammograms, and More Managing Money Activity Student Loans Taking Control of Your Finances The Power of Compounding A Brief Review: Powers and Roots Using Technology: Powers Using Technology: The Compound Interest Formula Using Technology: The Compound Interest Formula for Interest Paid More than Once a Year Using Technology: APY in Excel Using Technology: Powers of e A Brief Review: Three Basic Rules of Algebra Savings Plans and Investments Using Technology: The Savings Plan Formula A Brief Review: Algebra with Powers and Roots Using Technology: Fractional Powers (Roots) Loan Payments, Credit Cards, and Mortgages Using Technology: The Loan Payment Formula (installment Loans) Using Technology: Principal and Interest Payments Income Taxes Understanding the Federal Budget PART THREE Probability and Statistics Statistical Reasoning Activity Cell Phones and Driving Fundamentals of Statistics Using Technology: Random Numbers Should You Believe a Statistical Study? Statistical Tables and Graphs Using Technology: Frequency Tables in Excel Using Technology: Bar Graphs and Pie Charts in Excel Using Technology: Fine Charts and Histograms in Excel Graphics in the Media Correlation and Causality Using Technology: Scatter Diagrams in Excel Putting Statistics to Work Activity Bankrupting the Auto Companies Characterizing Data Using Technology: Mean, Median, Mode in Excel Measures of Variation Using Technology: Standard Deviation in Excel The Normal Distribution Using Technology: Standard Scores in Excel Using Technology: Normal Distribution Percentiles in Excel Statistical Inference Probability: Living with the Odds Activity Lotteries Fundamentals of Probability A Brief Review: The Multiplication Principle Combining Probabilities The Law of Large Numbers Assessing Risk Counting and Probability A Brief Review: Factorials Using Technology: Factorials Using Technology: Permutations Using Technology: Combinations PART FOUR Modeling Exponential Astonishment Activity Towers of Hanoi Growth: Linear versus Exponential Doubling Time and Half-Life A Brief Review: Logarithms Using Technology: Logarithms Real Population Growth Logarithmic Scales: Earthquakes, Sounds, and Acids Modeling Our World Activity Bald Eagle Recovery Functions: The Building Blocks of Mathematical Models A Brief Review: The Coordinate Plane Linear Modeling Using Technology: Graphing Functions Exponential Modeling A Brief Review: Algebra with Logarithms Modeling with Geometry Activity Eyes in the Sky Fundamentals of Geometry Problem Solving with Geometry Fractal Geometry PART FIVE Further Applications Mathematics and the Arts Activity Digital Music Files Mathematics and Music Perspective and Symmetry Proportion and the Golden Ratio Mathematics and Politics 625 Activity Congressional District Boundaries Voting: Does the Majority Always Rule? Theory of Voting Apportionment: The House of Representatives and Beyond Dividing the Political Pie 665 Credits Answers
About the Book: The book `Fundamental Approach to Discrete Mathematics` is a required part of pursuing a computer science degree at most universities. It provides in-depth knowledge to the subject for beginners and stimulates further interest in the topic. The salient features of this book include: Strong coverage of key topics involving recurrence... more... Nonlinear media exhibit a variety of spatio-temporal phenomena. Circular waves, spiral waves and self-localized excitations are the most familiar examples. How to use these phenomena to perform useful computations is the main theme of this book. more... A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict... more... Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical... more... Recent applications to bioscience have created a new audience for automata theory and formal languages. This is the only introduction to cover such applications. With over 350 exercises, many examples and illustrations, this is an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning. more... Reviews the origins and aims of cybernetics with reference to Warren McCulloch's declared lifetime quest of 'understanding man's understanding'. This book examines implications for neuroscience and Artificial Intelligence (AI). It is suitable for researchers in AI, psychology, cybernetics and systems science. more... Dealing with uncertainty, moving from ignorance to knowledge, is the focus of cognitive processes. Understanding these processes and modelling, designing, and building artificial cognitive systems have long been challenging research problems. This book describes the theory and methodology of a new, scientifically well-founded general approach, and... more...
Intermediate algebra Book Description: Pat McKeague's passion and dedication to teaching mathematics and his ongoing participation in mathematical organizations provides the most current and reliable textbook series for both instructors and students. When writing a textbook, Pat McKeague's main goal is to write a textbook that is user-friendly. Students develop a thorough understanding of the concepts essential to their success in mathematics with his attention to detail, exceptional writing style, and organization of mathematical concepts. Intermediate Algebra: A Text/Workbook, Seventh Edition offers a unique and effortless way to teach your course, whether it is a traditional lecture course or a self-paced course. In a lecture-course format, each section can be taught in 45- to 50-minute class sessions, affording instructors a straightforward way to prepare and teach their course. In a self-paced format, Pat's proven EPAS approach (Example, Practice Problem, Answer and Solution) moves students through each new concept with ease and assists students in breaking up their problem-solving into manageable steps. The Seventh Edition of INTERMEDIATE ALGEBRA: A TEXT/WORKBOOK has new features that will further enhance your students' learning, including boxed features entitled Improving Your Quantitative Literacy, Getting Ready for Chapter Problems, Section Objectives and Enhanced and Expanded Review Problems. These features are designed so your students can practice and reinforce conceptual learning. Furthermore, iLrn/MathematicsNow™, a new Brooks/Cole technology product, is an assignable assessment and homework system that consists of pre-tests, Personalized Learning Plans, and post-tests to gauge concept mastery.
Grading There will be five quizzes, two exams (October 13 and December 1), and a cumulative final exam. Your final grade will be based on 400 points: Quizzes due to serious illness or other emergency is possible only with prior or immediate notice and will be granted at my discretion. Learning Objectives Students should understand the limit concept. They should know the formal definition of a limit and be able to verify simple limits using the definition. They should be able to evaluate limits using limit rules. Students should know the definition of a continuous function and its meaning in relation to the graph of the function. They should be able to determine the continuity of functions. Students should know the definition of the derivative function and be able to find derivatives using the definition. They should understand the meaning of the derivative in terms of tangent lines and rates of change. Students should know the techniques of differentiation and be able to use them to find the derivatives of various functions. They should be able to use derivatives to solve a variety of problems. Course Description MAT 131-132 Elementary Calculus A more rigorous introduction to calculus for entering students with good backgrounds in mathematics. Recommended for students considering a major in mathematics. Topics include the real numbers, functions, limits, the derivative and applications, the integral and applications, and techniques of integration. Not open to those who complete MAT 117 or MAT 118. Prerequisite: Departmental permission through placement for any student with documented disabilities. If you have a disability and believe that you require accommodation, please contact the Dean of Studies Office.
Quick Links 4 — The Homework Book Homework is a vital part of studentsí learning. Our Homework Book provides homework for every Lesson, allowing students to extend their learning beyond the classroom. All worksheets can be detached for ease of grading. Key features of our Homework Book: Each assignment reinforces the CA Math standard objective Hints and tips to extend those from the textbook Worked example in every sheet to provide additional reinforcement of teaching Questions increase in difficulty to provide practice for all abilities Extensive support for parents and suggestions for parental involvement
Palm CalculusSimilarly, as in a spoken or written language the sciences and mathematics have their rules connecting the theory. To become fluent, the rules must be mastered by each student studying that subject. Repetition and problem drills make the new information part of the student's working knowledge and are a mustHe started developing a strong passion for mathematics in middle school when he learned about Newton's Principia. In high school he obtained A grades in mathematics and further mathematics. He obtained a B.
Interactive Software Demos for Learning Differential Equations Since the time of Isaac Newton, differential equations have been useful for modeling of a wide variety of dynamical physical systems. For example, the motion of a mass acted upon by a force can be modeled by a second-order differential equation using Newton's second law. The objective of this project is to visualize solutions to basic differential equations used in various undergraduate courses on applied mathematics, physics, and engineering. The visualization is provided by real-time web-enabled software technologies. It is expected that the interactive software demos smooth out the student's learning curve and help instructors in lecturing the undergraduate courses. Learning Goals: Classify critical points of the dynamical system and local stability of critical points. Match solutions of differential equations and trajectories on a phase plane of the system. Understand differences between finite and infinite trajectories on a phase plane. Identify the separatrix curves on the phase plane. Control behaviour of the system by changing initial values of the system. Understand the role of damping for motion of the pendulum. Learning Goals: Understand hypotheses and constraints of mathematical modeling. Classify critical points of the dynamical system. Understand differences between local and global stability of critical points. Match population cycles of the predator-prey system and periodic solutions of the dynamical system. Learning Goals: Identify limit cycles on a phase plane of the system. Control the flow of trajectories that draws the global phase portrait of the system. Understand global stability of critical points and limit cycles. Utilize the Hopf bifurcation of the dynamical system. Software Requirements: The software demos work with Microsoft Internet Explorer. They are read-only with other browsers such as Netscape. Before starting the demos, maximize the browser window and close other applications on your computer.
Product Details See What's Inside Product Description By Linda Sheffield, Susan Johnsen Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K–12 schools. The book describes—and demonstrates with specific examples from the CCSS—what effective differentiated activities in mathematics look like for top learners. It shares how educators can provide rigor within the new standards to allow students to demonstrate higher level thinking, reasoning, problem solving, passion, and inventiveness in mathematics. By doing so, students will develop the skills, habits of mind, and attitudes toward learning needed to reach high levels of competency and creative production in mathematics fields. Customers Who Bought This Also Bought... The Center for the Study of Mathematics Curriculum (CSMC) leaders developed this volume to further the goal of teachers having opportunities to interact across grades in ways that help both teachers and their students see connections in schooling as they progress through the grades. Each section of this volume contains three companion chapters appropriate to the three grade bands—K–5, 6–8, and 9–12—focusing on important curriculum issues related to understanding and implementing the CCSSM. Connect the process of problem solving with the content of the Common Core. The first of a series, this book will help mathematics educators illuminate a crucial link between problem solving and the Common Core State Standards. How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)? This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for high school. Discover what students should learn and how they should learn it, including deep support for the Mathematical Modeling conceptual category of the CCSS. Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You'll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students. Extensive tools to implement a successful and coherent formative assessment and RTI response are included. How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)? This leader companion to the grade-level teacher guides illustrates how to sustain successful implementation of the CCSS for mathematics. School leaders will discover how to support and focus the work of their collaborative mathematics teams for significant student achievement and improvement. Readers will receive explicit guidance and resources on how to lead and exceed the assessment expectations of the common core. How do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)? This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematicsHow do you help your students demonstrate mathematical proficiency toward the learning expectations of the Common Core State Standards (CCSS)? This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for grades 3–5. Discover what students should learn and how they should learn it at each grade level, including deep support for the unique work for Number & Operations—Fractions in grades 3–5 and learning progression models that capstone expectations for middle school mathematics readiness. This highly practical, comprehensive guide combines NCTM's wealth of knowledge from experts in the fields of formative and summative assessment with research-based data and offers a library for understanding both formative and summative assessment. Transform math instruction with effective CCSS leadershipThis professional development resource helps principals and math leaders grapple with the changes that must be addressed so that teachers can implement the practices required by the CCSS. The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
AcademicsCalculus Course Outline: The course will follow chapters 0 - 5 and 8 of Himonas and Howard's "Calculus: Ideas and Applications" (Wiley). After this we will briefly consider one or more advanced topics depending on the interests of the class (possibilities include multivariable calculus, differential equations and power series) The program will follow a strict schedule that includes drill and practice routines for developing a familiarity with the common tools of calculus alongside discussions surrounding the concepts behind the subject. This is a four-credit course and there is much to learn. Please keep in mind that this course requires a daily commitment. The best way to successfully learn the material is to stay ahead of the game and work through the assignments as soon as possible after the material is covered in class. Grades: Here is the breakdown for how your grade will be calculated: Graded homework assignments: 30% 3 take-home quizzes: 5% each 3 in-class quizzes: 5% each Final exam: 40% Prompt submission of homework and class attendance and participation are expected. Your overall grade will be affected by upto one letter grade by these factors. Homeworks: Bold numbered problems in the homework assignment section below are to be handed in for grading. Plaintext numbered problems are more drill and practice material that should be worked through to keep up with course material. By 4pm each Friday you are expected to hand in your solutions to the appropriate bold numbered questions (exactly which questions these are will be announced on the Thursday beforehand). You may wish to discuss any assignments that you find difficult.
Maths Skills for Health Science These pages will allow you to learn about or revise the maths topics covered in the Numeracy Diagnostic Questions presented on the Public Health 1A MyUni site. Pages relating to each question are listed below. Follow the links labelled with any diagnostic questions you found difficult. Don't forget that The Maths Drop-In Centre is open 10am to 4pm Monday to Friday during the semester if you'd like to discuss anything from these pages (or any maths/stats in your studies) with a tutor.
Math A graduate degree in mathematics can help students hone their skills in a specialty area, from algebra and number theory to discrete mathematics and combinatorics. These are the best graduate-level math programs.
Math Homework Answers 0.00 (0 votes) Document Description GetAdd New Comment Get Math answers from TutorVista. Math is a difficult subject for most students. TutorVista makes this difficult subject simple and easy for you to understand. Our online tutors help you understand math homework for free from our tutors who are available online 24/7. You can also get your assignment done online with TutorVista. Our Math Homework help service is very affordable ... Mathematics is one of the most dreaded subjects for school children. For many school kids, mathematical sums are always complicated and getting the A grades in a math exam a distant dream. However, ... Content Preview Math Homework Answers GetMath answers Step by Step From Framing of Formulas to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations you get all Math Homework Answers online using our well structured and wel thought out Math tutoring program. Students get not just the answer but answers step by step. Below is provided a demo example of getting math answers step by step from us: Example: Find out the area of a triangle, height 8 cm, base 6 cm. Answer: 242 cm Steps to follow: 1. Since, Area of a triangle formula = 1/2 x b x h (b = base, h = height) 2. Here, base = 6 cm and height = 8 cm 3. Therefore, the area of the given triangle = 1/2 x 6 cm x 8 cm 4. Math answer to the given problem = 242 cm This is a geometry example. Likewise get free answers to al your math problems. Now make your math easy with Tutorvista.
doing an extra credit assignment for algebra 2. We are supposed to write a paper on the algebra needed for the career path you want. It would be helpful if I could get some examples of formulas or anything else that could help me write this paper for being a physical therapist. Cereal044 Feb 23, 2009, 10:04 PM I am going to school for physical therapy, I am not sure what you are learning in you class but the most common we use that deals with math is angles of pull and torque. All the muscles in your body work at different angles to get the job done. Some muscles use bones (like the knee cap) to increase the angles, therefore increasing the efficiency of the muscle. Some muscles are made to help with more movement. Like you biceps while others are made to be more powerful like you deltoids. Let me know if this helps you. Remember to be a good PT you need to understand the way the muscles and everything else in the body works, so you can help it get better! Good luck!
Costs Course Cost: $175.00 Materials Cost: None Total Cost: $175 Special Notes State Course Code 02074AlgebraA graphing calculator is recommended, but not required. A graphing program (Gcalc) available throughout the course. Description This is comprehensive course featuring geometric terms and processes, logic and problem solving. Includes topics such as parallel line and planes, congruent triangles, inequalities and quadrilaterals. Various forms of proof are studied. Emphasis is placed upon reasoning and problem solving skills gained through study of similarity, areas, volumes, circles, and coordinate geometry. This course has been specifically built with the credit recovery student in mind. The course content has been appropriately chunked into smaller topics to increase retention and expand opportunities for assessment. With each topic, diagnostic quizzes are presented to the student, allowing students to pass through areas of content that they have previously studied successfully. Post-topic quizzes are presented with each topic of content. Audio readings are included with every portion of content, allowing auditory learners the opportunity to engage with the course. Test pools and randomized test questions are utilized in pre- and post-topic quizzes as well as unit exams, ensuring that students taking the course will not be presented with the same exams.
If you are currently enrolled in MATH2241, you can log into UNSW Blackboard for this course. Course Overview An introduction to mathematical models for the circulation of the atmosphere and oceans. The equations of motion are exploited so as to provide simplified models for phenomena including: waves, the effects of the Earth's rotation, the geostrophic wind, upwelling, storm surges. Feedback mechanisms are also modelled: the land/sea breeze, tornadoes, tropical cyclones. Models for large-scale phenomena including El Nino and the East Australian Current will be discussed as well as the role of the atmosphere-ocean system in climate change.
University preparation: mathematics Try using our navigation bar across the top to find upcoming events, or use the search just below the navigation if you are looking for a specific upcoming event. This course prepares students for future study of mathematics at university level by developing an understanding and application of algebra, geometry and calculus. Students will practise effective techniques for studying mathematics as well as learning to read and write mathematics clearly and intelligibly. Students will also develop an appreciation of the patterns which arise in mathematics and how they are applied in a number of different subject areas. Before considering a University Preparation Course please review important information to determine if you are eligible for the Mature Age Entry Scheme and how to go about qualifying and applying
Mathematics for Elementary Teachers 9780321447173 ISBN: 0321447174 Edition: 2 Pub Date: 2007 Publisher: Addison-Wesley Summary: Elementary school classrooms are increasingly relying on a discovery method for the teaching of mathematics. Mathematics for Elementary Teachers thoroughly prepares preservice teachers to use this approach as it has been proven to increase their depth of understanding of mathematics. In this text, topics are organized by operation, rather than number type, and time is spent explaining why the math works, rather than ...just on the mechanics of how it works. Fully integrated activities are found in the book and in an accompanying Activities Manual. As a result, students engage, explore, discuss, and ultimately reach true understanding of the approach and of mathematics Shows some signs of wear, and may have some markings on the inside. 100% Mo... [more]ALTERNATE EDITION: Instructor's Edition. Shows
The AP Calculus AB course is designed to provide students with a learning experience equivalent to that of a college course in single variable calculus. This course will develop students' understanding of the concepts of calculus and provide experience with its methods and applications. The course will emphasize a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Course Goals: Students will be able to: * work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. * understand the meaning of the derivative in terms of a rate of change and local linear approximation and they should be able to use derivatives to solve a variety of problems. * understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems. * understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus. * communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems. * model a written description of a physical situation with a function, a differential equation, or an integral. * use technology to help solve problems, experiment, interpret results, and verify conclusions. * determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. * develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment. The AP Exam: All students enrolled in AP Calculus AB are expected to take the AP exam in May of 2012. Several weeks of class time prior to the AP will be spent preparing for the exam. Text: The text for this class is Calculus - Graphical, Numerical, Algebraic, by Finney, Demana, Waits, and Kennedy (1999). Recommended Supplies: You will need: 1) a separate composition or spiral notebook with graph paper for homework, 2) a binder for class notes and handouts, 3) a stash of #2 pencils (all exams MUST BE DONE IN PENCIL), and 4) a graphing calculator. Homework: Math is a participatory sport not a spectator sport, so applying what you learn in class is essential. Homework will be assigned daily. Each problem must be copied into your notebook and appropriate work must be shown in order to receive credit. Homework is due the next scheduled class after it is assigned and may be checked in class. All homework will be carefully evaluated and graded while assessments are given. If you are absent, you are responsible for making up any missed assignments within two days of your return to school. (If you are absent on the day of a scheduled test or quiz, be prepared to make it up during a free period or after school upon your return.) For extended absences please see me. Grading: Your grade each quarter will be determined according to the following: 75% Quizzes and Tests 25% Homework/Classwork/Projects/Activities Your final grade will be an average of your four quarterly grades and your midterm and finals grades. Grading Scale: A = 93.0 -100 C = 73.0 - 76.9 A- = 90.0 - 92.9 C- = 70.0 - 72.9 B+ = 87.0 - 89.9 D+ = 67.0 - 69.9 B = 83.0 - 86.9 D = 63.0 - 66.9 B- 80.0 - 82.9 D- = 60.0 - 62.9 C+ = 77.0 - 79.9 F = 59.9 and below Any unexcused absence during a scheduled quiz or test will result in a grade of "0%" NO EXCEPTIONS! Do not schedule any guidance appointments, projects or other "out-of-class" experiences during a scheduled quiz or test!! If you know that you are going to be out, please let me know in advance. Classroom Rules: All Personal audio devices such as cell phones, iPods/other MP3 players must be off and out of site. Please do not wear hats, hoods or sunglasses during class. No food or drink, except water, permitted in class (unless we are having a party!)

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.