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MATH 213: Foundations for Higher Mathematics
This course will serve as a bridge between introductory and advanced mathematics. The context of set theory and logic will be used to develop the skills of constructing and interpreting mathematical proofs. Topics include principles of logical argument, congruence modulo, induction, sets, functions, relations, equivalence relations, countability and uncountability of sets. Fall. Prerequisite: MATH 104 or MATH 110, or permission of instructor.... more »
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Calculus I (Math 207) can have a strong impact on
how one looks at many situations.To make calculus a valuable class, there is one constant reminder a
student needs to believe:"I
have the potential." In
other words, one must assure oneself of their ability to make a success out of
Calculus I.Success is not the
grade you receive but rather the understanding and applying of the acquired
knowledge to life.
To achieve this success, I will mention what I wish
I knew the first week of class.I
wish I knew that calculus does pertain to everyday life.It will help the student with problem
solving, analysis, thinking skills, and (needless to say) patience.Also, calculus can be related to things
one encounters everyday—frogs approaching the ends of diving boards,
volumes of tulip petals, airplane descent, food product structure, and
economics.In addition to everyday
experiences, this class will provide a challenge and require
self-discipline—so keep a good attitude.
Besides maintaining a good outlook on the class, one
might want to review some math fundamentals—trigonometry and
algebra.As a suggestion, one
might ask the professor for a past Math 151 exam in order to review key
pre-calculus concepts.One should
also practice graphing skills.In
a majority of calculus, the graph will help with the understanding of many
problems and test questions.
For me, I have found difficulty at times to
understand some concepts. Calculus may at times seem exotic and foreign; and
sometimes the professor's doctorate-understanding definition does not
seem clear to the student.However, there is a solution:write down the professor's definition, try some problems in the
homework, and even read the book.Then, once you understand the concept, write the definition in your own
words in your notes.This will
help a lot when one gets to the tests.
Understanding
is essential in a smooth transition to college mathematics, and even in
everyday college life. It is just as important to persist at calculus until one
understands the concepts as it is to understanding that your roommate might get
upset if one accidentally locks his or her roommate out when you leave not
remembering he or she if just down the hall.In a new experience, mistakes happen. But to improve, one
needs to remember certain things.However, in college mathematics one can no longer memorize
formulas.One must understand how
to use formulas. To attain this understanding I suggest practice, practice, and
more practice.So, when one
becomes discouraged, take a break.Don't give up mid way through the semester!You can always get help from tutors and
the professor.Tutors help
students to talk out the problem and find out where the error was.Asking the professor for help is a
great way to establish a one-on-one relationship with him or her.All the effort from homework and help
is sure to pay off in one's ability to understand calculus.
From what I have mentioned, calculus may seem
overwhelming.To aid in retaining
the great accumulation of calculus knowledge along with two to four other
classes, one should make a smooth transition into college life.One should eat and sleep well as well
as find ways to relieve stress and allow for some rewarding free time.All of these will help with one's
patience, motivation, and happiness—essentials in making college a
success!
Calculus I has offered me a challenge.I assure that myself and other Calculus
I students will use the acquired understanding in problem solving and
situational analysis; and one does learn some interesting things.After all, I have acquired the ability
to find the volume of a triple-scoop waffle cone.And if I don't understand the problem at first, I can
figure out the rate at which the waffle cone is decreasing!
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Although finding the limits of the difference quotients in the definitions of the derivative is troubling for many students, a difficulty that preceded this confusion was observed: students were not able to correctly set up the difference quotients as required in the definitions. The purpose of this study is to uncover student errors in setting up the difference quotients and to discuss what these errors reveal about students' thinking of functions, and evaluations of the difference quotients. At the end of the study, a framework that aggregates criteria used (by past studies and this study) to assign student membership into a function conception category will be produced in an attempt to move towards a systematic classification of students' cognitive processes. Implications from this study can inform teaching practices and curriculum development, by helping students connect difference quotient evaluation with function composition.
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This course examines an important and interesting part of the history of mathematics and, more generally, the intellectual history of human kind: the history of mathematics in the Islamic world. Some of the most fundamental notions in modern mathematics have their roots here, such as the modern number system, the fields of algebra and trigonometry, and the concept of algorithm, among others. In addition to studying specific contributions of medieval Muslim mathematicians in the areas of arithmetic, algebra, geometry, and trigonometry in some detail, we will examine the context in which Islamic science and mathematics arose, and the role of religion in this development. The rise of Islamic science and its interactions with other cultures (e.g., Greek, Indian, and Renaissance Europe) tell us much about larger issues in the humanities. Thus, this course has both a substantial mathematical component (60-65 percent) and a significant history and social science component (35-40%), bringing together three disciplines: mathematics, history, and religion. The course is a part of the Islamic Civilization and Cultures Program, and fulfills the QR requirement. No prerequisite is needed beyond high school algebra and geometry (but a solid knowledge in algebra and geometry is needed).
This course focuses on choosing, fitting, assessing, and using statistical models. Simple linear regression, mulitple regression, analysis of variance, general linear models, logistic regression, and discrete data analysis will provide the foundation for the course. Classical interference methods that rely on the normality of the error terms will be thoroughly discussed, and general approaches for dealing with data where such conditions are not met will be provided. For example, distribution-free techniques and computer-intensive methods, such as bootstrapping and permutation tests, will be presented. Students will use statistical software throughout the course to write and present statistical reports. The culminating project will be a complete data analysis report for a real problem chosen by the student. The MATH 106-206 sequence provides a thorough foundation for statistical work in economics, psychology, biology, political science, and many other fields. Prerequisite: MATH 106 or MATH 116. Offered every springThis course introduces students to mathematical reasoning and rigor in the context of set-theoretic questions. The course will cover basic logic and set theory, relations--including orderings, functions, and equivalence relations--and the fundamental aspects of cardinality. Emphasis will be placed on helping students in reading, writing, and understanding mathematical reasoning. Students will be actively engaged in creative work in mathematics. Students interested in majoring in mathematics should take this course no later than the spring semester of their sophomore year. Advanced first-year students interested in mathematics are encouraged to consider taking this course in their first year. (Please see a member of the mathematics faculty if you think you might want to do this.) Prerequisite: MATH 213 or permission of instructor. Offered every semester.
This course will focus on the study of vector spaces and linear functions between vector spaces. Ideas from linear algebra are highly useful in many areas of higher-level mathematics. Moreover, linear algebra has many applications to both the natural and social sciences, with examples arising often in fields such as computer science, physics, chemistry, biology, and economics. In this course, we will use a computer algebra system, such as Maple or Matlab, to investigate important concepts and applications. Topics to be covered include methods for solving linear systems of equations, subspaces, matrices, eigenvalues and eigenvectors, linear transformations, orthogonality, and diagonalization. Applications will be included throughout the course. Prerequisite: MATH 213. Offered every fall.
Looking at a problem in a creative way and seeking out different methods toward solving it are essential skills in mathematics and elsewhere. In this course, students will build their problem-solving intuition and skills by working on challenging and fun mathematical problems. Common problem-solving techniques in mathematics will be covered in each class meeting, followed by collaboration and group discussions, which will be the central part of the course. The course will culminate with the Putnam exam on the first Saturday in December. Interested students who have a conflict with that date should contact the instructor. Prerequisite: MATH 112 or equivalent.
This course will explore the theory, structure, applications, and interesting consequences when probability is introduced to mathematical objects. Some of the core topics will be random graphs, random walks and Markov processes, as well as randomness applied to sets, permutations, polynomials, functions, integer partitions, and codes. Previous study of all of these mathematical objects is not a prerequisite, as essential background will be covered during the course. In addition to studying the random structures themselves, a concurrent focus of the course will be the development of mathematical tools to analyze them, such as combinatorial concepts, indicator variables, generating functions, discrete distributions, laws of large numbers, asymptotic theory, and computer simulation. Prerequisite: MATH 112 or permission of the instructor. Offered every other year.
Patterns within the set of natural numbers have enticed mathematicians for well over two millennia, making number theory one of the oldest branches of mathematics. Rich with problems that are easy to state but fiendishly difficult to solve, the subject continues to fascinate professionals and amateurs alike. In this course, we will get a glimpse at both the old and the new. In the first two-thirds of the semester, we will study topics from classical number theory, focusing primarily on divisibility, congruences, arithmetic functions, sums of squares, and the distribution of primes. In the final weeks we will explore some of the current questions and applications of number theory. We will study the famous RSA cryptosystem, and students will be reading and presenting some current (carefully chosen) research papers. Prerequisite: MATH 222. Offered every other year.
Abstract algebra is the study of algebraic structures that describe common properties and patterns exhibited by seemingly disparate mathematical objects. The phrase "abstract algebra" refers to the fact that some of these structures are generalizations of the material from high school algebra relating to algebraic equations and their methods of solution. In Abstract Algebra I, we focus entirely on group theory. A group is an algebraic structure that allows one to describe symmetry in a rigorous way. The theory has many applications in physics and chemistry. Since mathematical objects exhibit pattern and symmetry as well, group theory is an essential tool for the mathematician. Furthermore, group theory is the starting point in defining many other more elaborate algebraic structures including rings, fields, and vector spaces. In this course, we will cover the basics of groups, including the classification of finitely generated abelian groups, factor groups, the three isomorphism theorems, and group actions. The course culminates in a study of Sylow theory. Throughout the semester there will be an emphasis on examples, many of them coming from calculus, linear algebra, discrete math, and elementary number theory. There will also be a couple of projects illustrating how a formal algebraic structure can empower one to tackle seemingly difficult questions about concrete objects (e.g., the Rubik's cube or the card game SET). Finally, there will be a heavy emphasis on the reading and writing of mathematical proofs. Prerequisite: MATH 222 or permission of the instructor. Junior standing is usually recommended. Offered every other fall.
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Secondary Mathematics Program Information
The Quebec Education Program at the secondary level is broken down into two Cycles:
Cycle One and Cycle Two. In addition, each Cycle is broken down into years. More specifically:
Secondary Cycle One, Year One
Secondary Cycle One, Year Two
Secondary Cycle Two, Year One
Secondary Cycle Two, Year Two
Secondary Cycle Two, Year Three
Secondary Cycle One is comprised of two years: Year One and Year Two. In Cycle
One, students complete the same mathematics program over the period of two years.
Secondary Cycle Two is comprised of three years: Year One, Year Two and Year Three.
In Secondary Cycle Two, Year One, students complete the same mathematics program over one year.
At the end of this year, they must select a mathematics option for the remainder of the Cycle
depending upon their personal interests, aspirations and skill set.
The three Mathematics Options for Cycle Two, Year Two and Three are:
Mathematics - Science Option
Mathematics - Technical and Scientific Option
Mathematics - Cultural, Social and Technical Option
A brief overview of the Mathematics Options for Cycle Two, Year Two and Year Three can be found
here.
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MATH E-3 Quantitative Reasoning: Practical Math
This course reviews basic arithmetical procedures and their use in everyday mathematics. It also includes an introduction to basic statistics covering such topics as the interpretation of numerical data, graph reading, hypothesis testing, and simple linear regression. No previous knowledge of these tools is assumed. Recommendations for calculators are made during the first class. Prerequisite: a willingness to (re)discover math and to use a calculator.
(4 credits)
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Systems of linear equations occur when using Kirchhoff's laws in Physics to solve for currents/resistances in electric circuits.
2. Matrix transformations are used extensively by computer graphics systems. For example OpenGL makes extensive use of vectors and matrices to render objects in 2D/3D.
3.
...I also have years of experience as a youth baseball coach. One component that I emphasize with students with whom I work is the necessity of proper study skills. Organization and productive practice habits play a large role in academic success.
...In addition, the questions require applying these topics in real world scenarios. I
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Each spring, seniors present their research at the "Symposium in Undergraduate Mathematics" to other math students from colleges throughout the state.
Many of Doane's math majors pursue advanced study in mathematics, education, engineering, statistics and other subjects.
Teacher Education
Now is truly an exciting time to get into mathematics education. Teachers of mathematics are in high demand nationwide. Mathematics education at Doane has long been recognized for its excellence. For more than 30 years, every mathematics education graduate seeking a teaching position has received job offers.
Math education graduates take 12 credits toward a master's degree the summer following graduation, adding extra value to their first year as a teacher.
Specialized laboratories and flexible classrooms allow for more in-depth interaction among faculty and students. With four full-time math professors, and two half-time professors specializing in different areas of math, students can participate in a wide variety of courses and expand their knowledge of the fieldAn introduction to understanding and constructingythe different types of mathematical proofs,yinductive and deductive reasoning, functions,ycardinality and the real number system.yPrerequisite: Mathematics 235. Offered springyterm.
An introduction to the theoretical foundations ofycalculus. Students successfully completing thisycourse will: 1) understand the development ofyelementary calculus tools, 2) be familiar with theyhistory, theorems and conjectures of traditionalymathematical analysis, and 3) communicateymathematically through a variety of proofytechniques. Prerequisite: MTH-236 and 250.yOffered alternate fall terms.
An introduction to research in a selected area ofymathematics, mathematics education, or anyapplication in mathematics. The course increasesythe students' abilities to communicate theiryexplorations in mathematics. Each student exploresypossible topics and develops a plan of action foryhis/her Mathematics Seminar II project. Theystudent also develops research, writing, andypresentation skills to carry out an independentyresearch project. Prerequisite: Junior or seniorymathematics major and 12 credits at the 300 levelyor above, or permission.
In consultation with a faculty member, the studentyexecutes the plan of action created in MathematicsySeminar I. The project culminates in a formalypaper and oral presentation demonstrating theystudent's ability to independently research aytopic and effectively communicate mathematics.yPrerequisite: Mathematics 496 or permission.yOffered every term.
An introduction to the science and art ofyimplementing solutions to problems using ayhigh-level programming language. Upon completionyof this course, the student will be able to designysolutions to a variety of problems using top-downyand structured design techniques and implementythose solutions using programming constructs suchyas branching, loops, arrays, and functions oryprocedures. Prerequisite: Mathematics 105 oryequivalent.
A study of geometric topics encountered in middleyschool and high school mathematics. Topics includeythe van Hiele theory, measurement, congruence andysimilarity, fractals, polyhedra, coordinateygeometry, transformational geometry, andyapplications. Students who successfully completeythis course will be able to teach the geometricytopics at all levels covered in public schools.yPrerequisite: Two years of high school algebra oryMathematics 105. Offered spring term.
The beginning of the transition from student ofymathematics to teacher of mathematics. Studentsysuccessfully completing this course will: 1)yunderstand philosophically the difference betweenyteacher and student of mathematics, and 2) beycapable of determining the difference betweenytraditional Euclidean geometry topics for junioryhigh/middle school and secondary students.yGenerally taken during the sophomore year.yOffered spring term.
An examination of options and topics appropriateyfor seventh, eighth, and ninth grade mathematicsycourses. Students successfully completing thisycourse will: 1) be able to determine topicsyappropriate for general mathematics courses at theyjunior high level, 2) be able to organize topicsyfor pre-algebra preparation, and 3) becomeyfamiliar with pedagogy for students of varyingyabilities. Generally taken during the junioryyear. Offered fall term.
An examination of algebra topics from beginning toyadvanced algebra. Students successfullyycompleting this course will: 1) understandyappropriate pedagogy for beginning algebraystudents, 2) be able to assess the background ofystudents entering their first full year ofyalgebra, and 3) determine how to integrateyalgebra into other mathematics courses. Generallyytaken during the junior year. Offered springyterm.
A selection of topics not covered in Mathematicsy323, 324, or 325. Various teaching approaches andymethods are examined. Changes that are continuallyyoccurring in mathematics education are discussedyand appropriate techniques for the teaching ofymathematics in the public schools are presented,yincluding teaching from a constructivist point ofyview, becoming familiar with the vanHiele levelsyof learning geometry, observing master teachers,yand utilizing and integrating technology. Many ofythe ideas are examined from the viewpoint of theyNational Council of Teachers of Mathematics.yPrerequisite: Mathematics 323, 324, and 325,yenrolled in professional term, or permission.yOffered fall term.
Survey of Euclidean geometry, study of selectedytopics in non-Euclidean and other geometries.yPrerequisite: Sophomore standing. Mathematics 236y(may be taken concurrently) and 250. Offeredyalternate spring terms.
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About the book
Description
"Free ebooks + free videos = better education" is the equation that describes this book's commitment to free and open education across the globe. Download the book and discover free video lessons on the Author's YouTube channel.
"Engineering Mathematics: YouTube Workbook" takes learning to a new level by combining free written lessons with free online video tutorials. Each section within the workbook is linked to a video lesson on YouTube where the author discusses and solves problems step-by-step.
The combination of written text with interactive video offers a high degree of learning flexibility by enabling the student to take control of the pace of their learning delivery. For example, key mathematical concepts can be reinforced or more deeply considered by rewinding or pausing the video. Due to these learning materials being freely available online, students can access them at a time and geographical location that suits their needs.
Author, Dr Chris Tisdell, is a mathematician at UNSW, Sydney and a YouTube Partner in Education. He is passionate about free educational resources. Chris' YouTube mathematics videos have enjoyed a truly global reach, being seen by learners in every country on earth.
Preface
How to use this workbook
This workbook is designed to be used in conjunction with the author's free online video tutorials. Inside this workbook each chapter is divided into learning modules (subsections), each having its own dedicated video tutorial.
View the online video via the hyperlink located at the top of the page of each learning module, with workbook and paper / tablet at the ready. Or click on the Engineering Mathematics YouTube Workbook playlist where all the videos for the workbook are located in chronological order:
The delivery method for each learning module in the workbook is as follows:
Briefly motivate the topic under consideration;
Carefully discuss a concrete example;
Mention how the ideas generalize;
Provide a few exercises (with answers) for the reader to try.
Incorporating YouTube as an educational tool means enhanced eLearning benefits, for example, the student can easily control the delivery of learning by pausing, rewinding (or fast-forwarding) the video as needed.
The subject material is based on the author's lectures to engineering students at UNSW, Sydney. The style is informal. It is anticipated that most readers will use this workbook as a revision tool and have their own set of problems to solve -- this is one reason why the number of exercises herein are limited.
Two semesters of calculus is an essential prerequisite for anyone using this workbook.
Content
How to use this workbook
About the author
Acknowledgments
Partial derivatives & applications
Partial derivatives & partial differential equations
Partial derivatives & chain rule
Taylor polynomial approximations: two variables
Error estimation
Differentiate under integral signs: Leibniz rule
Some max/min problems for multivariable functions
How to determine & classify critical points
More on determining & classifying critical points
The method of Lagrange multipliers
Another example on Lagrange multipliers
More on Lagrange multipliers: 2 constraints
A glimpse at vector calculus
Vector functions of one variable
The gradient field of a function
The divergence of a vector field
The curl of a vector field
Introduction to line integrals
More on line integrals
Fundamental theorem of line integrals
Flux in the plane + line integrals
Double integrals and applications
How to integrate over rectangles
Double integrals over general regions
How to reverse the order of integration
How to determine area of 2D shapes
Double integrals in polar co-ordinates
More on integration & polar co-ordinates
Calculation of the centroid
How to calculate the mass of thin plates
Ordinary differential equations
Separable differential equations
Linear, first-order differential equations
omogeneous, first-order ODEs
2nd-order linear ordinary differential equations
Nonhomogeneous differential equations
Variation of constants / parameters
Matrices and quadratic forms
Quadratic forms
Laplace transforms and applications
Introduction to the Laplace transform
Laplace transforms + the first shifting theorem
Laplace transforms + the 2nd shifting theorem
Laplace transforms + differential equations
Fourier series
Introduction to Fourier series
Odd + even functions + Fourier series
More on Fourier series
Applications of Fourier series to ODEs
PDEs & separation of variables
Deriving the heat equation
Heat equation & separation of variables
Heat equation & Fourier series
Wave equation and Fourier series
Bibliography
About the Author
Dr Chris Tisdell is a mathematician within The School of Mathematics &
Statistics at the University of New South Wales (UNSW) in Sydney, Australia.
Chris is interested in freely available learning materials, known as
Open Educational Resources (OER). He has experimented with producing
and sharing educational videos online through YouTube. Recognition of
the success of this initiative has resulted in YouTube making Chris a
"YouTube Partner in Education''. Chris has been an early Australian
contributor to the online educational hub "YouTube EDU''.
Before becoming a professional mathematician, Chris was a disc jockey (DJ) for over 10 years. He performed at night clubs and music festivals throughout Australia and overseas alongside famous acts including: Fatboy Slim; Tiesto; Ferry Corsten; Chicane; Timo Maas; Faithless; Nick Warren; and Dave Seaman. He also ran a small recordstore. Some students believe this entertainment background helps Chris 'mathematical lectures to be more engaging than most.
Chris is also an active researcher, with interests in differential
equations and their extensions. He has published over 70 research
papers, most of which have been written during his 10 years at UNSW,
Sydney. Chris has held visiting academic positions at: Imperial
College London (John Yu Fellow); The University Of Hong Kong (Cheung
Kong Fellow); and The University of Queensland (Ethel Raybould Fellow).
Reviews
Adam
★★★★☆
26 March 2013
very good when it comes to tackling technical problems
Mohamed Anas
★★★★★
11 March 2013
AWESOME, it covers the sufficient amount of subject areas than I expected. And yeah YOUTUBE VIDEOS, <<--- PURE AWESOME
Aidan O'Brien
★★★★★
26 September 2012
It was an amazingly useful textbook. I was doing Engineering Maths at the time and the way that Dr Tisdell explained the concepts was a breath of fresh air from the hour long lecture format. It was a great way to understand the concepts. Definitely passed the subject with a lot less effort because of this textbook than I would have otherwise.
Anthony
★★★★★
25 September 2012
Dr Tisdell's book is an amzaing step into bridging the gap between classroom and out of class learning. His book not only explains the concepts extremely well, but has many examples related directly to the work, which he steps through in the videos which accompany the book. His enthusiasm and great personality also really help students like myself connect with him, making the maths a lot more fun. The book could easily be sold for a fee, and if it was printed in real life, it would be more informative to students than half the textbooks out there on the market currently.
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Course: MATH 3321, Fall 2008 School: U. Houston Rating:
Word Count: 1003
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The CHAPTER Laplace Transform
4.1 Introduction
The Laplace transform provides an eective method of solving initial-value problems for linear dierential equations with constant coecients. However, the usefulness of Laplace transforms is by no means restricted to this class of problems. Some understanding of the basic theory is an essential part of the mathematical background of engineers, scientistsMath 1314 ONLINE OrientationWebsites: The course homepage: online.math.uh.edu When you get to this page, click on the word here near the top of the page. Then follow the link in the left column to Math 1314. Once you are on the Math 1314 page, yo
Math 1314 Integration by Substitution Sometimes the rules from the last lesson aren't enough. In this lesson, you will learn to integrate using substitution. This is related to the chain rule that you used in finding derivatives. Using Substitution t
Math 1330 Section 3.4 Exponential and Logarithmic Equations and Inequalities An exponential equation is an equation of the form a b cx - d = f . To solve an equation of this type: Isolate the exponential expression on one side of the equation. T
Math 1330 Section 2.2 Polynomial Functions Our objectives in working with polynomial functions will be, first, to gather information about the graph of the function and, second, to use that information to generate a reasonably good graph without plot
Math 1330 Section 8.2 Equations of Ellipses An ellipse is the set of all points in the plane so that for every point on the ellipse the sum of its distances from two fixed points is a constant. The fixed points are called the foci of the ellipse. The
Math 1330 Section 3.2 Logarithmic Functions Definition: For x > 0, logb x is the power to which b must be raised to get x, where b >0, b 1. We read this as "log base b of x."We typically write logb x = y and note that b y = x . The form logb x = y 8.1 Equations of Parabolas A parabola is the set of all points in the plane that are equidistant from a fixed line (called the directrix) and a fixed point not on the line (called the focus). The line that passes through the focus a 5.1 Trigonometric Functions of Real Numbers Previously, we considered trig functions of angles. Now, we'll look at trig functions of real numbers. In a circle of radius r, we can find the arc length s of an arc intercepted by a cent
Math 1330 Section 8.3 Hyperbolas A hyperbola is the set of all points in the plane so that for every point on the hyperbola, the difference of its distances from two fixed points is a positive constant. The fixed points are called the foci of the hyp
Math 1330 Section 3.3 Laws of Logarithms For b > 0 and b not equal to 1, the logarithmic function with base b, denoted by log b x, is y given by log b x = y if and only if b = x. Thus, log b x is the exponent in which the base b must be raised to giv
Math 1330 Section 5.2 Graphs of the Sine and Cosine Functions In this section, we will graph the basic sine function and the basic cosine function and then graph other sine and cosine functions using transformations. Much of what we will do in graphiMath 1330 Prerequisites Topic 8 Inverses You should be able to determine if a function is one-to-one given either the function or a graph of the function. Example 1: Determine whether the following graph represents a one-to-one function.Example 2: Prerequisites Topic 14 Logarithmic Functions You should be familiar with a variety of skills from college algebra having to do with logarithmic functions. Example 1: Write the following equation in logarithmic form. 25 = 32Example 2: Writ
Math 1330 Prerequisites Topic 14 Logarithmic Functions You should be familiar with a variety of skills from college algebra having to do with logarithmic functions. Example 1: Write the following equation in logarithmic form. 25 = 32Example 2: Writ
Math 1330 Section 2.4 Applications and Writing Functions We can use techniques from this chapter to solve problems. First, however, we have to write functions from a description of a situation. Here are some hints for writing functions. Read the
Preparation of Abstracts for CCA2008: Two Page Abstract FormatFirst A. Author and Second B. Authoraffiliaton (all on one line if possible)Third C. Authoraffiliation1 2 3 4 5 6 7 8 9Abstract-These instructions show by example how to prepare y
A U.S. Perspective on Challenges for Scale-up of High Performance Coated ConductorsKen Marken Superconductivity Technology Center Los Alamos National LaboratoryUNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSASlide 1What is
Preparation of Abstracts for CCA2008: Two Page Abstract FormatFirst A. Author and Second B. Authoraffiliaton (all on one line if possible)Third C. Authoraffiliation1Abstract-These instructions show by example how to pre2pare your two page ab
Critical Currents and AC Losses in Coated ConductorsTakanobu Kiss Dept of EESE, Kyushu University, Fukuoka 819-0395, JapanThis work was supported in part by the New Energy and Industrial Technology Development Organization (NEDO) as the Project for
Impact of coated conductor architecture on conductor stability and ac loss for power applicationsRobert Duckworth, Yifei Zhang, and Fred ListOak Ridge National Laboratory Abstract- Conductor stability and ac loss are two interrelated operational is
Impact of conductor architecture on conductor stability and ac loss for power applicationsRobert Duckworth December 6, 2008Managed by UT-Battelle for the Department of EnergyCCA08 International Workshop on Coated Conductors for Applications Ho
AC Loss, Thermal Diffusion and Quench Propagation in YBCO Coils Implications for UseLASM/OSU M.D.Sumption M. Majoros E.W. CollingsFunded by the AFOSR under FA9550-06C-0016 (quench/stability) as well as an AF SBIR programDepartment of Materials
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Mathematica Tutorials
Starting in the fall of 2009 the required technology in most mathematics courses at Thiel College became Mathematica.
These sets of tutorials is being developed for calculus and linear algebra. In the future, other lessons will be added for higher level
math courses and probably also for some chemistry and physics courses
For more information about Mathematica, where to find it at Thiel College
or how to get your own copy click here. Although Mathematica is available on public
computers here at Thiel, students will find it more convenient to have it on their own computers. This is especially true for
students majoring or minoring in mathematics or the sciences.
These lessons are in PDF format and require the Acrobat Reader which is
available free form Adobe.
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Advanced undergraduates and graduate students studying quantum mechanics will find this text a valuable guide to mathematical methods. Emphasizing the unity of a variety of different techniques, it is enduringly relevant to many physical systems outside the domain of quantum theory. Concise in its presentation, this text covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. Appendixes offer useful information on Bessel functions and Legendre functions and spherical harmonics. This introductory text's teachings offer a solid foundation to students beginning a serious study of quantum mechanics. Reprint of the W. A. Benjamin, New York, 1962$18
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HOMEWORK QUICK START
This book is straightforward and easy-to-read review of arithmetic skills. It includes topics that are intended to help prepare students to successfully learn algebra, including: * Working with fractions * Understanding the decimal system * Calculating percentages * Solving linear equalities * Graphing functions * Understanding word problems
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Abstract
We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of embodied cognition and use conceptual metaphors such as the path-source-goal schema and the idea of fictive motion. We find that students solving the problem correctly and efficiently do not use overt mathematical language like multiplication or division. Instead, their gestures and ambiguous speech of moving are the only algebra used at that moment
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GeoGebra
GeoGebra is dynamic mathematics software for education in secondary schools that joins geometry, algebra, and calculus. On the one hand, GeoGebra is a dynamic geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions, and offers commands like Root or Extremum. It is a free and open source software
License
Free
File Size
28.22 MB
Version
4.2.36
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Search MSRI
Program
Organizers
David Austin, Bill Casselman and Jim Fix
Description
This workshop will introduce sophisticated techniques of computer graphics for use to explain mathematics in research articles, course notes, and presentations. It will begin with an introduction to graphics algorithms, and the languages PostScript and Java. Participants will spend afternoons and evenings during the first week in the computer labs on assigned exercises. The second week will be spent on assigned project themes, ending with student presentations.
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Geometry is one of the most practical areas of Mathematics. Geometry is happening in the world all around us. Geometry includes the study of angles, triangles as well as the study of perimeter, area and volume. Knowlege of geometry is absolutely necessary for everyone. The actual word geometry means earth measure. Here you will find a variety of books that teach and extend knowledge of many of the geometric concepts.
1) A Course in Modern Geometries This comprehensive book by Judith Cederberg is directed toward senior mathematics majors who may be entertaining the notion of teaching Math at the secondary school level. Topics addressed include: Finite Geometries, Fractal Geometry, Transformations of the Eucledian Plane, the ASA Theorem etc.
2) A First Course in Differential Geometry
A very advanced book in Geometry written by Chuan-Chin Hsiung. This particular book is highly recommended by the American Mathematical Society (AMS) and is on their 'Best Selling Publlications' List.Includes chapters on Eucledian Spaces, Curves, and Local and Global Theory of Surfaces.
3) Short Course in Geometry
Prentice Hall is well known for their easy to understand mathematical texts. Patricia Juelg provides a self-paced approach for late high school students wanting a better grasp of advanced geometric concepts. Addresses the following concepts: : logic, sets and set notation, systems of measurement, geometric figures (two- and three-dimensional), geometric relationships, area and volume, congruent and similar triangles and geometric constructions.
4) Basic Geometry A comprehensive course in basic geometry skills and concepts. Topics include coordinate and solid geometry, deductive reason, and transformations. For the high school student who has completed elementary geometry..
5) Children Learning Geometry
Ideal for younger students 7-10 years of age.Children enjoy learning and gaining geometric knowledge and their relationships to the world. This book provides some practical insight to use with children in in everyday situations. This practical approach in Geometry helps children represent and describe in an orderly manner the world in which we live.
6) Algebraic Geometry
Algebraic geometry is the study of geometries that come from algebra. This text is an introduction to algebraic geometry that focuses on the roots of algebraic geometry. Provides many examples and is geared toward the finishing highschool student.
7) Challenging Problems In Geometry
For grade 11 and 12 students. Provides some challenging problems in congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and many other topics. Solutions have been provided. Great practice for the secondary student with an interest in mathematics.
8) Fundamental Concepts of Geometry
This text provides a clear and concise approach for the relationships between many types of geometry. A superb teaching text, and it provides a very clear overview of the foundations and historical evolution of geometrical concepts. The history of mathematics is a part of most high school curriculum.
9)Dictionary of Curious and Interesting Geometry
This dictionary is chalf full of fascinating theorems and terms and facts about geometry. This excellent reference includes a chronological list of Mathematicians and their contributions to Geometry. An excellent alphabetized index of every possible geometric theorem, term and mathematician.
10) The Roads to Geometry
For the high school student. Calculus is a prerequisite for following 'The Roads to Geometry'.This text (March 2001) clarifies, extends, and unifies concepts discussed in high school geometry courses. Gives learners a comprehensive introduction to plane geometry while providing a historical aspect.
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This is the 2nd semester of a two semester course (following Algebra 2A). Students will be working through a number of units along the way that will take them through a variety of Algebraic concepts. Some of the major concepts covered will include: solving and graphing equations and inequalities, systems of equations and matrices. Further, we will cover polynomials (a major focus), complex numbers, functions, rational and radical equations and expressions .
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Free Math Help
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Math Lessons - Looking to understand a subject better, or maybe you don't
understand what your textbook is trying to tell you? We have a collection of algebra
and geometry lessons that you can view online right now.
Ask your question on our math help message board. Just be sure to explain what
you've tried to do and where you're stuck, and a friendly volunteer may try to assist
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Algebra Lessons
Browse our collection of algebra lessons , or some video lessons provided by various
partners on the right. If you need more algebra help, try the seach menu at the top.
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Free Math Help Free Math Help Math Lessons - Looking to understand a subject better, or maybe you don't understand what your textbook is trying to tell you? We have a collection of algebra and geometry lessons that you can view online right now. Ask your question on our math help message board. Just be sure to explain what you've tried to do and where you're stuck, and a friendly volunteer may try to assist you! Algebra Lessons Browse our collection of algebra lessons , or some video lessons provided by various partners on the right. If you need more algebra help, try the seach menu at the top. Geometry Help If you need help with geometry you may be interested in viewing a geometry lesson KnowMoreAboutFindthedomainofacompositefunction
Tutorcircle.com PageNo.:1/4 from our website. Browse our collection of geometry lessons as well as those from other websites. Trigonometry Help:- Looking for trig help? Calculus Help Chain Rule,Derivative of an Inverse Function,Derivative of a Polynomial ,Derivatives of Log and Exponentials,Derivatives of Trig Functions,Differentiation,Differential Equations,Derivatives of Implicit Functions,Derivatives of Products and Quotients Fourier Series,Infinite Series Expansion,Integration,Integration By Parts,Newton's Method,Related Rates,Simpson's Rule,U-Substitution This site provides information about basic math, algebra, study skills, math anxiety and learning styles and specifically addresses the needs of the community college adult learner. A student who is frustrated by college math can be helped by identifying his individual learning style and recognizing the instructor's teaching style. This site provides links for students and teachers to information about learning styles, study skills tips, and ways to reduce math anxiety and gives the students access to tutorials, algebra assignments, math videos, and a forum for discussing with the professor a variety of math topics. Trigonometry Definition Math Sheet This trigonometry definition help sheet contains right triangle definitions for sine, cosine, tangent, cosecant, secant, and cotangent. It also contains the unit circle definitions for all trig functions. This sheet describes the range, domain and period for each of the trig functions. There is also a description of inverse trig function notation as well as domain and range. ReadMoreAboutPigeonHolePrincipleProof
Tutorcircle.com PageNo.:2/4 Trigonometry Laws and Identities Math Sheet This trigonometry laws and identities help sheet contains the law of cosines, law of sines, and law of tangents. It also contains the following identities: tangent identities, reciprocal identities, Pythagorean identities, periodic identities, even/odd identities, double angle identities, half angle identities, product to sum identities, sum to product identities, sum/difference identities, and cofunction identities. Calculus Derivatives and Limits Math Sheet This calculus derivatives and limits help sheet contains the definition of a derivative, mean value theorem, and the derivative's basic properties. There is a list of common derivative examples and chain rule examples. The following derivative rules are also described: product rule, quotient rule, power rule, chain rule, and L'Hopital's rule. This sheet also contains properties of limits as well as examples of limit evaluations at infinity. A limit evaluation method for factoring is also included. Calculus Integrals Math Sheet This calculus integral reference sheet contains the definition of an integral and the following methods for approximating definite integrals: left hand rectangle, right hand rectangle, midpoint rule, trapezoid rule, and Simpson's rule. There is a list of many common integrals. Also included in this reference sheet is nice table for trigonometric substation when using integrals. Integration by substitution is defined as well as the integration by parts.
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Mathematics
Welcome to the RPS Mathematics website. Teachers are invited to visit the "Elementary" or "High School" link to view information about our new mathematics curricula and classroom resources. We have added a "Parent" link to support parents of elementary students in accessing the content of the math curriculum.
General Mathematics Announcements: SCMA (Saskatchewan Common Math Assessments) are now available for every outcome from Kindergarten to Grade 9 (French and English). Teachers may access these assessments by going to Blackboard and logging in. Call the Ministry Sector Support Desk at 1-866-933-8333 or e-mail Networkservices@gov.sk.ca if you need help logging in. (March, 2013)
Kursweil
Information about students who are using Kurzweil: Pearson will give students free access to an electronic version of the Math Makes Sense textbook to use with Kurzweil if the student has their own print version of the textbook. See instructions for ordering this resource. (Revised March, 2012)
NEW for 2013: U of R Mathematics Problem Solving Sessions U of R Mathematics Problem Solving Workshop - First Session is Tuesday January 14.
The Department of Mathematics and Statistics will once again be hosting a series of problem solving sessions aimed at interested students in Grades 7-12. The sessions will be held every 2nd Monday evening, starting on January 14th, from 6-8 PM, in the Riddell Centre room RC 286.
The focus of these sessions is twofold. First and foremost, they are an opportunity for students with an interest in mathematics to meet each other and be exposed to a range of mathematical subjects that would not be covered in the standard high school curriculum. The sessions also contain a strong problem-solving component. Students will work through a variety of mathematical problems in order to better understand specific problem solving strategies and to work toward participation in mathematics competitions such as the University of Waterloo Mathematics Contests or the Saskatchewan Math Challenge.
As always, attendance is free. Each session is an independent unit, so students can come to as few or as many of them as you wish. If you are planning to come to any session, please send us an e-mail in advance so that we know how many copies of problem sets and other work material to bring.
Session dates for the Winter/Spring are January 14th, January 28th, February 11th, February 25th, March 11th, March 25th.
For more information, contact Patrick Maidorn at maidorn@math.uregina.ca or 585-4013.
2013 SUM Math Conference The Saskatchewan Mathematics Teacher's Society (SMTS) is hosting the SUM (Saskatchewan Understands Mathematics) conference, being held Friday May 3rd and Saturday May 4th 2013 at the University of Saskatchewan. This year, we are bringing in two of North America's most prominent voices in mathematics education, Dan Meyer and Marion Small.
Dan's work will demonstrate how teachers can reframe the curriculum they currently work with to make it more engaging for students.
Marian's work will encourage teachers to think deeply about questioning techniques and how they are differentiating instruction in the classroom.
Until February 15th, we are offering an early bird registration fee of $90. We would like to encourage your school division to take advantage of these rates. After February 15th registration is $125. In addition, any pre-service teachers who are student teaching or interning in your schools can register at any time at a cost of 2 for $90. These rates include lunch and an SMTS membership. To register please visit the SUM 2013 conference page or contact Michelle Naidu at michelle@smts.ca,
2013 Saskatchewan Math Challenge - Information for Students and Teachers
The Saskatchewan Math Challenge will be held in Regina this year, the date for the competition is Saturday March 2nd. This competition is aimed at students in Grades 7-10. Students will register in teams of 3-5 and spend the day at the University, competing in the challenge exams and engaging in other fun activities. This is a great opportunity to get out and meet with other students and teachers interested in mathematics from across the province.
Teachers will need to register their students. A chaperone is usually required to accompany the team on the day of the competition. Interested students and parents should talk to a teacher to assist with registration. Students and teachers are also encouraged to get in touch with us at our Problem Solving Sessions, as part of their focus is to prepare students for all manner of mathematics competitions.
For more information on registration and past competitions, visit
2013 University of Waterloo Competitions
Contest registration deadlines for Grades 7-12 are staggered from January to March. For information on the annual mathematics contests at the University of Waterloo, please visit
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A Consortium for creating mathematics programs in which students learn the knowledge, skills, principles, and applications they can use throughout life to become smarter employees, consumers, citizens, and learners; and to build a coalition of schools and colleges in Maricopa County, CA. Fifteen Modules are available or under construction: Data & Graphs; Geometry; Linear Behavior; Mistakes Cost Money; Ratios and the Juggling Proportion; Exponential Growth and Decay; Non-linear Functions; Representations of Data; Sets and Logic; Patterns; Right Triangle Trigonometry; Sampling; Synthesis; Systems. Issues of the C-Cubed Newsletter are on the Web.
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The intent of the high school mathematics program is to prepare all students to use mathematics and problem-solving skills in further education or on the job. The program focuses on mastering the objectives of the SOL, problem-solving, communicating mathematically, reasoning mathematically, applying mathematics to real-world situations, and using technology.
The FCPS High School Mathematics program includes courses from Algebra through Calculus. Each course is based upon a Program of Studies aligned with the Virginia Standards of Learning and Principles and Standards for School Mathematics from the National Council of Teachers of Mathematics, 2000. High Schools offer either the College Board Advanced Program or the International Baccalaureate Progam in mathematics and computer science.
Mission
The Math Department seeks to offer quality classes that academically enrich students seeking more than just the basic math requirements necessary for graduation. In addition to providing a variety of curriculum, the department will also meet the academic needs of the diverse student population.Vision
The Math Department is committed to achieving the following goals:
Create an atmosphere of educational excellence and a desire for individual student achievement.
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Theme of Conference:
This workshop will give an introduction to Painleve
equations and monodromy problems suitable for postgraduate students and
postdoctoral researchers. Topics to be covered include:
Speaker:
Philip Boalch (ENS Paris)
Title:
"Algebraic solutions of the Painleve equations" (2 lectures)
Speaker:
Thanasis Fokas (Cambridge)
Title:
TBA (on asymptotic analysis of the Painleve equations) (2 lectures)
Speaker:
Nalini Joshi (Sydney)
Title:
"Asymptotics of Painleve equations" (2 lectures)
Speaker:
Jon Keating (Bristol)
Title:
"Random matrices and Painleve equations" (2 lectures)
Speaker:
Marta Mazzocco (Manchester)
Title:
"Hamiltonian structure of the Painleve equations" (2 lectures)
Speaker:
Frank Nijhoff (Leeds)
Title:
"Discrete Painleve equations" (2 lectures)
Speaker:
Kazuo Okamoto (Tokyo)
Title:
"Introduction to the Painleve equations" (4 lectures)
Speaker:
Hiroshi Umemura (Nagoya)
Title:
"Differential Galois theory and the Painleve equations" (4 lectures)
Speaker:
Yousuke Ohyama (Osaka)
Title:
"Classical solutions on the Painleve equations: from PII to PV" (2 lectures)
PAINLEVE EQUATIONS AND MONODROMY PROBLEMS: RECENT DEVELOPMENTS
in association with the Newton Institute programme entitled "The Painleve
Equations and Monodromy Problems" (4-29 SEPTEMBER 2006) and is
an activity of the Marie Curie FP6 RTN ENIGMA (European Network In
Geometry, Mathematical Physics and Applications)
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In North America, the most prestigious competition in mathematics at the undergraduate level is the William Lowell Putnam Mathematical Competition. This volume is a handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the Putnam and other undergrad... read more
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The Green Book of Mathematical Problems by Kenneth Hardy, Kenneth S. Williams Popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. Includes questions drawn from geometry, group theory, linear algebra, and other fields.
100 Great Problems of Elementary Mathematics by Heinrich Dörrie Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, etc. Features squaring the circle, pi, similar problems. No advanced math is required. Includes 100 problems with proofs.
A Concept of Limits by Donald W. Hight An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 editionExperiments in Topology by Stephen Barr Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and witProduct Description:
In North America, the most prestigious competition in mathematics at the undergraduate level is the William Lowell Putnam Mathematical Competition. This volume is a handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the Putnam and other undergraduate mathematical competitions. Indeed, it will be of use to anyone engaged in the posing and solving of mathematical problems. Many of the problems in this book were suggested by ideas originating in a variety of sources, including Crux Mathematicorum, Mathematics Magazine, and the American Mathematical Monthly, as well as various mathematical competitions. This result is a rich selection of carefully chosen problems that will challenge and stimulate mathematical problem-solvers at varying degrees of proficiency
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Algebra 1 Help
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Document Description
Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) is the branch of
mathematics concerning the study of the rules of operations and relations, and the
constructions and concepts arising from them, including terms, polynomials, equations and
algebraic structures.
Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one
of the main branches of pure mathematics.
Elementary algebra, often part of the curriculum in secondary education, introduces the
concept of variables representing numbers. Statements based on these variables are
manipulated using the rules of operations that apply to numbers, such as addition. This can be
done for a variety of reasons, including equation solving.
Algebra is much broader than elementary algebra and studies what happens when different
rules of operations are used and when operations are devised for things other than numbers.
Addition and multiplication can be generalized and their precise definitions lead to structures
such as groups, rings and fields, studied in the area of mathematics called abstract algebra
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Algebra 1 Help Algebra 1 Help Algebra (from Arabic al-jebr meaning "reunion of broken parts"[1]) Elementary algebra, often part of the curriculum in secondary education, introduces the concept of variables representing numbers. Statements Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields, studied in the area of mathematics cal ed abstract algebra. Know More About Z score Table
Math.Tutorvista.com Page No. :- 1/5 The Below are the merit points of our online tutoring program: ---- Expert tutors ---- 24/7 live tutor available ---- Sharing whiteboard facility ---- Usage of VoIP ---- Free demo session Topics Covered in Algebra Given below are some of the main topics covered in our Algebra Tutorial: ---- Algebraic equations ---- Linear equations ---- Radicals ---- Factoring polynomials ---- Inequalities Learn More z score chart
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Math.Tutorvista.com Page No. :- 3/5 ---- Statistics ---- Probability ---- Trigonometry ---- Geometry Chose any topic and get all the required help with math. Understand the topic in detail, workout related problems and complete your homework along with an online tutor and make your learning complete. Online Math Tutoring Online Math tutoring has its own benefits. It lets you learn at your own pace and time. Al wil help you experience the benefits of our tutoring first hand. Get free help now! Read More About Standard Deviation Formula
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Introduction to the Finite Element Method Theory, Programming and Applications
9780471267539
ISBN:
0471267538
Pub Date: 2004 Publisher: Wiley & Sons, Incorporated, John
Summary: The right balance of theory, programming, and applications Erik Thompson presents the theory, applications, and programming skills you'll need to understand the finite element method and use it to solve problems in engineering analysis and design. Offering concise, highly practical coverage, this introductory text presents complete finite element codes that can be run on the student version of MATLAB or easily conver...ted to other languages. Master the basic theory: The text promotes an understanding and appreciation of the theoretical basis of finite element approximations by building on concepts that are intuitive. Throughout, the text uses matrix notation to help you visualize the finite element matrices. Study problems reinforce basic theory. Experiment with the code: Numerical experiments show how to test programs for possible errors, experiment with boundary conditions, and study accuracy and stability. Code development exercises suggest ways to modify the codes to create additional capabilities. All codes are available on the book's web page along with sample data files for testing them. Each code can be immediately run using only the student version of MATLAB. Because each code is written using explicit programming, they also serve as pseudo-codes that can be used to develop programs in any computer language. Gain hands-on experience: Projects, representing a wide variety of engineering disciplines, enable you to conduct analyses of fairly complex problems. Many of these projects encourage you to investigate new techniques for using the finite element method
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Intermediate Algebra
9780321233868
ISBN:
0321233867
Edition: 7 Pub Date: 2006 Publisher: Addison-Wesley
Summary: The goal of Intermediate Algebra: Concepts and Applications, 7e is to help today's students learn and retain mathematical concepts by preparing them for the transition from "skills-oriented" intermediate algebra courses to more "concept-oriented" college-level mathematics courses, as well as to make the transition from "skill" to "application." This edition continues to bring your students a best-selling text that in...corporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. This edition has an even stronger focus on vocabulary and conceptual understanding as well as making the mathematics more accessible to students. Among the features added are new Concept Reinforcement exercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter
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2. From this window you will
see the topics for the course, the first of which is the orientation to
the tutorial program.
3. Open the Orientation
topic and work through all the exercises until you feel comfortable using
the system. The exercises will teach you how to form the math symbols
you need to input your answers and so forth. Every topic has a fairly
useful Help screen if you need immediate help with math or detailed help
with using the program.
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The Row Operations Tutor helps you manipulate matrices with the three fundamental row operations: swap, scale and add. The arithmetic for row operations can be tedious and mistakes can be hard to catch, so use the tutor to check your work!
Features & Benefits
The Row Operations Tutor helps you manipulate matrices with the three fundamental row operations: swap, scale and add. The arithmetic for row operations can be tedious and mistakes can be hard to catch, so use the tutor to check your work.
Tutor completes row operations for you
Hints given for Gauss-Jordan method
Hints given for finding inverses
Gauss-Jordan Solver
Matrix inverse Solver
Mail solver's solutions
Exact answers are shown as fractions
Review row operations, with examples
Review Gauss-Jordan Method, with examples
Review matrix inverses, with examples
10 sample problem templates included
Enter your own problems
Enter data as fractions or decimals
Custom keyboard for easy data entry
Export matrices as HTML or CSV
Import problems into Simplex Tutor
Save matrices as pictures
Work problems with up to 14 rows and 14 columns
Not only does the tutor perform the arithmetic of row operations for you, but it will also give you hints when solving a system of linear equations with the Gauss-Jordan method or when finding the inverse of a matrix with row operations. When you are stuck on such a problem, and not sure how to proceed, you can request a hint guiding you to the solution. The more hints you ask for the more guidance you will receive. Eventually, when using the Gauss-Jordan method or when you are finding a matrix inverse with row operations, the tutor will tell you a correct row operation to use. If the problem is not solvable the tutor will tell you so. This way the techniques are continually reinforced and soon you will not need to ask for hints.
If you want more than hints, turn on the solver from the settings view. Now step by step solutions for Gauss-Jordan or matrix inverse problems will be given. Turn problems into fully worked examples with the Row Operations Tutor.
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LEARNING AND APPLYING GEOMETRY
Building a Teen Center: An Integrated Algebra Project by Mary Ann
Christina. A Key Curriculum Publication with blackline activity masters for
grades 6-10. This is a concept to completion project in which students work in
teams to conceive of, design, and build a model of a recreational center for
teenagers. 178 pages. Key-3102. $15.26-D. Click link for more details.
Geometry Grades 6-8. Milliken Publishing, no date. This book clearly
presents the
theorems and principles of basic geometry, along with examples and exercises for
practice. The concepts are explained in an easy-to-understand fashion to help
students grasp geometry and form a solid foundation for advanced learning in
mathematics. Each page introduces a new concept, along with a puzzle or riddle
which reveals a fun fact. Thought-provoking exercises encourage students to
enjoy working the pages while gaining valuable practice in geometry. Pages are
reproducible and the answers are in the middle. 44 pages. BTH-4748. $8.06-D
Geometry 7-10by Sara Freeman. Milliken, 2002. This easy-to-use
workbook is chock full of stimulating activities that will jumpstart student
interest in geometry while providing practice with the major geometry concepts.
A variety of puzzles, mazes, games, and self-check formats will challenge
students to think creatively as they sharpen their geometry skills. Each page
begins with a clear explanation of the featured geometry topic, providing extra
review and reinforcement. A special assessment section is included at the end of
the book to help students prepare for standardized tests. A great supplement for
grades 7-10. 48 pages. BTH-4747. $7.16-D
Geometry
for the Primary Grades,
a Steck-Vaughn reproducible book. Available for grades 1-3. This
supplement to any basic math curriculum models basic geometric concepts through
real-world and hands-on applications. The activities transition from concrete to
pictorial, and then to abstract. The books include manipulative activities,
self-explanatory lessons that are ideal for independent work (presuming students
have already received instruction in the specific skills covered in the
lessons), a bound-in answer key, letters for parents and students, a student
progress chart, an NCTM Standards Correlation chart, and 96 perforated
pages. Books are $10.79-D each.
Geometry the Easy Way, Third
Edition, by Lawrence Leff. This book is an ideal student self-help
supplement. It offers valuable overviews of course work and extra help with difficult
subject areas. Covers the "how" and "why" of geometry. Includes
hundreds of examples and exercises with solutions. Includes more than 700 drawings,
graphs, and tables. Paperback / Pages / 7-13/16" x 10-7/8" / Cat.# BAR-01102 /
$13.46-D
Table of Contents
Building a Geometry Vocabulary
Measure and Congruence
Angle Pairs and Perpendicular Lines
Parallel Lines
Angles of a Polygon
Proving Triangles are Congruent
Applying Congruent Triangles
Cumulative Review Exercises: Chapters 1-7
Geometric Inequalities
Special Quadrilaterals
Ratio, Proportion, and Similarity
The Right Triangle
Cumulative Review Exercises: Chapters 8-11
Circles and Angle Measurement
Chord, Tangent, and Secant Segments
Area and Volume
Coordinate Geometry
Locus and Constructions
Cumulative Review Exercises: Chapters 12-16
Some Geometric Formulas Worth Remembering
Glossary
Answers to Chapter Exercises
Solutions to Cumulative Review Exercises
Index
STUDIES
IN GEOMETRY SERIES: This series explores the topics of
Constructions, Triangles, Circles, and Proofs. Each of the books develops the
subject it covers through explanation, modeling, and practice. For Middle and
Secondary Grades. Consumable Each book is $9.89-D.
Mathematical Quilts--No Sewing Requiredby Diana Venters and E.K. Ellison. Published by Key Curriculum Press. For
grades 6-12. This book was born because two mathematics teachers who worked together also
took quilting classes together and began to see the quilt possibilities in many of the
mathematical concepts in texts and journals. They became convinced of the value of
designing quilts as a learning tool. The activities in this book help student improve
their visualization skills, as well as their skills in analysis, informal deduction, and
formal deduction - levels one -four of the van Hiele model of the five levels of learning
geometry. This book should be especially helpful to those students who have trouble with
formal geometry but are otherwise capable students because its activities take these
students through the first three levels of learning successfully so that they are able to
also be successful in the fourth level.
The book is divided into three sections,
each featuring quilts with similar designs: "Golden Ratio Quilts," "Spiral
Quilts," "Right Triangle Quilts", and the "Tiling Quilts." After
students are introduced to the theme, they encounter a series of activities that guide
them through the mathematical concepts related to that particular kind of quilt
design. Each section includes research activities, technology activities for graphing
calculators and computers, and Internet activities. In conclusion students recreate the
quilt pattern with an emphasis on the art of the design. Students can actually learn how
to sew the quilt if they are interested in doing it. 168 pages. More than 50
blackline activity masters
included. Punched to fit standard three-hole notebook. Cat #BTH-482. $18.86-D
More
Mathematical Quilts--No Sewing Requiredby Diana Venters and E.K. Ellison. Published by Key Curriculum
Press. For grades 6-12. The authors are both mathematics teachers and quilters.
They saw the possibilities of using quilts to reveal the beauty within
mathematics and present in this book 15 additional quilts (to those presented in
their first book, Mathematical Quilts). Their visual introduction
to mathematical objects allows students to explore mathematical art as they
learn skills essential to future success. The book is divided into four thematic
sections, each of which contains guides for recreating the quilts and activities
that further develop the related mathematical concepts. From fractals to
shadows of four-dimensional shapes, students have opportunities for hands-on
exploration of important mathematical objects and to practice solving problems.
181 pages. BTH-481. $18.86-D
Middle
School Geometry, by Steck-Vaughn: Each of the three books in this series has
four units: concepts, computation, problem solving, and enrichment. There are 42 activity
pages in each book. The books meet NCTM standards and are reproducible for classroom use.
The three books in the series are
Painless
Geometry by Lynette Long. Publisher:
Barron's Educational, 2001. 307 pages. If geometry tends to
freak you out, this book will help you understand it and even enjoy learning it.
You'll begin to see that finding solutions to geometric problems is as much fun
as solving intriguing puzzles. And there are lots of diagrams to help you learn
the terms, theorems, and postulates that form the foundation of geometry. You'll
learn to work with angles of all kinds, find the relationships between parallel
and perpendicular lines, and discover the characteristics of shapes such as
triangles, quadrilaterals, and circles. The abstract concepts you learn will
become more concrete with experiments you can do. And the author also gives tips
on studying and using mini-proofs as first steps to understanding formal
geometry proofs.
For grade 8 and up.
BTH-409. $8.06-D Click title link to order with
shopping cart.
Patty
Paper Geometry by Michael Serra. A Key Curriculum Press book. Learn
how to use the translucent squares of paper used by restaurants to separate hamburger
patties to enhance the study of geometry. You may already use paper folding for geometry.
. Maybe you tried waxed paper and found it hard to write on, or used other paper that you
couldn't see through. Now there's patty paper, the perfect paper for geometric
investigations. Manufactured in perfect squares, you can write on the paper and see
creases and traces when you fold them. It's a great way to explore geometry from a
hands-on, tactile approach. And best of all, it's probably the world's cheapest
manipulative. Pick it up where restaurant supplies are sold.
Patty Paper Geometry includes dozens of
activities that foster cooperative learning, increase students' geometric vocabulary, and
motivate kids to read, write, and talk about geometry. Constructions are performed more
accurately and geometric discoveries are made faster with patty papers. At the end of
their investigations, students have discovered most of the properties of geometric figures
studied in high school geometry courses. Here is a list of the investigations included:
Set 1: Intersecting Lines
Set 2: Folding the Basic Geometric Constructions
Set 3: Points of Intersection
Set 4: The Big Three Conjectures
Set 5: Midsegment Conjectures
Set 6: Properties of Parallelograms
Set 7: Properties of Circles
Set 8: Shortcuts to Congruent Triangles
Set 9: Transformations
Set 10: Symmetry and Tessellations
Set 11: Area
Set 12: The Theorem of Pythagoras
Patty Paper Geometry is designed as two books. The first,
a blackline master book, contains twelve chapters of guided and open investigations. Open
investigations encourage students to explore their own methods of discovery, and guided
investigations provide more direction to students, or can be used as a teacher's guide.
Each chapter includes many spiraled exercise sets, providing constant review. A separate
student workbook is also available, containing all of the open investigations as well as
some exercise sets. Use Patty Paper Geometryas a supplement to
your geometry program or even as a major course of study.
This series presents the basic facts of the subjects
covered in each book. There is an assessment test at the beginning of each book. This
helps you determine what your student needs to learn. Then there is instruction (about
one-half page per lesson on the average) in a basic concept or skill. This is followed by
exercises which allow the student to practice the skill taught. At the end of the book is
a final test to see if the students have mastered the skills. These books are
reproducible.
BTH- 046. $9.86-D
If your students aren't quite ready for the full geometry
course yet, maybe you should start them with Pre-Geometry 1
(BTH-064)and Pre-Geometry
2 (BTH-065)from this same series. These help students progress from basic mathematics
to geometry and provide the mathematical skills to succeed in geometry groupings.
Abstractions and structured logic are kept to a minimum. Each pre-geometry topic includes
an explanation and multiple exercises to reinforce the explanation presented. These
books are 3.56 each.
Unfolding Mathematics with Unit Origamiby Betty Franco. Key Curriculum Press. Black Line Activity Masters, punched
to fit standard three-hole notebook. This book, with its elegant illustrations and
detailed folding and assembly directions, will show you and your students how to create
intriguing three-dimensional models. the sixteen activities, in blackline master form,
first present simple folding techniques that transform square pieces of paper into a
variety of geometric shapes. As students repeat the folding sequences, they create
identical units that combine to form tetrahedra, cubes, octahedra, and much more. After
they learn the basics, students can go on to invent their own unique polyhedra. These
activities can to used in middle and high school algebra and geometry classes. Most can be
finished in one class period. 115 pages.
Cat # BTH-1420. $17.06-D
Unfolding Mathematics with Origami Boxes
by Arnold Tubis and Crystal Mills, 2006. This book combines the ancient art of paper folding with high
school mathematics to help students discover important concepts in geometry.
Detailed folding instructions help students fold 28 unique boxes ranging from
simple, open designs to self-contained decorative models. Blackline masters and
a teacher-friendly design make the activities easy to implement. 180 pages.
BTH-4980. Click link for current price and availability. If out of stock, I can
order for you.
What's Wrong with
This Picture? Critical Thinking Exercises in Geometry by Michael Serra,
Key Curriculum Press. Blackline masters. For grades 8-10. This book takes
advantage of student's enthusiasm for finding errors in handouts and books to
exercise their basic geometry skills and visual thinking. it contains 72 pages
that are perfect as warm-up exercises, homework, or group activities. Each page
has up to four problems, of which at least one is worked correctly and at least
one contains an error, optical illusion, or conflicting information; students
reason out the problems to find the incorrect one. BTH-1407. $16.16-D
Zome Geometry: Hands-on Learning with Zome Models by George W. Hart and Henri Picciotto, 2001. This book uses more
than 60 easy-to-follow activities and over 150 explorations to help students
build spatial, conceptual, visualization, and geometric skills. They will
explore a wide variety of geometry topics, including proportion, symmetry, area,
volume, and coordinates. They will learn to prove there are only five Platonic
solids and to analyze the thirteen Archimedean solids. They will also discover
Euler's theorem and verify Descartes' theorem of angular deficit. They will
have an opportunity to investigate space filling, duality, fractals, and the
fourth dimension. Included is an eight-page color insert of full color images of
various constructions. 265 pages. Answers and index are found at the back. Can
be used with middle school students, but is intended for high school. BTH-4981.
Follow link to check availability and current price. If I'm out of stock, I can
order this for you.
|
Texas Instruments TI Nspire CAS Computer Software
Please Note: Pricing and availability are subject to change without notice.
TI-Nspire CAS Computer Software
Features Summary
TI-Nspire CAS Computer Software for Math and Science is the computer software component for students with the same functionalities of the TI-Nspire CAS handheld. Thanks to TI-Nspire CAS Computer Software, seamless creation and transitions of classroom materials is possible:
Teachers should try TI-Nspire CAS Computer Software - Teacher Edition with a handheld emulator and enhanced document editing to create materials for students using handhelds.
Students can easily transition their work between the handheld device and computer and share it with teachers for assessment.
TI-Nspire™ CAS Student Software
Features Summary
TOOLS FOR SCHOOL AND HOME
TI-Nspire CAS Student Software for homework. The TI-Nspire CAS or new full-color TI-Nspire CX CAS graphing calculator for class assignments. Identical handheld-software functionality. Take what you've started in class on the handheld and finish on your home PC or Mac® computer.
Classroom-to-Homework Mobility
Transfer class assignments from handheld to personal/home computer. Complete your work outside of school, at home, on the bus, in the library.
Interactive Learning
Calculate, graph, write notes, build spreadsheets and collect data, all with one software. View multiple representations of a concept on a single screen.
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The only series based on the latest research about how students
learn and engage Mathematics
Pearson Mathematics is based on the latest
pedagogical research on how students learn best. We've
researched:
What makes a good maths question?
Pearson Mathematics is based on the latest pedagogical research
on how students learn best. Centred on research by Peter Sullivan,
the lead writer of the Australian Mathematics Curriculum on 'What
makes a good Mathematics question?', Pearson Mathematics features
carefully selected grading, combined with thoughtful open-ended
questioning.
Game-based Learning
More than thirty 'Outside the Square' and 'Mathspace' games have
been specifically written for each student book. These are based on
The Horizon Report 2011 research, which annually introduces six
emerging technologies or practices in education.
The 5e Instructional Model for Inquiry
Learning
All investigations throughout the series are structured to the
e5 model to ensure a thorough inquiry-based approach throughout the
series.
Working Memory and the Acquisition of Higher Order
Skills in Mathematics
Fluency questions in every exercise have been rigorously graded
into columns with small, incremental steps.
The Shallow Teaching Syndrome in Australian Mathematics
Classrooms
Every exercise has been graded, with the sub-headings Fluency,
Understanding, Reasoning and Open-ended - which consistently
develops students' understanding beyond the basics of maths to
higher complexity problems.
Pearson Reader 2.0 - Collaborate, Assess, Learn
Pearson Reader 2.0 has been upgraded, with
a new context for content. You will benefit from an enhanced
interface for all student book content and embedded, tracked
assessment!
Giving you interactive access to questions from the activity
books, designed specifically to improve student outcomes in the
context of chapter and unit content.
Pearson Assess - Better results in every class
Pearson Assess allows you to quickly build
tests on any topics within Pearson
Mathematics for the Australian Curriculum. Teachers
can assign tests, and students
can create tests for their own revision,
on any device. All tests auto-correct and collect results
for teachers to review student progress across the year.
Product features:
Access on any device - PC/Mac, Android
tablet, iPad.
Select from a huge range of test
questions separated for students and teachers, so
students can revise and teachers can assign tests with the
assurance that questions will be different.
Vary the number of questions in a topic
test and change the time allowed.
Pearson eBook 3.0 - Any device, every school
Pearson eBook 3.0 takes your student book
online or offline for any
device, while retaining the integrity of the printed page.
With access to linked interactive activities when they're online,
your students will be engaged at school and at home.
Product features:
Available online or offline on any device -
PC/Mac, Android tablet, iPad and smartphone
Faithful to the layout of the student book, so
you can reference the printed page and direct students straight to
content
Links to student activities, such as quizzes,
drag-and-drop activities, crosswords and more
Links to teacher resources for every chapter,
such as worksheets, quizzes and more.
A unique solution for the mixed ability classroom.
The 'Navigator' feature at the start of each exercise offers
three customised pathways for foundation, standard and advanced
learners, and differentiated assessment is available online with
Pearson Reader.
Differentiated assessment is available online
with Pearson Reader.
Pearson Mathematics is the only series with a
bridging workbook, a write-in workbook which
'bridges the gap' between primary and secondary
Mathematics, and supports struggling learners with a pathway into
the Year 7 student book.
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Complex Analysis for Mathematics, Science, and Engineering
This book provides a comprehensive introduction to complex variable theory and its applications. The Second Edition features a revised and updated ...Show synopsisThis book provides a comprehensive introduction to complex variable theory and its applications. The Second Edition features a revised and updated presentation that reflects the latest theories and their applications to current engineering problems
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The seventh edition of this classic text has retained the features that make it popular, while updating its treatment and inclusion of Computer Algebra Systems and Programming Languages. Interesting and timely applications motivate and enhance readers' understanding of methods and analysis of results. This text incorporates a balance of theory with techniques and applications, including optional theory-based sections in each chapter. The exercise sets include additional challenging problems and projects which show practical applications of the material. Also, sections which discuss the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitate the integration of technology in the course. Furthermore, the text incorporates programming material in both FORTRAN and C. The breadth of topics, such as partial differential equations, systems of nonlinear equations, and matrix algebra, provide comprehensive and flexible coverage of all aspects of numerical analysis.
This is a thoroughly revised edition of a classic basic statistics text, ideal for students with a good mathematics background who are starting to learn statistics. This fourth edition includes a chapter on multiple regression, has additional material on acceptance sampling, and places greater emphasis on graphical methods of data analysis. Like earlier editions, it is packed with examples, exercises, and larger projects, including plenty of computing exercises in Minitab. [via]
S-PLUS is a powerful tool for interactive data analysis, creating graphs, and implementing customized routines. Originating as the S language of AT&T Bell Laboratories, its modern language and flexibility make it appealing to data analysts from many scientific fields. This book explains the basics of S-PLUS in a clear style at a level suitable for people with little computing or statistical knowledge. Unlike the S-PLUS manuals, it is not comprehensive, but instead introduces the most important ideas of S-PLUS through the use of many examples. Each chapter also includes a collection of exercises which are accompanied by fully worked-out solutions and detailed comments. The volume is rounded off with practical hints on how efficient work can be performed in S-PLUS. The book is well-suited for self-study and as a textbook. [via]
Nicholas Lemann's The Big Test starts off as a look at how the SAT became an integral part of the college application process by telling the stories of men like Henry Chauncey and James Bryant Conant of Harvard University, who sought in the 1930s and '40s to expand their student base beyond the offspring of Brahmin alumni. When they went into the public schools of the Midwest to recruit, standardized testing gave them the means to select which lucky students would be deemed most suitable for an Ivy League education. But about a third of the way through the book, Lemann shifts gears and writes about several college students from the late '60s and early '70s. The reasons for the change-up only become clear in the final third, when those same college students, now in their 40s, lead the fight against California's Proposition 209, a 1996 ballot initiative aimed at eliminating affirmative action programs.
Do these two stories really belong together? For all his storytelling abilities--and they are prodigious--Lemann is not entirely persuasive on this point, especially when he identifies the crucial moment in the civil rights era when "affirmative action evolved as a low-cost patch solution to the enormous problem of improving the lot of American Negroes, who had an ongoing, long-standing tradition of deeply inferior education; at the same time American society was changing so as to make educational performance the basis for individual advancement." Lemann's muddled transition is somewhat obscured by frequent digressions (every new character gets a lengthy background introduction), but a crucial point gets lost in the shuffle, only to reappear fleetingly at the conclusion: "The right fight to be in was the fight to make sure that everybody got a good education," Lemann writes, not to continue to prop up a system that creates one set of standards for privileged students and another set for the less privileged. If The Big Test had focused on that issue, where equal opportunity is genuinely at stake, instead of on the roots of standardized testing, where opportunity was explicitly intended only for a chosen few, it would be a substantially different book--one with a story that almost assuredly could be told as engrossingly as the story Lemann chose to tell, but perhaps with a sharper focus. --Ron Hogan[via]
More editions of The Big Test: The Secret History of the American Meritocracy:
George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs. [via]
The Princeton Review realizes that scoring high on the AP Statistics Exam is very different from earning straight As in school. We dont try to teach you everything there is to know about statisticsonly the strategies and information youll need to get your highest score. In Cracking the AP Statistics Exam, well teach you how to
·Use our preparation strategies and test-taking techniques to raise your score ·Focus on the topics most likely to appear on the test ·Test your knowledge with review questions for each statistics topic covered
This book includes 2 full-length practice AP Statistics tests. All of our practice questions are just like those youll see on the actual exam, and we explain how to answer every question. [via]The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study. [via]
Econometrics has moved from a specialized mathematical description of economics to an applied interpretation based on empirical research techniques - and the modern approach of this innovative book is proof. Introductory Econometrics bridges the gap between the mechanics of econometrics and modern applications of econometrics by employing a systematic approach motivated by the major problems currently facing applied researchers. Offering a solid foundation for social science research, the book provides important knowledge used for empirical work and carrying out research projects in a variety of fields. [via]
The Jackknife and bootstrap are the most popular data-resampling methods used in statistical analysis. This book provides a systematic introduction to the theory of the jackknife, bootstrap and other resampling methods that have been developed in the last twenty years. It aims to provide a guide to using these methods which will enable applied statisticians to feel comfortable in applying them to data in their own research. The authors have included examples of applying these methods in various applications in both the independent and identically distributed (iid) case and in more complicated cases with non-iid data sets. Readers are assumed to have a reasonable knowledge of mathematical statistics and so this will be made suitable reading for graduate students, researchers and practitioners seeking a wide-ranging survey of this important area of statistical theory and application. [via]
The development of statistical theory in the past fifty years is faithfully reflected in the history of the late Sir Maurice Kendalls volumes The Advanced Theory of Statistics. The Advanced Theory began life as a two volume work (Volume 1, 1943; Volume 2, 1946) and grew steadily, as a single authored work until the late fifties. At that point Alan Stuart became involved and the Advanced Theory was rewritten in three volumes. When Keith Ord joined in the early eighties, Volume 3 became the largest and plans were developed to expand it into a series of monographs called the Kendall's Library of Statistics which would devote a book to each of the modern developments in statistics. This series is well on the way with 5 titles in print and a further 7 on the way. A new volume on Bayesian Inference was also commissioned from Tony O'Hagan and published in 1994 as Volume 2B of the Advanced Theory. This Volume 2A is therefore the completely updated Volume 2 - Classical Inference and Relationship. A new author, Steven Arnold, was invited to join Keith Ord and they have between them produced a work of the highest quality. References have been updated and material revised throughout. A new chapter on the linear model and least squares estimation has been added. [via]
More editions of Kendall's Advanced Theory of Statistics: Classical Inference and and the Linear Model:
Emory University, Atlanta, Georgia. Statistics in the Health Sciences Series. Programmed text on this particular mathematical model for students in epidemiology, or for practitioners unfamiliar with statistical methods. [via][via]
What mathematics should be learned by today's young people, as well as tomorrow's workforce? "On the Shoulders of Giants" [via]
More editions of On the Shoulders of Giants: New Approaches to Numeracy:Here is a unified, readable introduction to multipredictor regression methods in biostatistics, including linear models for continuous outcomes, logistic models for binary outcomes, the Cox model for right-censored survival times, and generalized linear models for counts and other outcomes. The authors describe shared elements in methods for selecting, estimating, checking, and interpreting each model, and show that these regression methods deal with confounding, mediation, and interaction of causal effects in essentially the same wayThis book introduces you to the study of statistics and data analysis by using real data and attention-grabbing examples. The authors guide you through an intuition-based learning process that stresses interpretation and communication of statistical information. They help you grasp concepts and cement your comprehension by using simple notation-frequently substituting words for symbols. [via]
This book is written for the introductory statistics course and students majoring in any field. It is written in an approachable, informal style that invites students to think about how to reason when data is available. Stats: Data and Models (SDM), as compared to Intro Stats, offers Math Boxes, which present the mathematical underpinnings of the statistical methods and concepts, and advanced topics (Ch. 28-31) that are often covered in a two-semester course, plus the inclusion of non-parametrics. SDM carries a core focus on statistical thinking and understanding analyses throughout the text, emphasizing how statistics helps us to understand the world. The book also recognizes the central role that technology plays in statistics. SDM is organized into short teachable chapters that focus on one topic at a time, offering instructors flexibility in selecting topics while students receive digestible chunks of information that build on previous material before moving on. [via]
Designed for medical students, junior doctors, practising physicians, and indeed anyone who reads medical literature, this book acts as a guide to how to read and digest the information presented in medical literature. [via]
More editions of Studying a Study and Testing a Test: How to Read the Health Science Literature:
Twentieth-Century British Political Facts is the definitive record of the who, the what and the when of British political history in the 1900s, providing reliable information which could not otherwise be found without many hours of digging in a library. Refined and updated since the seventh edition, this unique work has become as standard reference book for scholars, journalists, politicians, civil servants, students and all readers with an interest in political history.
Scientists have recently discovered a new law of nature. Its footprints are virtually everywhere - in the spread of forest fires, mass extinctions, traffic jams, earthquakes, stock-market fluctuations, the rise and fall of nations, and even trends in fashion, music and art. Wherever we look, the world is modelled on a simple template: like a steep pile of sand, it is poised on the brink of instability, with avalanches - in events, ideas or whatever - following a universal pattern of change. This remarkable discovery heralds what Mark Buchanan calls the new science of 'ubiquity', a science whose secret lies in the stuff of the everyday world. Combining literary flair with scientific rigour, this enthralling book documents the coming revolution by telling the story of the researchers' exploration of the law, their ingenious work and unexpected insights. Mark Buchanan reveals how the principle of ubiquity will help us to manage, control and predict the future. More controversially, he claims that it may well contain the beginnings of a mathematics of cultural and historical change. Every decade sees a major scientific breakthrough that has implications that go way beyond science. 'Ubiquity' is one of them. This book, the world's first on the topic, will change how we think about the world and our place in it. Chaos Disorder from order. Complexity Complexity from simplicity. UBIQUITY World has a natural 'rhythm': there is a mysterious archetypal organisation that works in the world at all levels and which gives rise to a universal pattern of change - in groups of people, things or ideas. [via]
More editions of Ubiquity: The Science of History . . . or Why the World Is Simpler Than We Think:
Readers of medical literature are often overwhelmed by the language of statistics and research methodology while trying to extract the best clinical evidence available. 'A-Z of Medical Statistics' is an essential medical statistics dictionary for non-statisticians, and is therefore an invaluable companion for reading medical literature and critically appraising what is read.Statistics and research methods explained in the book's user-friendly A - Z format allow the reader to locate the information required and avoid the time-consuming process of scanning through whole chapters for relevant information. The book provides clear and succinct explanations of those terms frequently encountered in medical statistics, clarifying their meaning and showing the inter-dependency between various important concepts. [via]
More editions of A-z of Medical Statistics: A Companion for Critical Appraisal:
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Teachers and Tutors: Ends and values below
and site lessons and
lesson ideas will help you provide your students with a stronger
base for calculus and for earlier high school mathematics. Explore this
site for lesson ideas if you were press-ganged into mathematics instruction or
if you would like ideas and methods for easing and avoiding common fears
and difficulties.
Welcome. Online books and further webpages on learning and
teaching mathematics and pattern based reason may develop critical
thinking, improve reading and writing, and provide a base for learning
or teaching college and high school mathematics. Site
books are online in full with prequels and postscripts.
Kind reviews implies some site
chapters and lessons may entertain and inform.
More starting point suggestions - not bad - for site exploration
Test or improve reading, writing critical thinking and problem
solving skills with the leading
logic chapters in Volume 2. Logic mastery may ease or avoid
learning difficulties, and so make further studies easier - just add
effort. lotsa of it.
Improve the quality of written work in mathematics with this
formula evaluation format. It and its vertical alignment of equal
signs shows how to do and record evaluation steps, so that they can
be seen and checked. The format here can and should also be used with
arithmetic expressions, step by step. The format here for "showing
work" makes the domino effects of care and mistakes easier to
see.
Why do we study slopes, factored polynomials and the max-min analysis
of functions in high school? Answer are given by this light calculus
preview and then online chapters 2 to 7 in
Volume 3, Why Slopes and More Math.
Check basic arithmetic skills with the
exercises in Chapter 7 of Volume 2, Three Skills for Algebra.
These exercises with hints of algebra are for students in senior high
school mathematics, or the first days of calculus. Answers are
provided. Success in mathematics requires respect for how later
skills and concepts depend on earlier ones.
If one site element is not to your liking, try another. Each one is
different. Study what you need now for the next test or final
examination, good luck. Then explore more site material, as much as you
can swallow or digest, before your next mathematics course begins. Site
books and sections include many more lessons in arithmetic, algebra,
geometry, calculus and real analysis.
The essay Mathematics ... which way to go,
how and why below introduces site aims and content. Site material is not
perfect - parts need to be rewritten. But site content in the essay
below and in site lessons or lesson ideas give possible remedies, remedies
which need to be tried, tested and even improved, for many problems facing instruction
aimed at student mastery of ideas and methods, those of service to
daily and adult life and/or college studies. Site lessons and lesson
ideas in giving or describing how to teach logic and mathematics directly
provides a standard to meet or exceed in direct and indirect
course design and delivery.
"Would you tell me, please, which way I ought to go from
here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long
enough." (Alice's Adventures in Wonderland, Chapter 6)
--
Different ends and values for instruction leads to disagreement on what
should be met, how and why. No position on mathematics education will
please all. The site position is based on a technical view of how later
concepts and skills depend on earlier ones, and in particular on what
mastery of calculus requires from earlier studies at the high school and
even primary school level. However, preparation for calculus should not
be the only aim for earlier schooling. For more context and motivation
and for less student alienation, ideas and methods with take-home value
clear to students and their parents may provide another focus, a maximal
one, for early instruction. Clear ends and values may focus and motivate
mathematics education and in the process lead to fewer topics. Then skill
and concept development may proceed with quality first and quantity
second.
Site Origins & Limitations
Writing began offline in the last few days of 1990 to address two
mathematics education obstacles:
First, common fears and difficulties may be explained by
concept and skill development steps to big for most, not all.
Second, student alienation from mathematics mastery may be
explained by those fears and difficulties, combined with an
absence of reasons or context for mastery of concepts and
skills, one at a time, one after another.
Since 1990 or so in Canada, the UK and the USA, many teacher
education programs advocate pychological theories of learning in
which instruction aimed at student mastery of given ideas and
methods is regarded as substandard and unreliable end for
instruction. Unreliability may be reduced by addressing the two
obstacles just mentioned. However in practice for decades before
and after 1990, educational authorities have set final
examinations which hope for mastery of ideas and methods in
mathematics and other disciplines in a repeatable and
reproducible manner. If the conflict seen here between
educational theory and practice leads to course design and
delivery with little or no respect for how later ideas and
methods depend on earlier ones, then we have a third obstacle to
student mastery of higher level ideas and methods in mathematics.
While holding student back a grade or two will harm their
self-esteem, the continual promotion of students in schools
without respect for how mastery of later ideas and methods stands
on mastery of earlier ones will eventually undermine and destroy
student skills and confidence. Site material in providing lessons
and lesson ideas, and in offering ends and values below may,
albeit not all certain, ease the foregoing problems in logic and
mathematics education.
The composition of ideas and methods, offline in 1990 and online
since summer 1995, was and remains an iterative affair. It was
guided by inductive
principles for instruction aimed at student mastery of given
skills and concepts. met in 1981 outside of mathematics.
Every master of mathematics knows how mathematical induction
may fail, and by analogy how such instruction may fail. In
particular, Common fears and difficulties may be explained by
steps missed and by steps too big, not for all, but for most.
Remedies may follow from smaller or alternative steps to make
mastery of key skills and concepts easier and quicker. Site
technical and wordy remedies for common fears and difficulties
will fail when and where students and schools do not respect
how later skills and concepts depend on earlier ones.
The student or school wanting algebra be taught well without a
previous mastery of exact arithmetic with decimals, fractions
and signs is setting the stage for a mastery of algebra too
weak for strong courses in mathematics at the college and
senior high school level. Skill and concept development to
succeed has to respect how later ideas and methods stand on
earlier ones.
While no amateur nor professional has the right to impose a
mathematics education program on students, parents and
educational authorities, today any one may propose one online.
The reforms or remedies here like those elsewhere need to be
tried and tested before general use. Incomplete ideas for reform
rushed into service may disrupt education more than it helps.
Principles for instruction no matter how good need to be fully
supported by lessons and lesson plans likely to work in a
repeatable and reproducible manner for more.
By fall 2011, site lessons and lessons ideas for addressing
content, that is concept and skill, mastery difficulties were
essentially online in full but in some need of editing and
pruning. Between spring 2012 and 2013, the issue of why and what
to learn or teach in logic and mathematics was addressed first in
a first phase program for mathematics and logic instruction, and
then in the ends and values outlined below. Here again, there is
some work to be done in identifying and presenting skills and
concepts with take-home value for daily or adult life in ways
that may also serve further instruction. While the site author
has a doctorate in mathematics with ten plus years of experience
in instruction, the composition of site material in the last two
decades has been generally without further classroom experience.
So the composition of site ends, values and lesson ideas has
mostly been a post-classroom experience driven by inductive
principles and standards for concept and skill development,
and by kind reviews.
For students, which way to go in mathematics and how far depends on the
motivation found in school or which they bring to school. High marks
provides motivation for those who like to perform for themselves or for
parents and teachers. Further motivation of a social nature comes if a
student likes a teacher, belongs to a group of students who are competing
academically, or has parent who favours hard work in school and college.
But the apart from that, the short- and long-term end and values below
offer sounder context for skill and concept development.
Courses in mathematics and science are in part like movies or books. What
a course covers, how and why, is often a mystery before its end and to
often after. For most students, the question why learn or study a subject
or a topic appears. The appearance is a sign of intelligence. Some
students have parents who say mathematics mastery is important. But nany
have parents who in recalling their experience express a dislike for
mathematics after primary school. But if we combine ends and values from
earlier times, we may arrive at overlapping sets of ends and values for
learning and teaching primary and high school mathematics. These ends and
values are easily understood and repeated, and likely to be just right
for some. The first two ends reflect the actual or potential needs of
adult or daily life, and in trades and activities that do not require
common studies. The third end reflect the needs of calculus-based college
programs and of advanced, senior high school science courses. The first
two ends are more immediate than the third end. For the first two ends,
if not the third, over-preparation is better than under-preparation to
students and their families earn their livelihoods and to rationally
defend their interests in a world where daily behaviour, and contracts
involving money matters or income have huge consequences for individuals
and their families.
For mathematics and logic instruction, preparing children and teenagers
to earn income as adults may meet the need of employers, but more
importantly, it may and should meets the needs of students and their
families for earning income in employment or self-employment, and
defending their own interests while changing jobs or being fired from a
long-term post. While high school, trade school, undergraduate
university programs and graduate university programs may open doors for
gainful employment, education too long or too much may also distract
from gainful employment. Showing students early how to handle money
matters in daily and adult life from not going into debt while buying
or selling to evaluating the immediate or long-term value of a
mortgage, a pension plan or the income stream and benefits of a job
with or without benefits may help them face or avoid common situations
and difficulties.
Early mathematics skill development may serve common arithmetic and
geometric needs in daily and adult life. That may include say the
common needs of precollege trades and professions. Preparation for
daily or adult life at home, at work and in travel requires us to
count, measure and calculate with money, time, length, area, volume,
speed and rates of change on paper or with the geometric help of
maps, plans and diagrams carefully drawn to scale. Arithmetic mastery
may include formula evaluation. Early skill development should make
us want to avoid the domino effects of errors. That has value for all
multistep methods in- and out-side of mathematics. Early skill
development, well done, may make mastery of routine skills and
concept common, while providing a partial base for college studies.
Focus mostly on method and ideas with actual and then take-home value
may lead students and their families to value and want mathematics
and logic in early instruction.
The scout motto "be prepared" for what may come applies. For better
and worse, numerical and logical skills and concepts are needed in
daily and adult life to understand others, to read and write
instructions precisely, and to correct yourself or others. There is
a great risk of making incorrect decisions if you do not fully
understand the numerical and logic reasoning used in arguments and
agreements between yourself and others. Mastery of logic and basic
mathematics, the more the better, will help you quietly recognize
faulty decision making, yours or that of others.
In early or later development of mathematics, or of reading and
writing abilities, logic mastery leads to more or full precision in
reading, writing, speaking and listening. This precision will ease or
avoid confusion in following and giving instructions in many arts and
disciplines at home, in school and in the workplace. Logic mastery
sooner rather than later is best for its take-home value. But when
may depend on each student. Before or beside logic mastery, early
skill development may emphasize how to do and record measurement and
arithmetic steps precisely, so that the steps can be seen and
verified, and so that students become aware of the need to avoid the
falling domino effect of errors. In this falling domino effect, a
mistake in one step leads the following steps to being in error,
except in the lucky case where a second or further mistake cancels
the effect of the earlier ones. For that, there should be no credit.
Plug: The leading math-free chapters of online Volume Three
Skills for Algebra on implication rules and their use in
deductive reason may lead the not too young to logic mastery.
Mid- and senior- high school mathematics and logic skill development
may build on early development to serve the needs of senior high
school science and technology courses, and the needs of
calculus-based college programs in commerce, science, engineering and
technology. Calculus in the first instance consists of calculation of
slopes for linear and nonlinear curvers y =f(x). The key role of
slopes in calculus explains why slopes and rates of change need to be
mastered in earlier studies. Hint, Hint Site volume 3 with its
light calculus previews offer a context for the study of slopes,
factored polynomials and function maxima and minima may amuse and
inform students in courses leading to calculus and in the first weeks
of calculus.
Students heading for calculus-based, college programs in business, if
they avoid demanding high school science courses, will not see senior
high school mathematics used before arriving in college. To compensate,
long-term value needs to be emphasized - the calculations and logic of
college level programs requiring calculus will be more difficult to use
and bend to our future requirements with a weak mastery of mathematics.
Site volumes 2 and 3 in forming and reforming the views of students and
teachers in senior high school mathematics as indicated above may inform
and amuse, and in the process provide some context and motivation for the
study of slopes, factored polynomials, function maxima and minima, and
calculus too.
All the ideas described briefly below are explained in more detail in
site algebra starter lessons and in site Volume 2, Three Skills and
Algebra. The arithmetic related ideas could have been placed with site
arithmetic lessons instead.
Arithmetic and algebraic expressions are often to complicated to
read aloud, term term by term. Diagrams too are better seen than "read
aloud". Outside of mathematics, a picture is worth a thousand words. In
mathematics, a symbol, an expression or a diagram better seen and
grasped in silence may also be worth a hundred to a thousand words.
There has been a great silence in arithmetic, algebra, geometry and
calculus because mathematical ideas and methods are often better
written and drawn in silence instead of being expressed and explained
aloud. Yet we may deliberately use more words to introduce skills and
concepts clearer, to talking unifying themes, and to improve
communication in circumstances where writing or drawing is not
possible. While demonstration how appears in site material, we will
identify where the greater use of words is possible. There is more to
mathematics than be given a formula, and numbers to use in it. But
remember, pictures and diagrams too can be employed alone and besides
words to make skills and concepts easier to learn and teach.
Before and besides the role of letters and symbols in algebra, we may use
words and numerical examples to talk about about and show how to
calculate totals and products by adding and multipling subtotals and
subproducts. We may also talk informally but precisely about counts and
measures as being known or not, constant or not, forgotten or not, and
variable or not. Many technical terms may be introduced and understood
before and besides the letters and symbols. Moreover, to gossip or talk
about people, places and activities, we need names, labels and phrases to
identify them. In mathematics, names and descriptive phrases such as the
compound growth formula, the rectangular area calculation, the
distributive law and the Chinese Square Proof of the Pythagorean Theorem
allow us to gossip and talk about calculations and further ideas in
situations where symbols and diagrams cannot be formed nor read. Most
formulas, methods and practices in mathematics and logic are named. For
people wanting and able to talk about what they learning with others,
learning the names becomes an asset and not a burden.
In describing how to calculate averages and how to compute the
perimeter of a polygon, word descriptions of how may be simpler or
not to understand and explain than formulas. As a first example,
the average of a set or sequence of numbers is given by their total
divided divided by the number (count) of set or sequence elements. As a
second example, the perimeter of a polygon is given by the sum of the
lengths of it sides, or more briefly by the instruction: add the sides.
As a third example, the total area of a region consisting of
non-overlapping subregions is given by a sum of subareas. In early
mathematics instruction, how to compute this or that may be easier to
understand and explain with words with the use of letters or symbols
being more complicated. But for the compound interest or growth
formula, for the quadratic formulas and later for the chain rule - do
not worry what computations these phrases name or identify, the the
letters and symbols in them are worth a thousand words. The greater use
of words advocated for earlier instruction here is not possible in
later instruction. So the silence will return.
Using rules and formulas forwards and backward, and talking about it
may end a further silence. Talking and writing about the forward and
backward use of rules and formulas provides a unifying verbal theme for
the study of logic, mathematics and science in school and college
studies. Most if not all rules and formulas are not only used directly in
a forward sense but also indirectly or backwards. Determing the constant
in a proportionality relation uses the relationship, an equation,
backwards. Once it is found, the proportionality relations may then be
used or rewritten forwards and backwards to compute or express the value
of one number or quantity in terms of others. The example here may not be
familar to you if you have not seen them, but by talking about the
forward and backward use of rules, formulas and proportionality
relations, the backward use will be expected and not be another surprise
for students weak and strong of mathematics, logic and science. This
forwards and backwards use is common pattern previously met and mastered
case by case in silence. Talking and writing about it introduces or
extends the oral dimension of skill and concept development.
Site algebra starter lessons and the online chapters of Volume 2, Three
Skills for Algebra, material, show how to learn and teach skills and
concepts with words, forwards and backwards. Algebra starter lessons
include a geometric, stick diagram introduction for solving linear
equations in a way that visually proves or improves fraction skills and
sense. Here fractional operations on stick diagrams are suppose to make
the algebraic solution of linear equations easier to grasp. However, in
entertaining a group of students during a one hour, substitute teaching
assignment, one keen student could not make the transition from solving
with stick diagrams to solving algebraically. It was not my place to give
him extra instruction. He may have been better served by more stick
diagram examples, or by a leap to the algebraic method. I cannot say.
Geometry too can help with the introduction of calculus and in providing
motivation or context for the study of slopes (remember the domain name
is whyslopes.com) and the study of factored polynomials alone and in
ratios (rational expressions). See site Volume 3, Why Slopes and More
Mathematics, online in full with a fall 1983 why slopes prequel. Volume 3
in a preview of calculus provide geometric motivation for the study of
slopes and factored polynomial to the location of maxima and minima of
functions.
The site introduction of complex numbers is geometric instead of
algebraic. It follows or re-invents a path in a 1951 book on Secondary
Mathematics (possibilities) by Howard Fuhr, a mathematician who
masqueraded as a mathematics education professor at Columbia University
and who as part of the NCTM leadership in the 1960s help develop and
implement the college-oriented Modern Mathematics Programs for skill and
concept development in primary and high school mathematics from counting
to calculus. The level of rigour in this geometric introduction of
complex numbers is not less than that in the geometric introduction of
trigonometry using triangles and/or the unit circles drawn in a Cartesian
plane.
The big steps in modern mathematics programs were too hard for
many to follow. Site material offer smaller steps to compensate. Before
modern mathematics programs, instruction had a greater focus on skills
and concepts with value for daily and adult life - work, mortgages and
investments included. The discussion of ends and values above suggests
preparation for daily and adult life as much as possible first and
foremost, and on preparation for college second while emphasing
anything in the latter that could have take-home value.
Site composition was driven by a search to remedy the skill and concept
development difficulties stemming from steps too big and steps without
clear value for students and their families in earlier programs in
mathematics and logic education - programs which aimed for student
mastery of selected skills and concepts. In consequence, site lessons and
lesson ideas include many expositional innovations to aid skill and
concept development. Most, if not all, are mathematically correct, with a
few small departures from earlier views to make instruction simpler.
In calculus and secondary mathematics, late primary mathematics too,
there are many different starting points for instruction.
For example, the site development of prime numbers begins with a
definition that is not the most general but with a definition that is
likely the easiest for students to understand and apply. For a second
example, the site essay on what is a variable, by talking or writing
about numbers and quantities varying in one sense or another, we
provide a prequel to the later, more formal and more algebraically
advanced view of what is a variable, a prequel that is easily
understood because it is wordy and pre-algebraic. For more examples,
see the site geometric development of complex numbers before trig, and
see light calculus preview in Volume 3, Why Slopes and More Math, and
see, still in Volume 3, the decimal prequel to the epsilon-delta view
or definitions of limits and continuity.
The choice of starting point need not reflect the conventions of higher
mathematics, conventions that may be arbitrary despited being widely
accepted. Instead, the choice of starting point may reflect the objective
of making skill and concept development simpler for students and their
teachers. The harder starting points may be left to advanced studies
involving fewer students and teachers.
Mathematics Literacy: Since students may leave school early,
we need to show them and give them mastery of reading, writing,
arithmetic and geometry with actual or potential take-home value for
their daily and adult life in local and distant communities. While
learning mathematics with comprehension is best, the take-home value
of basic and routine skills needed for daily and adult to important
to insist upon mastery with comprehension. In this course design and
delivery should emphasize the domino effect of errors in multistep
methods, numerical or geometric. And in arithmetic, students should
be shown how to do and record steps in a manner that their skills can
be seen and checked as done or later. In practical, skill-based arts
and disciplines from cooking to mathematics, skills needs to be
demonstrated to be believed, and indeed to be both taught and
mastered. In general, there are too many skills for a student to find
them or their refined form by discovery. The challenge for early
mathematics instruction is to identify and provide observable and
thus verifiable skills with take-home value that serves common or
routine needs while seamlessly preparing students for late
instruction.
Geometry with Proportionality First: To quickly support the
common, actual or potential, geometric use of maps, plans and
diagrams drawn to scale in daily and adult life, and in precollege
trades and professions, the site webvideo exposition of geometry may
include SAS, ASA and SSS methods or practices for the construction of
similar or proportional triangles, and in general assume that in
maps, plans and diagrams drawn to different scales that corresponding
angles are equal and corresponding lengths are proportional. So the
similarity or proportionality present in maps, plans and diagrams
drawn to scale may be exploited to indirectly measure angles and
lengths, and quantities computed from them. Trigonometry may then be
introduced as a way to calculate angles and lengths instead of
obtaining them direct from measurements, actual or of the
corresponding angles and lengths on maps, plans and diagrams drawn to
scale. The early mastery of common, and easily understood and
repreated practices with maps, plans and diagrams drawn to scale
provides a context for and even implies the assumptions and axioms of
Euclidean Geometry.
Geometry with Congruence or Isometery Second: For simpler or
more accessible account of Euclidean geometry, the site account does
not include a proof of the Pythagorean thereom. The Chinese Square
Dissection proof provides a more accessible alternative. The latter
is presented online in Volume 2, Three Skills for Algebra. Without
the Pythagorean thereom, Euclidean geometry may be easy enough to
return to the North American classroom in a way that shows high
school or college students how logic in the form of implication rules
alone and in direct deductive chains of reason appears in
mathematics.
Counting and Arithmetic with Decimals: Decimal place value is
the key to counting. We assume every set of fewer than 10, 100, 1000
and 10000, etc, can be divided into a group of upto 9 units, a group
upto 9 groups of ten, upto 9 groups of 100 and upto 9 groups of 1000
in manner that the count between 0 and 9 of units, 10s, 100s and
1000s are unique, albeit the division of set elements into groups of
units, 10s, 100s and 1000s is not unique. The foregoing division or
partition gives a unique, multidigit decimal way to write and record
the count or number of set elements in which each unit has a place
value. The concept of place value leads to and easily justifies
arithmetic counting shortcuts involving the addition, comparision,
subtraction and multiplication and even division of decimals. The
details are given in the site arithmetics section along with North
American, metric (or SI) and UK-German methods for writing and
reading aloud with words multidigit decimals without and then with a
decimal point. Comprehension of operations with decimals enriches
early instruction and may help some master these operations. Others,
most others perhaps, may find full explanation of why some operations
work too complicated for their liking. For them skill and confidence
in decimal methods may follow learning how to use the methods to
obtain repeatable and reproducible results via steps observable and,
if need-be correctable.
Counting and Arithmetic with Fractions: The fraction three
quarters when written or read aloud means three times a quarter. A
quarter ¥ is a unit fraction. Proper and improper fractions with the
same denominator all give a number or count of a unit fraction, that
associated with the same denominator. With the aid of decimal
representations forms of numerators, it is an easy matter to count,
add, compare, subtract and even divide multiples of a single unit
fraction. It also an easy matter to multiply a multiple of a single
fraction by a whole number - to form a multiple of a multiple. By
long division and regrouping, each improper fractions is equivalent
to a mixed numbers. In primary and secondary school, students may be
shown how to add and subtract fractions with unlike denominators by
raising terms to convert each fraction to another equivalent
fraction, so after conversion, each has a common denominator and so
is a multiple of a common unit fraction. Following this, students may
be shown how to compare, multiple and divide fractions by rote. Site
fraction lessons in contrast show how raising terms to obtain like
denominators explains and justifies methods to compare and divide
fractions while raising terms to ensure the numerator of the
multiplicand is a multiple of the denominator of the multiplier
explains and justify methods for fraction multiplication. The
justification of arithmetic with fractions sets the stage for the
justification of arithmetic with decimal fractions (multiples of
one-tenth, one hundredth, one thousandths) that usually denoted by
multidigit decimals with digits after and even before a decimal
point.
Comprehension of operations with fractions agains enriches early
instruction and may help some master these operations. Others, most
others perhaps, may find full explanation of why some operations work
too complicated for their liking. For them skill and confidence in
decimal methods may follow learning how to use the methods to obtain
repeatable and reproducible results via steps observable and, if
need-be correctable.
Prime Numbers and Fractions: For algebra alone or as part of
calculus, and for operations with complex numbers, students need an
efficient command of arithmetic with fractions where the denominators
are say less than 200. Prime factorization of whole numbers less than
200 is useful here. The development of prime number factorization
methods in the site arithmetic section shows how to use time tables
to recognize small primes, and how to use an olde square rule method
to quickly and efficiently obtain prime number factorization of whole
number less than 289 = 172, and to recognize primes less
than 289 as well. The foregoing path as demostrated in site
arithmetic section may be easier for people to learn and teach.
Prime factorization is also useful for a "simplification" of roots
involving whole numbers or their fractions, a simplification often
seen in trig and calculus. Mastery of exact arithmetic in high
mathematics requires mastery of some cosmetic standards or
conventions for the expression of fractions, roots and radicals.
Arithmetic with units and denominate Numbers - missing. Units
of measure and counting appear directly in daily and adult life, and
also in science and technology. Units of measure also appear in the
description of speed, acceleration and other first and second order
rates - rates that may be described as derivatives in calculus.
Modern mathematics programs did not mention nor sanction the use of
units and their multiples (denominate numbers) in high school and
college studies, albeit this use appear in science courses and in
some practical examples met in mathematics courses in trigonometry
and before. The site account of arithmetic and fractions with units
compensates for this. Albeit, the compensation is given in a do this,
do that manner, because of a lack of words on my part to provide
greater comprehension. Readers are invited to provide remedies. Early
algebra courses today may introduce monomials (products of letters or
"variables" to various powers) and operations on them alone and in
fractions before students understand the computational significance
of monomials and operations on them. Site algebra starter lessons
explanation of equivalent computation rules may provide a remedy for
that. But before or besides algebra, The same exercises with
monomials given by numerical multiple of products of units to various
powers may be more meaningful to students, while be a prerequisite to
the numerical description of rates and proportionality constants.
Algebra Starter Lessons. Showing students how to do and record
numerical and algebraic steps in ways that can be seen and checked when
done or later makes their mastery of multistep methods observable, and
hence verifiable or correctable. Showing should also make students
aware of the domino effects of mistakes, and the care needed to avoid
or correct such errors. The introduction and assumption of methods to
compute totals and products using subtotals and subproducts employs
practices that are too complicated in high school instruction to derive
from the usual axioms for arithmetic with real numbers. But the
assumption of these methods or practices extends the usual axioms and
from the perspective of advance mathematics gives a very redundant set
of axioms. But the same redundancy is justified as it makes early
instruction easier and more effective, and the extra assumptions have
immediate take-home value for daily and adult life not present in the
usual axioms. Now the usual axioms are best understood besides or after
a math-free mastery of logic. The usual axioms for the distributive,
commutative and associative law are algebraically described. Many
students find the algebraic description too remote or abstract. But if
we introduce the concept that each algebraic expression give a unique
computation rule, one that that be evaluated on paper or with the aid
of a program on a calculator or computer, we may observe from numerical
examples that different computation rules appear to be equivalent in
the sense that they give the same result. This small step of
introducing the concept of equivalent computation rules provides
another context, a different starting point, for understanding and
explaining distributive, commutative and associative laws in arithmetic
with many kinds of numbers, and eventually with numbers being replaced
by computation rules - those with numerical values.
Arithmetic without Calculators: To be over-prepared is better
and less risky than being under-prepared. A written, calculator-free
mastery of arithmetic with signs, decimals, fractions; with units of
measures; and with number theory practices is needed for a full,
traditional, mastery of algebra, trigonometry, complex numbers and
calculus. A full mastery of arithmetic with units of counting and
measures also has value for adult and daily life, and for further
studies in commerce, science, engineering and even mathematics
itself.
In modern urban life we depend on machines to simplify our daily
life. But calculators usage both simplifies and weakens mathematics
mastery, or that needed to understand decimals, fractions, algebra,
trigonometry and calculus. As a master of my subject with standards
for skill and concept development, I see the student who can only do
arithmetic with the aid of a calculator as being handicapped from
being too spoilt in earlier instruction. Any expectation that
quantitative skills and disciplines can be well-taught without a
written mastery of arithmetic with decimals and fractions is false.
Again, manually learning how to do and record work in steps that can
be seen and corrected as done or later may begin with evaluation of
arithmetic expressions and algebraic formulas. While calculators are
useful, failure to require manual student mastery of arithmetic
removes a starting point for observable skill and concept
development. In particular, mastery of observable steps that can
be seen and confirmed or corrected as done or later is also is key
part of showing and demonstrating abilities in problem solving, in
writing proofs and employing multistep methods at home, at work and
in studies in many arts and disciplines.
Mathematics after primary school has been difficult and without immediate
value for many generations of students. While some students have parents
who did well or who encourage skill and concept development, other
students have parents who may say mathematics after arithmetic is a waste
of time. High school and college students may attend courses because
those courses are required. In high school and college, students who base
their efforts only on whether or not their teachers are pleasing have a
shallow context and motivation for learning. Students for whom doing well
in tests and finals is the only motivation also have shallow reason for
learning. Cultural values for learning may appeal to some. But practical
ends and values may appeal to more.
In primary school, students and their families may see the 4Rs (reading,
writing, reasoning and arithmetic) as being useful in adult and daily
life. There-in lies content and motivation. But at the junior- and
mid-high school level, some mathematics and logic lessons are of actual
or potential service to daily and adult life for decision-making and
money-matters at home and the work place. Other lessons only have
long-term value for college programs that some students may never enter
or complete. Instruction may lean to the first kind of lessons initially
to provide ends and values easily understood and appreciated by students
and their families. Emphasizing the more useful methods and concepts
first may help retain student motivation and also help those who have
leave school early. But eventually, high school and college mathematics
has less and less take-home value besides more and more value for future
studies or courses that students may not see. Here again, instruction may
focus on the take-home value, when present to provide motivation.
At the precalculus level, instruction should focus on two kinds of skills
and concepts, those that have actual or potential take-home value for
daily & adult life, and for precollege trades and activities; and
those that prepare students for a light and then deeper command of
calculus. In the former, I would include a set-based development of
probability theory. In both streams, I might include matrix operations
but not linear programming. The latter can be left to college programs in
commerce, science, engineering and technology. I would restrict high
school mathematics to computations and proofs that are lead to repeatable
and reproducible results, and to the computation of averages useful in
small business for estimating demand for products and services being
sold. Further elements of descriptive statistics, I would leave to
college studies, or to high school courses on critical thinking.
The recommended focus may mean fewer topics are taught. For students not
heading for calculus-based studies, less with a focus of skills and
concepts with take-home value may be best. In the preparation of students
for calculus and senior high school mathematics, multiple topics with no
short-term value may be met. That short-term value will vary between
students. Students in courses required to prepare for calculus who do
take mathematically demanding, senior high school courses will see more
short-term value. In general, calculus and preparation for calculus is a
long demanding path which many find difficult or hard to complete. But,
here is a plug, site Volumes 2 and 3, make the path easier and throught
calculus preview make calculus and precalculus easier and more appealing.
To serve the skill and concept needs of the common person in the street,
we need to put first those skills and concepts with actual or potential
value for daily and adult life. Then students may attend school and go
home with methods that help themselves or their families in money and
other matters. Near the end of school coverage of arithmetic, geometric
and logic (or reading and writing) skills and concepts with actual or
potential service for daily and adult life, more algebra and higher level
geometry skills may be introduced to revisit and reinforce the foregoing
service while being of service to more trades and activities at the
precalculus level, and also being of service or preparation for senior
high school science courses and perhaps later studies in calculus. The
multiple ends and values in the foregoing need to be balanced. The
balance may depend on the local or immediate needs of students and their
families, that is, how long students are likely to remain in school; on
whether or not, they are likely to see all all ends and values served;
and on whether or not, the students are quick or slow learners.
The concept and skill development standards and principles for
instruction in results-oriented arts and disciplines, as espoused in site
material, seek to provide students with an observable and verifiable
know-how of the ideas and methods currently forming and characterizing
each art or discipline. The latter presents a moving targets as best
practices in each may vary over time and place. But in a moving target,
concept and skill mastery may be seen or empirically measured by student
response to questions. In each such art and discipline, students are
expected to retain know-how and build on it in a progressive manner, with
regression being a sign of weakness, or absence too long from practice in
an art or discipline. Each art or discipline comes with different
cultural and practical values, some more important than others in ways
that may justify its instruction or not in each school or school system.
Morover, course design and delivery needs to acknowledge that there are
multiple intelligences in learning and teaching styles. A style that is
suitable for instruction in the humanities where conclusions are highly
subjective is not suitable for instruction in mathematics and science
where the benefits, origins and limitations of ideas and methods need to
be indicated and mastered in all or part.
In modern mathematics programs for secondary mathematics
education, direct instruction aimed at student mastery of given
concepts and skills has been uncertain and unreliable due to steps too
big or hard for most to follow, and due a college-oriented choice of
concepts and skills with value too long-term for students and their
families. Those steps too big undermined course design and delivery.
However, direct instruction can address its own problems by serving
short- and long-term ends and values in the selection and arrangement
of course topics, and in offering smaller, more accessible and reliable
steps for concept and skill mastery. The key question is whether or not
remedies based on the smaller and alternative steps in site lessons and lesson ideas,
alone or with the proposed ends and values above, will be
effective..
Site lessons and lessons ideas from counting to calculus provide a
foundation for college level studies of modern mathematics. Site lessons
and lesson idea offer student and their teachers a mastery of concepts
and skills with comprehension, if that be wanted, based on a redundant
set of practices and axioms, whose redundancy can be explained and
removed in college course in or leading to modern mathematics. The ends
and value further offer reasons for mathematics and logic mastery that
students and their families are more likely to appreciate before
preparation for calculus becomes the main focus of instruction at the
senior high school level. For calculus, Chapter 14 of site Volume 3, Why
Slopes and More Mathematics, offers a decimal, error control development
of limit and continuity concepts that may stand alone, or be used to make
the epsilon-delta development much easier to understand and explain. Site
departures in early instruction from modern mathematics are intended to
provide TCPITS an more accessible view, but they are also intended to
develop the logical and algebraic maturity needed for college and senior
high school students to study modern mathematics if they choose or where
it appears in their programs of study.
Indirect Instruction Benefits and Limits
Indirect instruction has the advantage of enriching skills and concept
mastery in classes where there is time for individual and group
creativity. But the subjective nature of that enrichment means direct
instruction is needed to develop or at least consolidate mastery of core
skills and concepts, those on which later methods and ideas stand,
Moreover, for student mastery of skills and concepts of importance for
their take-home value, or importance for further mastery, direct
explanations seem more reliable and certain than indirect ones, and
easier to design and provide.
When and where direct instruction clear steps or lessons to
provide mastery of important skills and concepts, to aid student to
follow the steps and lessons as is or in briefer form, teachers may
provide circumstances and pose questions to indirectly lead student to
formulate ideas and skills and gain the experience on which direct
instruction may stand. But where direct instruction lacks those clear
steps and lessons, it is doubtful that indirect instruction will
provide a practical and clearer path to to student mastery of the given
skills and concepts. The ability to explain matters directly is likely
a prerequisites to the ability to provide skill and concept mastery
indirectly.
Each program of instruction aim at mastery of given ideas and methods has
varying degrees of success and failure, and of motivation and alienation
for students and their families. In the case of modern mathematics
programs for secondary and college studies, the very rigour that attract
some students repelled many more, and include steps too big and also, I
will missing, in course design and materials. Missing steps were missing
not only in modern mathematics programs for algebra alone and in advance
courses, but also in earlier methods or paths for concept development.
The missing steps represent old gaps inherited in the design and redesign
of mathematics instruction over many, many decades, if not a century or
two. Site material in providing smaller steps allows steps too big to be
recognized and gives remedies - full or not - to be tried and tested.
Given that students have multiple abilities levels, a situation inherited
from nature, how far students may go in mastery of mathematics depends on
their will and natural talent. Smaller steps should allow more to go
further
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A new model for graphing functions of complex numbers
4DLab plots complex functions in an integrated way: the domain and the range of a function are not shown apart. In fact, complex functions are plotted analogously as the real functions are plotted.
The traditional graphing procedure —in textbooks and in other plotting software— is to separate the function domain from the function range; this is because the domain is usually a plane region of a plane, and the range is usually a surface. But 4DLab follows the new transcomplex numbers approach, where the complex numbers are extended to 4–dimensional ordered pairs.
At last, the graphs of the functions of complex variables are meaningful!
The transcomplex numbers system is an extension of the complex numbers system to 4 dimensions. Complex variables are 2–dimensional while transcomplexs are 4–dimensional. There are other four entries numbers systems, like, for example, the quaternions. But only the transcomplexs combine the simplicity of the real numbers with the power of the complex numbers. But where the transcomplexs shine above all the others is in the graphs it produces: visually simple and beautiful; no more abstract "surfaces", no more dual and disintegrated plotting. 4DLab is the software made specially to plot transcomplex surfaces, but since mathematics is an integrated and unified field, 4DLab also follows this model. Thus, in the same way that 3–dimensional surfaces are plotted, the 2–dimensional real functions are also plotted: you use the same equation editor. Just write-in —the editor will check your syntax— and choose the type of rendering you wish.
Math can be inspirational!
4DLab was also a program made to produce aesthetically appealing images. There are many choices and parameters to choose or change. So, if you wish, your plots can be done over an appealing background, you can add your name, or the equation involved, etc.
4DLab is a new tool for learning math and a new tool for graphing 3D equations and 2D equations. This free software is a3D and 2D graphing software. Choose a picture —any picture; a texture, a landscape, a photograph— and plot it against a surface and you will visually grasp the concept of one-to-one (1–1) mapping. Complex math can be made simple by bringing some abstract concepts down to the point that it becomes personal.
Overall Features of 4DLab:
With 4DLab the function domain can be any rectangular shape; not necessarily square. Graphs can also be made of any rectangular sub domain of the main domain.
Surfaces can be shown in grid-only mode, or opaque with or without showing the grid mesh. Axes are shown exactly where they belong: intersecting the surface at the exact points.
For any function, the domain-to-range relation can be seen instantly by just moving the mouse over the the domain region. The corresponding point of a domain can be seen as a moving point, or as a line connecting the domain with the range. This is an useful tool, especially when a point in the space is relate to another point in the space far away, or not directly above, as with real functions plots.
The program incorporates a dedicated calculator to compute the coordinates of any point coordinates for any equation set, be them part of the equation domain or not.
The program can maintain a list of your favorite website links with editable comments. You can click on any of the saved links for immediate reference.
Decorate any of your math pictures with any background of your preference.
The coordinates axes names can be changed to adapt to your needs. So, instead of X, Y, or Z, the axes labels can be named: Ohms, or Degrees, or Distance, etc.
Surface or line pictures can be labeled as Fig.1, Fig. 2, etc, or the user can insert, his/her name or a copyright notice. Other labels are available. The notes are saved as part of the pictures.
Surfaces or line plots can be rotated and viewed from any angle. The program can show the surface plots intersection with the XY, or iZY planes. Pictures can be resized manually with the mouse, or can be resized exactly to any desired dimension with pixel precision.
The center of coordinates can be moved away from the center of the picture frame for better composition of those offset plots.
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(I previously reviewed the DVD tutorial for Algebra ½, and much of that information applies to Algebra I as well.)
In the past few years, our family has used the DVDs from Teaching Tape Technology to give additional instruction in Saxon Math for grade levels 4th through Advanced Math. We have been (and still are) extremely satisfied with these videos and the teacher, so when I had the opportunity to review the Algebra 1 (3rd edition) DVDs from Mastering Algebra "John Saxon's Way," I was intrigued--yet a bit hesitant. Could these videos measure up? Could I be objective? I can honestly answer "yes" to both questions.
These Algebra 1 DVDs come in a hard plastic case with clear sleeve protectors for each disc. There are 11 DVDs, covering over 20 hours of Saxon Math instruction (120 lessons) in a classroom setting. Each disc has about 12 lessons. To see the concepts that are covered in Algebra 1, visit the following link on the usingsaxonmath.com website: In addition, by using this outline of lessons covered in Saxon Algebra 1, you could correlate the DVDs to another pre-algebra curriculum.
Art Reed is a fantastic instructor. He is engaging and inspiring, but his approach is also straightforward and no nonsense--without a lot of fluff. But then again, he also has a great sense of humor. He is a professional through and through, and he knows his stuff. It is obvious that he enjoys teaching math and wants his students to master the material. I like his confident way of presenting each lesson, but he is also the first to say that he makes mistakes like everyone else. He expects students to take responsibility for their work and do what it takes to learn the material. He does not spoon feed, but he does explain each concept thoroughly and provide encouragement. He gives extra tips and information to make everything easier to understand, and I think his approach fosters a much-needed character-building "learning style." I also like the way he uses visual aids and manipulatives when needed to reinforce certain concepts.
Art Reed was a contemporary and friend of John Saxon, who passed away in 1996, so he has a firm grasp on how the program is to be used. Although now retired, Mr. Reed has over 12 years of classroom teaching experience using Saxon Math, and he has been a Saxon homeschool consultant during the last nine years. In addition, he is the author of the hands-on guide Using
John Saxon's Math Books, designed to help homeschool educators successfully use Saxon Math and save money too.
The cost of this DVD set for Algebra 1 (3rd Edition) is $49.95 with free shipping. You can visit the usingsaxonmath.com website for more information or to download sample lesson videos.
Overall, I think this is a wonderful set for homeschool families who use Saxon Math. The DVDs are the perfect solution for moms (or dads) who need a bit of assistance in teaching higher-level math. The students have access to an experienced instructor, and they can replay the videos as many times as they need to master the material. Personally, I was thrilled to find yet another great resource for Saxon Math instruction to add to our collection. I highly recommend Art Reed and the Mastering Algebra "John Saxon's Way" DVDs as a great investment in your child's mathematical education.
Product review by Amy M. O'Quinn, The Old Schoolhouse® Magazine, LLC, May 2010
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High School Algebra
This book is a handbook on topics in High School Algebra. We have covered the topics like - Ratio, Proportion, Variation, Progressions, Surds, Imaginary Quantities, Quadratics, Permutations, Combinations, Mathematical Induction, Binomial Theorem, Logarithms, Inequalities, Probabilities and Determinants.
Each chapter is follows a simple structure. A definition of terms and detailed explanation of concepts; followed by derivation of useful formulas through first principles. A few problems are solved in order to give a flavor of the problem solving process. This book is intended to help the student to understand ways to build an airtight reasoning on how the problem solving process moves towards the final answer. This serves as a demonstration of our understanding of the subject - basics, formulas and methods of manipulation. Students interested in solving additional problems may refer to the books "Problems in High School Algebra" and "Challenges in High School Algebra".
show more show less
Edition:
N/A
Publisher:
CreateSpace Independent Publishing Platform
Binding:
Trade Paper
Pages:
230
Size:
5.50" wide x 8.50" long x 0.52 High School Algebra - 9781463715458 at TextbooksRus.com.
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This class is basically 3 mini courses of Matrix algebra/manipulation, Advanced Calculus, and Complex Variables. The matrix stuff is almost a rehash of what you leaned in undergrad math classes (341 maybe?). Advanced calc and complex variables gets a bit tougher, but with a good professor, these shouldn't be too bad.
Good teacher. Very friendly and encourages class interaction. Interjects a good bit of humor into his class as well. Explains stuff very clearly and speaks clearly. Homeworks and tests were always graded promptly and fairly.
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Finite Mathematics & Calculus Applied To The Real World - 96 edition
Summary: Designed for a two-semester sequential course in finite mathematics or an elementary/survey of calculus for students in management or the natural or social sciences, this text helps answer the students' question: What is this stuff good for? by focusing on the relevance of the material, which is emphasized through an abundance of applications based on real data from actual companies and products. This approach fosters students' understanding of mathematical concep...show morets and by stressing the "rule of four," which is used where appropriate. The authors review each mathematical concept from the numeric, geometric, and analytic points of view and often ask students to give written responses. Optional use of graphing calculators and graphing software is provided throughout. You're the Expert sections put students in decision-making roles and guide them through the modeling process. ...show less
Coordinates and Graphs Functions and their Graphs Linear Functions Linear Models Quadratic Functions and Models Solving Equations Using Graphing Calculators or Computers You're the Expert--Modeling the Demand for Poultry
Chapter 2: Systems of Linear Equations
Systems of Two Linear Equations in Two Unknowns Using Matrices to Solve Systems with Two Unknowns Using Matrices to Solve Systems with Three or More Unknowns Applications for Systems of Linear Equations You're the Expert--The Impact of Regulating Sulfur Emissions
Exponential Functions and Application Continuous Growth and Decay and the Number e Logarithmic Functions Applications of Logarithms You're the Experts--Epidemics
Chapter 10: Introduction to The Derivative
Rate of Change and the Derivative Geometric Interpretation of the Derivative Limits and Continuity Derivatives of Powers and Polynomials Marginal Analysis More on Limits, Continuity and Differentiability You're the Expert--Reducing Sulfur Emissions
The Indefinite Integral Substitution Applications of the Indefinite Integral Geometric Definition of the Definite Integral Algebraic Definition of the Definite Integral The Fundamental Theorem of Calculus Numerical Integration You're the Expert--The Cost of Issuing a Warranty
Chapter 14: Further Integration Techniques and Applications of the Integral
Integration by Parts Integration Using Tables Area between Two Curves and Applications Averages and Moving Averages Improper Integrals and Applications Differential Equations and Applications You're the Expert--Estimating Tax Revenues
Chapter 15: Functions of Several Variables
Functions of Two or More Variables Three Dimensional Space and the Graph of a Function of Two Variables Partial Derivatives Maxima and Minima Constrained Maxima and Minima and Applications Least-Squares Fit Double Integrals You're the Expert--Constructing a Best Fit Demand Curve765.7688 +$3.99 s/h
Good
HC Outlets Knoxville, TN
0065018168 Some shelf wear. Did not see any writing or highlighting. No dogeared pages. Binding is good
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Appendix A. On Linear Algebra: Vector and Matrix Calculus - Pg. 503
Appendix A On Linear Algebra: Vector and Matrix Calculus · Throughout the book we profit from the convenience of vector and matrix notation and methods. This allows us to carry out the analysis of optimization problems involving two or more variables in a transparent way, without messy computations. A.1 INTRODUCTION The main advantage of linear algebra is conceptual. A collection of objects is viewed as one object, as a vector or as a matrix. This makes it often possible to write down data and formulas and to manipulate these in such a way that the structure is presented in a transparent way.
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Basic Mathematics
Description
Basic Mathematics, by Goetz, Smith, and Tobey, is your students' on-ramp to success in mathematics! The authors provide generous levels of support and interactivity throughout their text, helping students experience many small successes, one concept at a time. Students take an active role while using this text through making decisions, solving exercises, or answering questions as they read. This interactive structure allows students to get up to speed at their own pace, while also developing the skills necessary to succeed in future mathematics courses. To deepen the interactive nature of the book, Twitter® is used throughout the text, with the authors also providing a tweet for every exercise set of every section, giving students timely hints and suggestions to help with specific exercises.
Features
The highly interactive approach combines concise instruction with a clean,innovative design to ensure that students are actively engaged in the material.
Guided Practice exercises are designed to sit alongside the examples in the text. Students navigate through finding a solution to a problem similar to the example they are shown.
Interactive Definitions accompany Examples and Guided Practice as appropriate to help students develop an understanding of a critical or difficult mathematical term.
"Do you Understand?" questions follow the Interactive Definitions, ensuring that students have absorbed the material. Students are then asked to determine if they've "Got it" or need to "Get Help."
The clean design includes a subtle yellow background on all pages to make reading easier on the eyes.
Topic-specificFlow Charts appear as appropriate throughout the book to walk students through the thought process needed to solve a particular type of problem.
Study tips are designed to reach today's students. Twitter® is used throughout the text, with the authors also providing a tweet for every exercise set of every section, giving students timely hints and suggestions to also help with specific exercises.
Vocabulary is heavily integrated in the exposition to reinforce comprehension.
Vocabulary Preview appears at the very beginning of each section. This familiarizes students with the key vocabulary for the section before they encounter it in context.
The second time the vocabulary is introduced is through Interactive Definitions; these appear with Examples and Guided Practice when students need to develop an understanding of a critical or difficult mathematical term. At the end of the feature, students see an additional "Do You Understand" question, followed by "Got It" or "Get Help."
Vocabulary Review appears at the start of every end-of section exercise set.
Students are given many opportunities to practice skills and reinforce concepts at every level of the text.
Objective Practice exercises appear after the examples, Guided Practice, and Concept Checks. Exercises are numbered, so they can easily be used as in-class work or assigned for homework.
End-of-Section Level:
Self Assessments appear at the end of the exercise set of the first section of every chapter after Chapter 1. Students are asked to evaluate how they did on their last test and how well they felt they had prepared for it.
Question Logs appear after the exercise set in each section. Students are provided an organized space to write down questions for their instructor.
Section Exercises are two-fold: they review all basic skills just learned and then incorporate those skills with higher-level thinking questions that include applications, analysis, and synthesis.
End-of-Chapter Level:
The Chapter Organizer appears at the end of the chapter. It serves as an additional review of key concepts, vocabulary, and procedures. Students are able to use this as a study aid for each chapter.
Chapter Review exercises follow the Chapter Organizer. Exercises are organized by section so students can refer back through the text for help.
Chapter Test follows every Chapter Review and covers the key topics within each chapter.
This text is available through the Pearson Custom Library. If your course does not cover all the chapters in this text, we encourage you to build a version that more closely matches your syllabus. Visit the Pearson Custom Library for more information.
Table of Contents
1. Whole Numbers
1.1 Understanding Whole Numbers
1.2 Adding Whole Numbers
1.3 Subtracting Whole numbers
1.4 Multiplying Whole Numbers
1.5 Dividing Whole Numbers
1.6 Exponents, Groupings, and the Order of Operations
1.7 Properties of Whole Numbers
1.8 The Greatest Common Factor and Least Common Multiple
1.9 Applications with Whole Numbers
Chapter 1 Chapter Organizer
Chapter 1 Review Exercises
Chapter 1 Practice Test
2. Fractions
2.1 Visualizing Fractions
2.2 Multiplying Fractions
2.3 Dividing Fractions
2.4 Adding and Subtracting Fractions
2.5 Fractions and the Order of Operations
2.6 Mixed Numbers
Chapter 2 Chapter Organizer
Chapter 2 Review Exercises
Chapter 2 Practice Test
3. Decimals
3.1 Understanding Decimal Numbers
3.2 Adding and Subtracting Decimal Numbers
3.3 Multiplying Decimal Numbers
3.4 Dividing Decimal Numbers
Chapter 3 Chapter Organizer
Chapter 3 Review Exercises
Chapter 3 Practice Test
4. Ratios, Rates, and Proportions
4.1 Ratios and Rates
4.2 Writing and Solving Proportions
4.3 Applications of Ratios, Rates and Proportions
Chapter 4 Chapter Organizer
Chapter 4 Review Exercises
Chapter 4 Practice Test
5. Percents
5.1 Percents, Fractions, and Decimals
5.2 Use Proportions to Solve Percent Exercises
5.3 Use Equations to Solve Percent Exercises
Chapter 5 Chapter Organizer
Chapter 5 Review Exercises
Chapter 5 Practice Test
6. Units of Measure
6.1 U.S. System Units of Measure
6.2 Metric System Units of Measure
6.3 Converting Between the U.S. System and the Metric System
Chapter 6 Chapter Organizer
Chapter 6 Review Exercises
Chapter 6 Practice Test
7. Geometry
7.1 Angles
7.2 Polygons
7.3 Perimeter and Area
7.4 Circles
7.5 Volume
7.6 Square Roots and the Pythagorean Theorem
7.7 Similarity
Chapter 7 Chapter Organizer
Chapter 7 Review Exercises
Chapter 7 Practice Test
8. Statistics
8.1 Reading Graphs
8.2 Mean, Median and Mode
Chapter 8 Chapter Organizer
Chapter 8 Review Exercises
Chapter 8 Practice Test
9. Signed Numbers
9.1 Understanding Signed Numbers
9.2 Adding and Subtracting Signed Numbers
9.3 Multiplying and Dividing Signed Numbers
9.4 The Order of Operations and Signed Numbers
Chapter 9 Chapter Organizer
Chapter 9 Review Exercises
Chapter 9 Practice Test
10. Introduction to Algebra
10.1 Introduction to Variables
10.2 Operations with Variable Expressions
10.3 Solving One-Step Equations
10.4 Solving Multi-Step Equations
Chapter 10 Chapter Organizer
Chapter 10 Review Exercises
Chapter 10 Practice Test
Appendices
A. Additional Practice and Review
Section 1.2 Extra Practice, Addition Facts
Section 1.3 Extra Practice, Subtraction Facts
Section 1.4 Extra Practice, Multiplication Facts
Mid Chapter Review, Chapter 1
Mid Chapter Review, Chapter 2
Mid Chapter Review, Chapter 9
B. Tables
Basic Facts for Addition
Basic Facts for Multiplication
Square Roots
U.S. and Metric Measurements and Conversions
Author
Brian Goetz has helped students of all levels achieve success in mathematics for sixteen years. As a curriculum specialist for the Grand Rapids Area Precollege Engineering Program, he created numerous materials to motivate and inspire underserved populations. Brian also ran a math learning center at Bay de Noc Community College, where he helped students exceed their expectations of success. Brian has been teaching at Kellogg Community College for eight years. A common thread throughout all his teaching experiences is that an active and supportive environment is needed for students to succeed. With this belief close to his heart, Brian finds working with the other authors to be one of the most rewarding experiences of his career. When he isn't working, Brian spends quality time with his family and friends, mountain bikes, and kayaks. He dreams of spending a summer kayaking around Lake Superior.
Graham Smith has spent his life immersed in education. He was raised in a family of six teachers, where dinner conversations often centered on public education. Since then, Graham has gained sixteen years of classroom experience, and spent the last 9 years teaching full-time at Kellogg Community College (KCC). The majority of Graham's professional life has been focused on the education and success of the under-prepared student, which he continues through this work as the Developmental Mathematics Coordinator at KCC. Graham's substantial training and experience in mathematics and education, as well as his training and certification in developmental education through the Kellogg Institute at Appalachian State University and the National Center for Developmental Education, provide a comprehensive understanding of developmental mathematics. This background and experience provide the author team with a well-developed perspective. In his spare time, Graham enjoys spending time with his wife Amy, catching big fish, playing the guitar, and tinkering with his car that runs on recycled vegetable oil.
Dr. John Tobey currently teaches mathematics at North Shore Community College in Danvers, MA where he has taught for thirty-nine years. Previously Dr. Tobey taught calculus at the United States Military Academy at West Point. He has a doctorate from Boston University and a Master's degree from Harvard. He served as the mathematics department chair for his college for five years. He has authored and co-authored eight college mathematics textbooks with Pearson. He is a past president of New England Mathematics Association of Two Year Colleges (NEMATYC) and is an active member of the American Mathematics Association of Two Year Colleges (AMATYC). In 1993 Dr. Tobey received the NISOD award for excellence in teaching.
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Algebra and Trigonometry: Enhanced with Graphing Utilities the graphing utility to enhance the study of mathematics. Technology is used as a tool to solve problems, motivate concepts, and explore mathematical ideas. Sullivan's Series Enhanced with Graphing Utilities provides clear and focused coverage. Many of the problems are solved using both algebra and a graphing utility, and the text illustrates the advantages and benefits of each approach. Technology is used to solve problems when no algebraic solution is available and to help students visualize certain concepts. Topics such as cur... MOREve fitting and data analysis and ClBL projects are incorporated as appropriate. Written by the authors while using graphing utilities in their own classrooms, these texts fully utilize graphing utilities in order for students to explore and discover important precalculus concepts. This series combines the successful writing style of the authors with cutting edge technology. Professors and students alike will find that these texts present the material at the correct pace -- with an appropriate emphasis on the technology as a tool and mathematics as the subject.
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A hiker finds himself overexerted after he reaches the summit of Mount Algebra and radios for help. Two hikers converge and then work together to get down the mountain and meet the paramedics.
This poster accompanies an assessment (available separately) that is an exercise in writing functions from context and using tables, graphs, and equations to provide an extended solution to a problem scenario. It includes both independent and collaborative elements and takes students directly to the heart of drafting meaningful solutions: a solution to a problem illustrates, generalizes, communicates, and verifies the results; an answer is just a number.
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Algebra
Algebra is perhaps best defined as the study of "algebraic structures." Broadly construed, algebraic structures are sets endowed with additional operations—think of the integers (a set) with addition and multiplication (additional operations). Usually, these operations allow elements to be combined in some way, but sometimes they're better described as allowing transformation of elements into each other—as, for instance, in the case of the category of sets endowed with the usual mappings between sets. Such structures are ubiquitous: integers and their various extensions, the vector spaces you studied in linear algebra, groups of transformations that encode symmetries, abstract categories that capture relationships between complex objects (like groups themselves) are all examples. Due to this ubiquity, algebra crops up in all areas of mathematics and has a host of applications.
The first two structures you are likely to encounter are groups and rings. In general, groups should be thought of as collections of transformations. That's because objects in a group can be composed (usually called "multiplication") and inverted, just like functions, but nothing else is required for a set to have the structure of a group. Groups are important and beautiful objects. For instance, the set of all invertible linear transformations of a vector space to itself is a group, as is the set of all rotations of space (of any number of dimensions). These examples also illustrate the interpretation of groups as symmetries of some other mathematical entity—in this case, a vector space. Groups also play this role in the setting of permutations (symmetries of finite sets), geometric rearrangements of shapes (symmetries of polygons), and Galois theory (symmetries of number systems).
This last example shows how groups can be connected to their more sophisticated cousins, rings. While a ring can be thought of as a group with additional structure, a ring is really a very different animal. Rather than functions and transformations, rings represent numbers. In this case, you can add them, take their negatives, and multiply them—but that's it. Since many natural number systems lack division (is one divided by two an integer?), it is excluded from the defining properties of rings. When a ring has it anyway, it is called a field—thus, we speak of the "ring of integers," but the "field of rational (or real, or complex) numbers." Rings serve as a natural generalization of the integers, and they provide a setting for the study both of abstract objects that resemble them and concrete number systems extending them, like the rational numbers, or the set of all numbers of the form a + b √5 with a, b integers.
Now, all of this is just the beginning. We haven't even mentioned the question of commutativity, or the fact that there is a natural way to think of rings as collections of functions (just ask an algebraic geometer). Nor have we really discussed the rich theory that results in studying the way algebraic objects interact with other mathematical entities. Nor the details of Galois theory. Nor categories. The list goes on and on. But Princeton offers many ways for you to get into these and other algebraic topics. This begins with an introductory sequence that starts with groups, develops the fundamental aspects of the theory behind them, then builds up elementary ring theory and the most important parts of classical Galois theory.
After you've completed the introductory sequence, you will be adequately prepared to jump into the more advanced courses that investigate the topics we've mentioned above.
Introductory Courses [Show]Introductory Courses [Hide]
Princeton's introductory algebra courses cover the three basic algebraic structures: groups, rings, and fields. A group is a structure with one binary operation, such as the set of permutations of {1, 2, …, n}, with the binary operation being composition. A ring is a structure with addition and multiplication, such as the set of polynomials with real coefficients. A field is a ring where each nonzero element has a multiplicative inverse, such as the set of real or complex numbers.
In the past, Princeton introduced students to algebra through two courses. One of these (MAT 323), was a basic course covering groups, rings, and fields. The other (MAT 322), focused more on rings and fields, and also covered Galois theory. However, Princeton has restructured its introductory algebra courses. Now, there will be a two-semester algebra sequence. Algebra I will mainly focus on groups, and will also cover some representation theory. Algebra Ii will cover ring theory, field theory, and Galois theory. No further information is available at this point, but please check the math department's undergraduate page for announcements.
Advanced Courses [Show]Advanced Courses [Hide]
What to take before? Introductory Sequence.
What to take after? Class Field Theory, Local Fields
What to take before? Algebraic Number Theory. MAT 447: Commutative Algebra
Please check registrar's page or math department website for information on this course.
What to take before? Introductory Sequence.
What to take after? Introduction to Algebraic Geometry What to take before? Commutative Algebra (not absolutely necessary)braelling semester.
What to take before? Commutative Algebra (a must).
What to take after? You'll be ready for anything tablesof
What to take before? Introductory Sequence th
What to take before? Introductory Sequence
What to take after? Algebraic Number Theory, Class Field Theory.
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essment
Patterns Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems, using algebraic language and skills.
We know this when the learner:
2.1 investigates and extends numerical and geometrical patterns to find relationships and rules, including patterns that:2.1.1 are presented in physical or diagrammatic form;2.1.2 are not limited to series with constant difference or ratio;2.1.3 occur in natural and cultural contexts; 2.1.4 are created by the learner him/herself;2.1.5 are presented in tables;2.1.6 are presented algebraically;
2.2 describes, explains and justifies observed relationships or rules in own words or in algebra;
2.3 represents and uses relationships between variables to determine input an output values in a variety of ways by making use of:2.3.1 verbal descriptions;2.3.2 flow diagrams;2.3.3 tables;2.3.4 formulas and equations;
2.4 builds mathematical models that represent, describe and provide solutions to problem situations, thereby revealing responsibility towards the environment and the health of other people (including problems in the contexts of human rights, social, economic, cultural and environmental issues);
2.7 is able to determine, analyse and interpret the equivalence of different descriptions of the same relationship or rule which can be represented:2.7.1 verbally;2.7.2 by means of flow diagrams;2.7.3 in tables;2.7.4 by means of equations or expressions to thereby select the most practical representation of a given situation;
2.8 is able to use conventions of algebraic notation and the variable, reconcilable and distributive laws to:2.8.1 classify terms like even and odd and to account for the classification;2.8.2 assemble equal terms;2.8.3 multiply or divide an algebraic expression with one, two, or three terms by a monomial;
2.8.4 simplify algebraic expressions in bracketed notation using one or two sets of brackets and two types of operation;2.8.5 compare different versions of algebraic expressions having one or two operations, select those that are equivalent and motivate the selected examples;2.8.6 rewrite algebraic expressions, formulas or equations in context in simpler or more usable form;
2.9 is able to interpret and use the following algebraic ideas in context: term, expression, coefficient, exponent (or index), basis, constant, variable, equation, formula (or rule
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A friend just made this statement to me, "this is sort of like Newton and calculus. He had a problem for calculus to work, it had to occur outside of time. Up until then, change had to involve a passage of time. So he invented a new law that said change could take place outside of time and then his whole... more »
I"m looking for the right cable to enable my TI86 to link with my laptop - Walmarts website says the TI Connectivity USB Cable is the right one but Amazons website site says this is not compatible with the TI 86 - so who is right?
Hi, I need help to figure how to do this problem: 10 x 1:12. My goal actually is to find the height of a ramp where the slope of each section is 1:12 (what does that mean?) and the base is 10.00 m. Thank you, Tone
Hello, [link] has some new opensource education software releases. These include: Math Scrabble (Windows/Linux) Math Crossword Builder (Firefox Web Browser, IE) Multiplication Station These are free packages and have recently had support added for multiple user accounts to accomodate classroom... more »
Hello, I am a new teacher. I am teaching a class called Foundations of Math for 9th graders who are not ready for algebra. I have a small class size of 17 students. All of my students are ELL and most are having a hard time with even the basic concepts of math. My big problem is that the book is terrible and there is no curriculum... more »
I have been doing research on the use of standardized curriculum in the classroom with the hope of implementing it into my personal teaching strategies and philosophies. Standardized curriculum provides a uniform education for all students in the classroom, and it also keeps teachers on a strict lesson plan with little to no room for deviation.... more »
Posted general 1st grade math requirements here [link] Posted general 2nd grade math requirements here [link] Hope this helps some out...we have been putting up a few printables and lesson plan ideas for Kindergarten and under Geometry...Trig is soon to... more »
It is not often that a new theorem of exquisite simplicity arrives - least of all in the context of Pythagoras. The world is vast, and time has aeons - so perhaps some other has made the same discovery. However, to me, and everyone I know this is a new discovery. It begins with the 3 4 5 triangle. You know - you create a square on side 3, add the square on side 4 and... more »
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revolutionary text covers single-equation linear regression analysis in an easy-to-understand format that emphasizes real-world examples and exercises. This intuitive approach avoids matrix algebra and relegates proofs and calculus to the footnotes. Clear, accessible writing and numerous exercises provide students with a solid understanding of applied econometrics. This new approach is accessible to beginning econometrics students as well as experienced practitioners. "A. H. Studenmund's practical introduction... MORE to econometrics combines single-equation linear regression analysis with real-world examples and exercises. Using Econometrics: A Practical Guide provides a thorough introduction to econometrics that avoids complex matrix algebra and calculus, making it the ideal text for the beginning econometrics student, the regression user looking for a refresher or the experienced practitioner seeking a convenient reference."--BOOK JACKET.
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's Them Engaged. Keep's Them Engaged Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly so they don't get "lost" when studying and reviewing. First, he gets students engaged in the study of mathematics by highlighting truly relevant, unique, and engaging applications. He explores math the way it evolved: by describing real problems and how math explains them. In do... MOREing so, it answers the question "When will I ever use this?" Then, Blitzer keeps students engaged by ensuring they don't get lost when studying. Examples are easy to follow because of a three-step learning system - - "See it, Hear it, Try it" embedded into each and every one. He literally "walks" the student through each example by his liberal use of annotations - - the instructor's "voice" that appears throughout.
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Devon Parham has no soul. Sitting in this class is like having a robot teach you the basics of discrete mathematics while your eyelids grow heavy with the weight of the world. She literally teaches you "by the book" and makes no attempt to make the material interesting or engaging in any capacity. In a nutshell, she's only as good as the book is, which isn't saying much because it's boring in the first place... just like her. The amount of homework she assigns is reasonable and her tests aren't terribly difficult. It's just that her class is basically a powerful sedative continuously injected into your bloodstream for ten weeks.
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Introduction to Engineering Math, Preliminary Edition
Rattan's Introductory Mathematics for Engineering Applications is designed is to improve student retention, motivation and success through application-driven, just-in-time engineering math instruction. It is intended to be taught by engineering faculty, not math faculty, so the emphasis is on using math to solve engineering problems, not on derivations and theory.
The book is a product of four NSF grants to develop and disseminate a new approach to engineering mathematics education. The authors have developed a course that does just this, and have recruited faculty at more than two dozen institutions to pilot aspects of this course in their own curricula. This approach covers only the salient math topics actually used in core engineering courses, including physics, statics, dynamics, electric circuits and computer programming. More importantly, the course replaces traditional math prerequisites for the above core courses, so that students can advance in the engineering curriculum without first completing the required calculus sequence. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math, and has had an overwhelming impact on engineering student retention.
Ideally, this text will serve as a a primary text for a first-year engineering math course, which would allow students to advance through the first two years of their academic program without first completing the required calculus sequence.
This course doesn't replace calculus. It simply allows students to advance through introductory engineering courses while they gain the maturity and motivation to succeed in calculus at a slower pace.
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Introduction to GeoGebra
GeoGebra is a dynamic mathematics software that integrates algebra, geometry, calculus, and statistics. It is capable of displaying data simultaneously: numerically, graphically, and algebraically. GeoGebra was created by Markus Hohenwarter in 2001. It has become an open-source software and is continually improved by programmers, mathematicians, and mathematics teachers around the world.
The diagram below is a screen shot of GeoGebra 4.2. The arrangement of buttons in other versions may slightly differ. Its latest version can be downloaded from All versions need a Java Virtual Machine that can be downloaded from If you want to get the latest and complete installation package (includes Java), download GeoGebra Webstartotherwise you also need to download and install Java separately.
The GeoGebra Window
The GeoGebra window is shown in the first figure. The leftmost pane is the Algebra view, where algebraic descriptions of objects on the Graphics view are displayed. The Graphics view is where constructions, drawings, and graphs are displayed. By default, the Coordinate axes are displayed when you open GeoGebra.
The uppermost part of the window is the Menu Bar. The menu bar is used for managing files, editing files, and modifying settings. Below the menu bar is the toolbar where tools for drawing, constructing, measuring, and manipulating objects are shown. The input bar is used for typing equations, algebraic commands, and computations.
The coordinate axes, the algebra window and the input bar can be displayed or hidden using the View menu.
To know more about GeoGebra, you can browse the Help menu after finishing this tutorial.
The Toolbar and the Tools
The toolbar contains the tools that are used to construct objects such as points, lines and other figures. Shown below are the categories of tools and the default tools displayed.
In the diagram above, the Move tool is highlighted by a blue border which means that it is the active tool. As long as a certain tool is active, it will construct the same drawing or perform the same task. You do not need to click it every time you construct the same object.
The icon of each tool has a triangular arrow located at the bottom-right of the tool that you can click if you want to display other tools. The third figure displays the tools if you click the Line through two points button.
If you want to draw a Ray through two points, you just have to click the arrow at the Line through two points tool then click it as shown above. The line icon will be replaced by the ray icon, which means that the latter is now active.
If you have clicked the Ray tool, we say that GeoGebra is in the ray mode. To deactivate the active tool, click Move tool or click the other tools.
Click here to go to GeoGebra Tutorial 1 and click here to view the list of my GeoGebra Tutorial Series.
Right click the blank space of the drawing pad, select Graphics view from the context menu. This will display the Graphics View dialog box. Be sure that the Axes tab is selected, then select the y-Axis tab (that is a tab with in a tab), then remove the check from the Check box button and click the Close button. Hope this helps.
Could you make all tutorials available on pdf format, please? I would like to print them all so that I can try one by one without having to flip from one screen to the programme screen and vice-versa. Many thanks.
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Starting at $19Normal 0 false false false KEY BENEFIT: TheBittinger Concepts and Applications Seriesbrings proven pedagogy to a new generation of students, with updates throughout to help todayrs"s students learn. Bittinger transitions students from skills-based math to the concepts-oriented math required for college courses, and supports students with quality applications and exercises to help them apply and retain their knowledge. New features such as Translating for Success and Visualizing for Success unlock the way students think, making math accessible to them. KEY TOPICS: Algebraic and Problem Solving; Graphs, Functions, and Linear Equations; Introduction to Graphing; Inequalities and Problem Solving; Polynomials and Polynomial Functions; Rational Expressions, Equations, and Functions; Exponents and Radicals; Quadratic Functions and Equations; Exponential and Logarithmic Functions; Conic Sections; Sequences, Series, and the Binomial Theorem MARKET: For all readers interested in algebra.
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Mathematics
Mathematics is a useful, exciting, creative and vital area of study that is taught and explored by faculty who foster an appreciation and sense of enjoyment for all students.
The rigorous and varied curriculum provides opportunities for students to develop their abilities to solve problems and reason logically.
The curriculum offers courses of study, which will enable students to explore and make sense of their world. The study of mathematics is an ongoing process that will extend to and enhance every facet of the students' lives.
As students reach the junior high years, their course placement will be determined by a variety of assessment tools. In 7th grade, students take Pre-Algebra at either the college placement or honors level. Occasionally 7th grade students are placed in Algebra I Honors. Most eighth grade students follow the progression to Algebra I or Algebra I Honors, while those students who successfully complete Algebra I Honors in 7th grade move to Geometry Honors.
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Generally, curved objects are beautiful but complicated. Differential geometry will help us to describe, understand, and make them. In this course, we will introduce tensor, nonlinear deformation of 3D objetcs, and reduced from it, due to the their geometry sepearations, the theory of elastica, plates and shells.
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Where do I start?
Choosing a first course in math or computer science
Find your programming background across the top, and your math background
down the left hand side, of the following table. The table entry
where they cross will tell you what math course and what CS course to take
first.
Programming background
Little or none
Half a year
w/grade of B
or better
4 on AP CS AB,
or 5 on AP CS A
5 on AP
CS AB exam
Math background
"Hate math",
took very little
MTH 101/102
MTH 101/102
MTH 101/102
MTH 101/102
CSC 160
CSC 171
CSC 172
see advisor
Haven't taken
pre-calculus
MTH 110/140
MTH 110/140
MTH 110/140
MTH 110/140
CSC 160
CSC 171
CSC 172
see advisor
Took
pre-calculus
Under 15/25 on
dept. placement test
MTH 110/140
MTH 110/140
MTH 110/140
MTH 110/140
CSC 160
CSC 171
CSC 172
see advisor
At least 15/25 on
dept. placement test
MTH 141
MTH 141
MTH 141
MTH 141
CSC 171
CSC 171
CSC 172
see advisor
4 on AP Calculus BC
or 5 on AP Calculus AB
MTH 142
MTH 142
MTH 142
MTH 142
CSC 171
CSC 171
CSC 172
see advisor
5 on AP
Calculus BC exam
see advisor
see advisor
see advisor
see advisor
CSC 171
CSC 171
CSC 172
see advisor
MATH 101 and 102 are independent courses; you may take either or both,
in either order. They are not remedial courses on math skills, but
conceptual courses intended to demonstrate, through interesting real-world
applications, the usefulness of mathematics and mathematical notation,
particularly for students who "hate math". Those considering computer
science or physical science will find MATH 101 particularly useful.
MATH 110 and 140 are both referred to as "Pre-calculus", but MTH 140 goes
a little bit faster and includes trigonometry. Students planning
to major in math, computer science, or physics must take MTH 140; those
majoring in most other subjects may take either one.
Students planning to major or minor in math or computer science, as well
as those who have always liked math but don't like calculus, should also
take CSC/MTH 156 some time in their first few semesters.
CSC 160 is primarily for students who have never written a program before;
it uses the simpler Scheme language in order to concentrate on concepts of
programming rather than language syntax.
Those with a strong background in math or programming (e.g. in Java or C++)
may take it if they wish, or may skip it and go straight to CSC 171.
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Riverdeep Mighty Math Astro Algebra Lab Pack
Product #: 1731
Company: Riverdeep Grades/Ages: Ages 12-15 Platform: PC/MAC
Astro Algebra teaches the concepts and problem-solving skills necessary to learn basic algebra. Students learn how to graph functions, translate word problems into solvable equations, and represent algebraic expressions using the Edmark® Virtual Manipulatives®. Hundreds of problems in over 90 space missions provide students with a solid foundation for success in algebra and beyond.
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MAA Review
[Reviewed by Allen Stenger, on 09/15/2008]
This book takes the "complex variables" view of elliptic curves. It uses a particular number-theoretic problem to drive the discussion: the problem of characterizing congruent numbers. A congruent number (no relation to congruences modulo a number) is defined as a number that is the area of a right triangle with all sides rational. Thus 6 is a congruent number because it is the area of the familiar 3-4-5 right triangle. There is an equivalent formulation in terms of whether the elliptic curve y2 = x3 - n2x has rational solutions. This enables us to bring the powerful machinery of elliptic curves to bear on the problem, and the book develops that machinery and culminates with a proof of Tunnell's (almost complete) characterization of congruent numbers.
I like the method of using a single difficult program to organize a book. I think it is not completely successful here, because the original problem drops out of view in the middle of the book, with many new concepts being introduced that are not clearly driven by it. The book travels though L and zeta funtions, elliptic functions, and modular functions and forms.
Silverman and Tate's Rational Points on Elliptic Curves is a very different approach to elliptic curves, through abstract algebra and geometry. There is surprisingly little overlap between the two books, considering that they are introductions to the same subject. Koblitz is much faster-paced, and contains a lot of intricate arguments. It covers a much larger amount of material and requires more mathematical maturity (it is correctly placed in Springer's Graduate Texts series, while Silverman and Tate is in the Undergraduate Texts series). I like both books, but I think Silverman and Tate is a better introduction.
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.
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weighted grade calculator Searches Results
The ultimate mortgage
spreadsheet calculator. The first Windows upgrade of the Matrix Calculator
orginally included with the F.L.A.P. mortgage software. Calculate payments,
loan amounts, terms, or interest rates on up to a 50x50 scrollable grid.
Twelve different configurations available for monthly and biweekly
mortgages. Generate loan summaries a... d... multi-plot/tabulate a function; solve 1-6 equations, minimums, maximums and definite integral of 2D/3D funct...
RMRUtils provides a fully featured calculator, but also quick and easy conversion between all common and (many, many less common) unit values, such as area, length, energy, speed and volume units, temperature scales, number formats. The program can also calculate dates, journey times, VAT and can suggest lottery numbers. Finally it offers infor...
It calculate...
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• composition book (to be used as a journal) • 2" or 3" binder • 10 dividers for the binder (to be used for English I and freshman seminar) • planner (provided by the school) • blue or black pens • #2 pencils • glue • red pen • highlighter(s) colored pencils or markers
All math classes require a graphing calculator. The following models are suggested:
TI-83 Plus or Silver Edition
TI-84 Plus or Silver Edition
TI-89 (*Calculus Only)
Casio fx-9750GII or fx-9860GII
(The calculators may be purchased at Office Depot, Office Max, Staples, Walmart, Target, Best Buy, etc. and are often on sale during the summer "back to school" promotions. You may also find a deal at a pawn shop or online through E-Bay!)
Parents, please click here to find out why graphing calculators are important to your child's success in math.
The most important supply needed for math is a graphing calculator. It is ESSENTIAL that students have one of these to use in class and at home. If they rely on the few calculators that the school can provide for in class use, they will have nothing to use at home. As a result, they will not be able to complete their homework properly. This means that they will not get the needed practice time and their chances of doing well in math diminish drastically. Be sure to read the note
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Algebra 1 Solving Equations Test test covers solving all types of equations, solving literal equations, and word problems that involve rate, time, and distance, consecutive integers, and perimeter. This test has 23 questions. Elizabeth Welch
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
173.71
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MAA Review
[Reviewed by Ana Momidic-Reyna, on 01/03/2011]
This book illustrates various elementary topics in number theory: irrationality and diophantine approximation, continued fractions and regular continued fractions, Euclidean domains, quadratic fields, primes and irreducibles, and Diophantine equations. The reader discovers the problem of representing numbers as sums of squares and learns about Padé approximants. There is a complete chapter devoted to different representations of real numbers.. Additionally, the book offers an introduction to exciting subjects in algebraic number theory. The last chapter focuses on different transcendence methods developed by Gelfond, Mahler, Schneider and Siegel.
The author combines rigor with clarity flawlessly, captivating the reader with the elegant simplicity of his prose. The methods used are deep and diverse. The book is both well written and pragmatic, while its material is pedagogical and comprehensive. There are clear explanations, concise definitions, and plenty of exercises along with their solutions.
There are twelve chapters, some of which are independent of each other. In every chapter one comes across a real gem. For example, the book discusses the famous problem of squaring the circle; the chapter contains the proof of Liouville's famous theorem, talks about cyclotomic fields, and deduces the the Padé approximants of the exponential function by the means of confluent hypergeometric functions. There is even an explanation of how Padé approximants yield good Diophantine approximations and irrationality results.
Each chapter contains carefully and appropriately selected exercises that help the reader understand the theory better. They should not be skipped! Complete solutions can be found at the end of the book. Many of the solutions introduce/define additional concepts related to the topics of that particular chapter or are given along with examples and important remarks which complement them. The book contains exercises with the well-known: Möbius function, the Riemann zeta function, Dirichlet series, the Legendre symbol, etc. The reader will find them engaging, well-thought-out, and genuinely entertaining. In addition, the examples given throughout the book are both relevant and illuminating.
Originally written in French, the book has been translated into several languages, including in Japanese and English. The exhibition of the beauty of the number theory, achieved on the basis of its own simplicity and clarity, is one of the best features of this book. However, the reader should have previous knowledge of abstract algebra, calculus, and complex analysis. Thus, the book is well-suited for graduate and advanced undergraduate students. This is a fantastic and very useful book, although I would have not minded seeing a list of suggested further reading. I would highly recommend it to everyone who is seriously interested in number theory.
A native of Macedonia, Ana Momidic-Reyna has an M.S. in Mathematics and has also worked for the high energy physicists at Fermilab. While waiting for the opportunity to work on her Ph.D. in mathematics, she keeps up with the field by reading as many mathematics books as she can.
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Basic Mathematics for Grade 9 Algebra and Geometry: Graphs of Basic Power and Rational Functions
The main reason I write this book was just to fullfil my long time dream to be able to tutor students. Most students do not bring their text books at home from school. This makes it difficult to help them. This book may help such students as this can be used as a reference in understanding Algebra and Geometry.
show more show less
Edition:
2012
Publisher:
Textstream
Binding:
Cloth Text
Pages:
544
Size:
6.50" wide x 9.25" long x 1.50 Basic Mathematics for Grade 9 Algebra and Geometry: Graphs of Basic Power and Rational Functions - 9781426997662 at TextbooksRus.com.
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Students don't know what quantity in a graph will answer the
question (coordinate, slope, or area).
(discover)
Many students lack the knowledge of exactly what
information the coordinate value, slope, or area under a graph
provides. This causes them to look for obvious features on the
graph to answer questions, regardless of the pertinence of those
features.
Students have difficulty relating real world motions to a graph
and vice-versa. (discover)
Many students lack the ability to properly graph the
position, velocity, and/or acceleration of an object whose motion
is exhibited for them. Likewise, they lack the ability to
demonstrate the motion represented by a position, velocity, and/or
acceleration graph given to them.
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Numerical Methods with VBA Programming provides a unique and unified treatment of numerical methods and VBA computer programming, topics that naturally support one another within the study of engineering and science. This engaging text incorporates real-world scenarios to motivate technical material, helping students understand and retain difficult and key concepts. Such examples include comparing a two-point boundary value problem to determining when you should leave for the airport to catch a scheduled flight. Numerical examples are accompanied by closed-form solutions to demonstrate their correctness. Within the programming sections, tips are included that go beyond language basics to make programming more accessible for students. A unique section suggest ways in which the starting values for non-linear equations may be estimated. Flow charts for many of the numerical techniques discussed provide general guidance to students without revealing all of the details. Useful appendices provide summaries of Excel and VBA commands, Excel functions accessible in VBA, basics of differentiation, and more!
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Elementary Algebra (7.5 ECTS credits)
The aim of the course is that the student should acquire basic skills in algebra, with focus on the logic structure of mathematics, proofs and how mathematical theory is constructed.
Algebraic expressions and inequalities, basic logic and set theory, relations and functions, proofs by induction, elementary number theory, complex numbers, polynomials and equations, linear systems of equations and matrices, geometrical vectors in plane and space, and determinants, are subjects dealed with in the course.
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Math Function Mania Math Function Mania is a fun multimedia game that teaches functions, algebra and problem solving skills. Functions are very important in math! By mastering them, you will greatly increase your math skills. This game teaches you by the "hands on" method - you will discover how functions work by... Topics covered include equations, algebra, problem solving, critical thinking, polynomials, factoring, remainders, number bases, and prime numbers. ... After mastering this program, your understanding of math will improve and your SAT math scores will benefit. - 877Kb
- Download - Screenshot
Talmagi Using... With the build-in editor, you can also design new puzzles. ... Handsome photo-quality graphic and a game focused on the gameplay. ... The operation of the game is simple. - 2Mb
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Brain Builder - Math Edition Brain Builder - Math Edition includes over 500 million problems presented in a fun multimedia format. Sharpen your problem solving and critical thinking skills by tackling math puzzles that are presented at precisely your learning level. The program includes Multiple Choice Warm-up games and... These Multiple Choice Warm-up games prepare you to play the Three, Four, and Five Number Puzzle games by making you familiar with using all of the operations of addition, subtraction, multiplication, and division in problem solving. - 109Kb
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Algebra Having trouble doing your Math homework? This program can help you master basic skills like reducing, factorising, simplifying and solving equations. Step by step explanations teach you how to solve problems concerning fractions,binomials, trinomials etc. ... Each type of problem has three levels to help you to start with easy problems and slowly building up your skills. ... Algebra has three different functionalities: you start learning each type of problem by seeing the program solve it step by step. - 895Kb
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EMMentor_Light Interactive multilingual mathematics software for training problem-solving skills offers more than 500 of math problems, a variety of appropriate techniques to solve problems and a unique system of performance analysis with methodical feedback. The software allows students at all skill levels to... Included are basic and advanced math topics, such as solutions of linear, quadratic, biquadratic, reciprocal, cubic and fractional algebraic identities, equations and inequalities, solutions of trigonometric and hyperbolic equations and more. - 3Mb
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Math Logic Math Logic 4. 0 ... 0,... - 6Mb
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Animated Arithmetic The ... Progressive help is given as needed when the student is having difficulty with a particular problem (not just a Wrong! ... Hints for solving the puzzles are available, or the child can have the computer solve the puzzle and enjoy the (mostly silly) animation. ftp://ftp.a-direct.com/adds/arith.zip - 6Mb
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Math Homework Maker The Math Homework Maker, is a FREE software which can solve all your Math homework. If you are a pupil or a student, needing help with your math homework or just want to check them,
Then you must have this software. The Math Homework Maker covers everything you need, from elementary school up to... Solving Quadratic Equation. ... Statistics Mean, Standard-Deviation ,Variance. ... And Much More. ... This software is so easy and friendly to use even if you are a parent who want to check your kids' homework, but have no knowledge at all in mathematics. - 409Kb
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Nottingham, PA GeometryAlgebra covers the basics of equation building and terminology. This is generally required as a prerequisite for other math courses and makes up a large percentage of standardized tests like the SAT or GMAT. Algebra 2 builds upon the basic algebra terminology and properties
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Microsoft Mathematics, Free Download
January 19 2011
Microsoft Mathematics provides a graphing calculator that plots in 2D and 3D, step-by-step equation solving, and useful tools to help students with math and science studies.
Microsoft includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equations.
Instructions
To install this download:
1. Download one of the files by clicking the Download button next to the appropriate MSetup.exe file (depending on the version you are interested in), and save the file to your hard disk.
2. Double-click the downloaded program file on your hard disk to start the Setup program.
3. Follow the instructions on the screen to complete the installation.
Instructions for use:
After you install this application, you can find it among your other programs under the name "Microsoft Mathematics".
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If you wish to create a complex expression with random elements, you do not need to create it as a single WIRIS variable. Say you want to create an exercise with an integral sign in the wording. You will want to make sure that the integral will not be evaluated and that it will not be shown in two different lines. Then you can make use of the following WIRIS quizzes feature.
You can add variables into a WIRIS editor expression. For example, you may define an integralRight under the Algorithm field, there is a drop-down list where the available languages are listed.
This page is related to WIRIS quizzes version 1.
Check our bank of examples in a demo Moodle. In it, you will find dozens of questions organized in different maths areas. It will be useful to grasp some ideas on the use of the tool for a specific type of question, and also to see programming examples in WIRIS cas.
If you want to access the platform in English, you can use the following accounts, depending on if you wish to access as a teacher (not editor) or as a student.This type of question does not allow the automatic evaluation of the answer, and so WIRIS quizzes supplies only the added value of permitting a wording containing random values. To discover how to insert randomness in an essay type of question, check the Randomness section of this manual.
1 Introduction
The Embedded answers (or Cloze*) type of question permits to embed the answer fields among the text of the question. That is to say, subquestions are created within a question, and logically, the types of subquestions can be combined. Subquestions can be Short answer, Multiple choice or Numerical in type.
The grading function can also be used in case of a Compound short answer type of question. In order to see the normal functioning of the functionality, check the Grading function in simple short answer section.
We will see an example of use of the functionality for this case. We will request the student to insert four numbers of different types, as stated by the wording:
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Mathematical Typesetting
Developed at Wolfram Research over nearly 20 years, Mathematica has by far the world's most sophisticated and convenient mathematical typesetting technology. Generalizing the concept of a computer language to allow 2D input, Mathematica allows both interactive and programmatic entry of arbitrarily complex typeset expressions, with publication-quality layout continuously maintained in real time.
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Math Welcome 122 Survey of Calculus and its Applications I1
Instructor: Quanlei Fang
Dept. of Math, University at Buffalo, Spring 2009
Instructor contact Information Text Grading In-class work/ Hw / Tests Make-up policy Special needs
Come to lectures regularly Do homework regularly Go to recitations regularly Prepare for the quizzes / tests Mark the test dates Make friends and help each other
Calculus is the study of change. In particular, it looks at the rates in which quantities change (i.e., areas, volumes, distances, etc.). It was developed in the later part of the 17th century by Gottfried Leibnitz and Isaac Newton.
The two key areas of Calculus are Differential Calculus (having a quantity and finding the rate of change) and Integral Calculus. (knowing the rate of change and finding the quantity)
The big surprise is that these two seemingly unrelated areas are actually connected via the Fundamental Theorem of Calculus.
If you choose a career path that requires any level of mathematical sophistication, you will need Calculus.
To succeed in Calculus (and Mathematics in general) you must be able to: solve problems, reason logically and understand abstract concepts..
Function a set of ordered pairs (x, y) such that for each x-value there is one and only one y-value. y = f Domain (x) of a function the set of all xs that we can input into the function. Range of a function all images y of all of the xs. Vertical line test Is it a function a not? If any vertical line intersects the graph more than once, then the graph is not a function.
Polynomial
y = x 5 , y = ( x + 10) 4 x 7
Algebraic
y = x + 4,
y = x , y = (x + 1) e
2 5
Rational
y=
x+6 2 , y= x2 + 5 x+4
Exponential and Logarithmic
x x x +4 y = e , y = 2 , y = 2e
y = ln(4 x 2 + 5)
Piecewise y= x Trigonometric* Inverse Trigonometric*
Linear function Quadratic function Cubic Function Absolute Value Function
y= x
Rational
Exp & Log
Differential Calculus
15 y
10
5
x -6 -4 -2 2 4 6 8
-5
Based on the rate of change of one variable in comparison to another. For example if y=x3 , we talk about the rate of change of y in comparison to x. Another example: if t=time and s= the distance travelled and s and t are related by the equation s=2t2+5. We then talk about the rate of change of the distance with respect to time.
Derivative Limit
as slope formula
definition of derivative
f '( x) = lim
h 0
f (x + h) f ( x) h
How
to compute derivatives
Applications
About Office hrs: Please write down your preferred time spots. For example, one spot could be: Monday 11:00am-11:50Welcome toMath 122 Lecture 4 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Group workYou will have 4 problems based on MTH 121. Form a group (no more than 3 for each group) a
Welcome toMath 122 Lecture 5 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Chapter 7 Functions of Several VariablesLast timeExamples of Functions of Several Variables 7.2
Welcome toMath 122 Lecture 10 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009!Integration by SubstitutionIf u = g(x), then 9.2Integration by Parts!Integration by Part
C-037_2006_IBC.titlepage.qxp12/12/200511:00 AMPage 1A Member of the International Code Family INTERNATIONAL BUILDING CODE2006Color profile: Generic CMYK printer profile Composite Default screen2006 International Building CodeFirst Printing: Janua
AD-AS analysis 10) Which kind of problem with the price system can lead to a break down in the coordination of economic activity? A) The price system works silently in the background. B) Prices can be slow to adjust. C) Prices may be flexible. D) all
Introduction to Economics 5) Because resources are limited: A) only the very wealthy can get everything they want. B) firms will be forced out of business. C) the availability of goods will be limited but the availability of services will not. D) peo
Ec 100FIRST MIDTERM SAMPLEName_ 1. Typical written questions are to discuss: A free market is great for society; what is it that free markets are bad at doing? Non-market systems of allocation; What makes a price elasticity high or low? Etc. (Not
Demand and Supply Most used concepts in economics Demand and supply are the forces that operate in the market to make it work. Microeconomics is about demand, supply, and market equilibrium.Copyright 2004 South-WesternMARKETS Where buyers an
Lecture 2Graphic Vocabulary Symbols Plan Views Elevations Sections and DetailsSymbolsIn construction drawings, standard symbols are used to show various construction materials and building elements such as plumbing fixtures & fittings, electr
Hong Kong International AirportGroup 6 Habacuc Flores, Mehrnaz Golzar, Kolotita FueIntroduction Why was it built? Who designed and constructed it? When was the airport started and completed? How much did it cost? The airport was constru
Civil Engineering ProgramCurriculumAccreditation ABET - Accreditation Board for Engineering and Technology Engineering programs must demonstrate that their students attain (Outcomes a through k): a) an ability to apply knowledge of mathematics
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MODERATORS
I'm currently an undergraduate math major and taking my first proof based class this quarter (linear algebra). Sadly, I am doing absolutely abysmally in the class and I have no idea why.
I enjoy math, in the sense that I like thinking about it and reading about it, and as a result I chose to study it. Additionally a big part of why I chose to declare math as my major was due to the ease with which I got through my computational lower divs. I am at a loss currently as to whether my failure to perform well is a result of me not putting enough work into studying, or whether I simply can't get it, or if I am not studying in the right way, or whatever.
If I could get some insight into the nature of undergraduate math studies I would greatly appreciate it. Has anyone else run into this kind of problem before?
When you're doing pure mathematics, it's all about understanding concepts well enough to prove theorems about them. Proof-writing itself takes a lot of practice to get good at, but you'll pick that up as you go.
However, learning the language and conventions of formal proof is only one part of it. Now that you're not just doing computation, you'll find that it's no longer enough to memorize formulas and theorems; coming up with a proof often requires insight, creativity, and intuition.
Surface-level understanding of the statements given in class will generally not be enough. Many times, I've done the reading, known all the relevant theorems, and followed their proofs, onlyWhen you get stuck like that, it means you need to do more problems. Reading is good, but it's not enough; the best way to get better in an area of math is to do problems yourself, and by that, I mean writing up the whole proof in a reasonable formal way, not just outlining an argument. If your method of studying just consists of reading or memorizing, you'll have a hard time gaining a deep understanding of the structures and patterns involved.
Of course, that's not to say you should do nothing but book problems for studying. Get help when you need it, and assuming the professor's okay with it, consider working with your peers on some problems -- not the whole proof, but enough so you grasp the basic parameters of the problem and the reasoning needed. But if there's one single thing that will improve your proof skills, it's this: pick a problem, think about it for a while, and prove it on your own.
Also, here's a bit of advice specific to linear algebra: If you're not already using Axler's Linear Algebra Done Right, I highly recommend it. He has a very well-written, straightforward presentation of the basics of linear algebra, and his proofs are generally elegant and informative. It's also a good source of exercises to try and figure out.
onlyAs a first year PhD student this is what I have spent a lot of my time doing, filling in gaps in my knowledge. I am however comfortable enough now to identify where the holes in my knowledge are and backtrack until I do understand what I need to, which is really fun.
I'm also currently in Linear Algebra, and I struggled a lot with it at first, but my biggest problem came from not seeing any applications. My professor refuses to do any applications, and I honestly feel as if I've just been manipulating symbols all semester, not really understanding the big picture. Not having something to relate the material to can make things significantly more difficult, especially for someone who is just experiencing abstract algebra for the first time. You aren't always going to understand the material the first time through, so don't be so hard on yourself and keep at it. Here are some things that helped me:
Chapter Zero - Just an intro. Also, a strange explanation for why he's in the past teaching Math to some king.
First Three Chapters are just review of matrices, inverses, transposes. Basic stuff that you should know before he can get into the course. We never did that in the course, it was meant to be "Read if you need it, but I won't lecture on it" material.
4 and 5 are all about vector spaces
6 is about bases.
7 is just a long proof for why the column space has the same dimension as the row space.
8 - Change of basis
9 - Determinants
10 - Eigenvalues, Eigenvectors and solving ODEs using them.
I also added in some of our exams and tests if you ever need them. If not, delete!
Personally, I find the way he introduced vector spaces really great. It gets slightly complicated and extra-rigorous towards the end. Understanding eigenvectors is better done on MIT OCW than through this textbook. But it's pretty rigorous for my standards.
I personally liked the fact that he didn't add COMMUTATION as an axiom for vector spaces, instead he proved it using the axioms.
Through that, he really drove home the concept of an axiom into everyone's head.
Disclaimer: This is meant to be an engineering math course. So, I apologize if it's not what you were looking for.
AFAIK its pretty common for students to struggle when first introduced to proofs after being used to more computational mathematics.
The general advice would be: Dont worry much about it if you are just starting. Practice a lot. Ask for help if you need, dont be shy about asking for help, ask your professor when in class if you dont understand, stalk your TA if its necessary ( however, be sure to think about the problem first, dont go just after you hit a wall each time, push your boundaries and think hard, be patient ). Check a lot of sources, from your notes, to different books to the internet, sometimes stuff clicks after you read it different than before.
Also, if you need help with some of the stuff you are struggling with you can PM me and I'll be glad to give you my email so we can talk.
I had pretty much the same experience. Up through calculus it's mostly memorizing a process and knowing where to apply it. In linear algebra, you're slammed with fundamentally new concepts and have to really understand their implications. I struggled, and I had the feeling that I was missing something, like it was a joke I wasn't in on. The only way to get better at it is to practice, unfortunately. But even if things don't click by the time you finish the class, you will walk away with a new perspective and as you continue to think in this way you will find all sorts of problems that linear algebra makes easy work of. It took me months after the class before I realized why I was learning what I was. Then, when the topics came up again in differential equations, things became even more clear. So I guess what I'm saying is, don't feel bad about hitting a point where math isn't just second nature anymore. It takes more and more study to get comfortable with topics as you go through higher and higher maths.
Can you explain a theorem to me? Is there something that you understand to such an extent that you could explain it to someone else, meeting their potential objections along the way?
Transitioning to proof-based mathematics is hard for everybody, not necessarily because they need to work harder (some do), but because they need to work differently and understand the core ideas. But it's worth it.
What kind of proofs are you doing? At my school my proof based linear algebra class did a great deal of proofs on matrix operations and stuff while barely covering vector spaces, dimensions, eigenvectors, and all the really cool stuff along with linear algebra. If you have a class like that, then push through it and things will get better.
I haven't taken linear, so take my advice with a grain of salt, but from what I understand, linear, even proof-based linear, is very different from other (IMO more legit) undergrad level math topics. I took Set Theory last semester; loved it. Real analysis this semester (yeah, without linear...I have no idea what a prereq is); loved it. Both were different from each other and from linear (on my understanding of linear).
As a professor, I see this all the time. Too many earlier courses are too much "plug-and-chug." Sadly, many students get the wrong impression of mathematics. They aren't forced to thinking abstractly, so they don't. Then they hit the upper level courses and the you-know-what hits the fan.
For immediate advice, all I can say is talk to your professor and keep trying. Make sure you understand everything. After reading a few proofs, close the book and do the proofs yourself. Alone. Don't rely on getting help from others until you've struggled with it yourself for a long time.
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Mathematics Years 10 - 11
The Mathematics curriculum in Years 10 – 11 is based on the University of Cambridge International general Certificate of Secondary Education (IGCSE). It aims to further develop the mathematical concepts and principles of the students. Students learn to apply Mathematics in other subjects, particularly science and technology and they acquire a foundation appropriate to their further study of Mathematics and other disciplines.
Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental in providing tools for understanding science, engineering, technology and economics. It equips the students with uniquely powerful ways to describe, analyse and change the world.
Mathematics is a creative discipline. The language of mthematics is international. The subject transcends cultural boundaries and its importance is universaly recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.
The Additional Mathematics Syllabus is intended for high ability candidates who have achieved , or are likely to achieve Grade A*, A or B in the IGCSE Mathematics examination. The curriculum objectives are therefore assessed at one level only (Extended).
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Intermediate Algebra + Text-Specific DVDs
ISBN10: 1-111-49154-2
ISBN13: 978-1-111-49154-3
AUTHORS: Kaufmann/Schwitters
INTERMEDIATE ALGEBRA employs a proven, three-step problem-solving approach—learn a skill, use the skill to solve equations, and then use the equations to solve application problems—to keep students focused on building skills and reinforcing them through practice. This simple and straightforward approach, in an easy-to-read format, has helped many students grasp and apply fundamental problem-solving skills. The carefully structured pedagogy includes learning objectives, detailed examples to develop concepts, practice exercises, an extensive selection of problem-set exercises, and well-organized end-of-chapter reviews and assessments. The clean and uncluttered design helps keep students focused on the concepts while minimizing distractions.
Problems and examples reference a broad array of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. Also, as recommended by the American Mathematical Association of Two-Year Colleges, many basic geometric concepts are integrated in problem-solving scenarios. The text's resource package—anchored by Enhanced WebAssign, an online homework management tool—saves instructors time while also providing additional help and skill-building practice for students outside of class.
Additional versions of this text's ISBN numbers
Purchase Options
List$226
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Integrated Arithmetic and Basic MESSAGE:Integrated KEY TOPICS: Adding and Subtracting Integers and Polynomials; Laws of Exponents, Products and Quotients of Integers and Polynomials; Linear Equations and Inequalities; Graphi... MOREng Linear Equations and Inequalities; Factors, Divisors, and Factoring; Multiplication and Division of Rational Numbers and Expressions; Addition and Subtraction of Rational Numbers and Expressions; Ratios, Percents, and Applications; Systems of Linear Equations; Roots and Radicals; Solving Quadratic Equations MARKET: For all readers interested in algebra and basic algebra. &> Integrated
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This outstanding text starts off using vectors and the geometric approach, featuring a computational emphasis. The authors provide students with easy-to-read explanations, examples, proofs, and procedures. Elementary Linear Algebra can be used in both a matrix-oriented course, or a more traditionally structured
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Overview: The word "discrete" means separate or
distinct. Discrete mathematics is the study of mathematical
objects that consist of separate pieces. This includes ssuch
topics as elementary number theory, which is the study of the integers,
graph theory, which is the study of relationships between finitely many
objects, and combinatorics, which uses mathematical techniques to
figure out how to count things without actually having to count.
Course Objectives:
To develop the ability to think abstractly and creatively about
mathematical and logical problems
To develop problem-solving strategies
To learn ways to communicate mathematics to a variety of audiences
To identify and use different methods of mathematical proof
To understand and use basic properties of the integers,
especially prime numbers and modular arithmetic
To explain and use the concepts of graphs and trees
To solve problems using counting techniques and combinatorics
Prerequisites: The formal prerequisite is MCS-121.
More to the point, you should be comfortable
with thinking algorithmically, discovering patterns, and applying
mathematical procedures to various types of problems.
Course web site: The best source of information about
this
course is available at
There you will find a
complete
syllabus,
course description, current homework assignments, and so on.
Books: Discrete
Mathematics with Graph Theory, second
edition, by Goodaire and Parmenter.
This book is intended to be read
thoroughly and thoughtfully. For each class session, you
are encouraged to read the pertinent portion of the text at least
once
beforehand and at least twice afterwards. Study the book with a
pencil
in hand. Make notes in it. Mark where you have
questions.
Do NOT try the exercises without reading the text; simply
skimming
the examples is not sufficient. You will find that it will
be necessary to read the text several times before attempting any
exercises. To survive this course, you must learn how to read a
math
book!
Count Down: Six Kids
Vie for Glory at the World's Toughest Math Competition, by Steve
Olson
This book describes several
mathematically gifted high school students and discusses issues that
are relevant to the mathematical education of all students. It
will be much easier to read than the textbook, and will provide us with
some good questions about teaching and doing mathematics.
Classes: Classes will be used for lectures,
problem solving, discussions, and other fun activities. You
should prepare for classes by doing the reading beforehand (reading
assignments are posted on the Web), thinking about the
problems
in the text, and formulating questions of your own. You should
also
participate as much as possible in class. Class meetings are not
intended to be a complete encapsulation of the course material.
You
will be responsible for learning some of the material on your own.
Attendance, both physical and mental, is required.
To help me keep attendance and to check on your preparation, you
will be expected to hand in a 3x5 index card at the beginning of each
class period. On this card, you should summarize the most
important points in the reading. If you have questions on the
reading, you should think carefully about the best way to phrase these
questions and then write them on your card. You can get three
points per class - one for being there, one for your index card and one
for participating in class. If you are not in class, you will not
get any points (even if you have a friend hand in a card).
Should you need to miss a class for any reason, you are still
responsible
for the material covered in that class. This means that you will need
to
make sure that you understand the reading for that day, that you should
ask a friend for the notes from that day, and make sure that you
understand
what was covered. If there is an assignment due that day, you should be
sure to have a friend hand it in or put it in my departmental mailbox
(in
Olin 324). You do not need to tell me why you missed a class unless
there
is a compelling reason for me to know.
We will be doing a lot of hands on activities in class, so you will
need to bring scissors, colored pens or pencils, a hadfull of pennies
and nickels, a glue stick, and a ruler or straightedge. You will
also find it handy to have a small stapler, paper clips, a package of
3x5 index cards, a two-pocket folder, and an eraser.
Problem solving journals: You will be
expected to keep a journal that helps you reflect on problem solving
strategies and techniques, ways to improve your ability to solve
mathematical problems, and ways to help others improve. You will
also be asked to respond to the book Countdown.
Project: Working in teams of two or three,
you will design an activity that introduces students in grades K-8 to a
concept in discrete mathematics. You will write a description of
what to do, produce the necessary materials, and write two descriptions
of the mathematics behind the activity, one for fellow teachers and one
for parents. We will try out these activities in class; we may be
able to try them out in the St. Peter schools. All the activities
will be collected into a book (or web page or both) for you to use as a
teacher.
Homework: I will assign homework at the beginning of
each
chapter by posting them on the web. The problems will be designated as
``practice problems'', ``homework problems'' or ``honor problems''.
Practice problems are meant to give you practice solving, writing
and
reading mathematics. For these problems, you will be assigned a
partner.
You may work on the problems with anyone you like except your
partner. You should write up your solutions and give them to your
partner
for peer review. These problems will not be handed in; however,
you will be graded on how many you do and on the quality of your
review.
Reading and evaluating others' work will greatly
help your performance on the other homework and on the tests.
Homework problems are homework problems which you hand in to
me. They will be graded on a scale of 0 - 10 per problem, where a
10 means that you've done a good job of solving the problem and writing
the solution up clearly. You are encouraged to work on doing
these problems with one or two other students in the class; if you do
so, then you should hand in a single set of solutions and the points
will be given to all the students in the group.
Honor problems are problems that each of you must do
individually.
You can think of these as miniature take-home tests; you are on your
honor
not to cheat by consulting other people or books. You must write
and sign the honor pledge on each of these assignments.
The first violation of the Honor Code will result in a score of 0 on
the assignment in question and notification of the Dean of
Faculty. Further violations will result in failing the course.
Course grade:
Attendance
15%
Journal writing
15%
Project
15%
Summary/ assesment
15%
Homework
40%
I may adjust your course grade based on the quantity and
quality
of your class participation.
Accessibility: Please contact me during the first week
of class if you have specific physical, psychiatric, or learning
disabilities
and require accommodations. All discussions will remain
confidential. You can provide documentation of your disability to the
Advising Center (204 Johnson Student Union) or call Laurie Bickett
(x7027).
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Math For Nurses - 8th edition
Summary: Compact and easy-to-use, Math for Nurses is a pocket-sized guide/reference to dosage calculation and drug administration. It includes a review of basic math skills, measurement systems, and drug calculations/preparations. Math for Nurses helps students to calculate dosages accurately and improve the accuracy of drug delivery. The author uses a step-by-step approach with frequent examples to illustrate problem-solving and practical applications. Readers will find it great for use in the clinical ...show moresetting or as a study aid. Practice problems throughout the text and end-of-chapter and end-of-unit review questions will aid students' application and recall of material. A handy pull-out card contains basic equivalents, conversion factors, and math formulas. ...show less
Used - Good Textbook only. Eighth28.97 +$3.99 s/h
New
EuroBooks Horcott Rd, Fairford,
New Book. Shipped from UK within 4 to 14 business days. Established seller since 2000.
$30.71
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Key to Algebra
Key to Algebra offers a unique, proven way to introduce algebra to your
students. New concepts are explained in simple language and examples are easy to follow.
Word problems relate algebra to familiar situations, helping students understand abstract
concepts. Students develop understanding by solving equations and inequalities intuitively
before formal solutions are introduced. Students begin their study of algebra in Books
1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books
8-10 extend coverage to the real number system. For grades 5-12
Please include title and BTH numbers when placing orders.
Or follow the links to order from our secure site at with a
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have to call you back or email you anyway. We do check our e-mail frequently
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This course is open to those who have proven their excellence in math. The AP-AB Calculus course consists of a full academic year of work in calculus. Topics that are covered include elementary functions, limits, differential calculus with applications and integral calculus with applications. The AP syllabus is equivalent to college level Calculus I. Additional topics are covered after the AP exam. Problems are approached using the "rule of four"; algebraically, verbally, graphically, and numerically. All students are required to take the AP/AB exam in May. This exam is not part of the course but a passing score (3-5) usually earns a semester course credit and placement in college.
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Developmental Mathematics
is written to provide students with a smooth transition
from arithmetic through prealgebra to algebra. This text
is a learning tool that will help students understand the
connections between arithmetic and algebra, develop reasoning
and problem-solving skills, and achieve satisfaction in
learning so that they will be encouraged to continue
their education in mathematics. The writing style gives
carefully worded, thorough explanations that are direct,
easy to understand, and mathematically accurate. The use of color,
boldface, subheadings, and shaded boxes helps students
understand and reference important topics. Each topic is
developed in a straightforward step-by-step manner. Each
section contains many detailed examples to lead students
successfully through the exercises and help them develop
an understanding of the related concepts.
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Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables
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Math a class named "Math", which provides a number of standard mathematical functions, using static methods, and mathematical values, using simple constants. This article describes all of the Math class members.
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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.
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Book Description: This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition
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Helpful Ways to Teach Geometry This video shows that visual aids such as pictures are helpful in teaching geometry. Dr. Stefan Forcey received his Ph.D. in mathematics from Virginia Tech University in 2004. He is currently teaching mathematics as an assistant professor at Tennessee State UniversityGraphing Linear Inequalities in Two Variables, Part III In this video, Sal Khan demonstrates how to graph a linear inequality. Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. (03:20 Celebrates its First Raider Walk Come experience the thrill and excitement of Texas Tech Football's Raider Walk! Cheer on the coaches and meet your favorite players. Raider Walk starts 2 hours and 15 minutes before each home football game near Dan Law Field and continues to the southwest corner of Jones AT&T Stadium. Author(s): No creator set
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How to Avoid the Freshman 15 Jamie Cooper, assistant professor in the Texas Tech University Department of Nutrition, Hospitality and Retailing, recommends some easy alternatives for college students to keep in mind to avoid the dreaded "freshman 15". Author(s): No creator set outlinedVoice-leading analysis of music 2: the middleground This unit continues our examination of 'voice-leading' or 'Schenkerian' analysis, perhaps the most widely-used and discussed method of analysing tonal music. In this unit, this method is explained through the analysis of piano sonatas by Mozart. The unit is the second in the AA314 series of three units ... Author(s): No creator set
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Multivariable Calculus This is a textbook for a course in multivariable calculus that has been used for the past few years at Georgia Tech. Author(s): No creator set
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This is a rigorous course in plane, solid, and coordinate geometry designed for the outstanding math student. There is an emphasis on proofs, using deductive and inductive reasoning. The course develops concepts in depth and deals with extensive applications of modern geometry.
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Problem- Solving StrategiesProblem- Solving Strategies Book Description
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
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The book Problem- Solving Strategies by Arthur Engel
(author) is published or distributed by Springer [0387982191, 9780387982199].
This particular edition was published on or around 1997-12-31 date.
Problem- Solving Strategies has Paperback binding and this format has 406 number of pages of content for use.
This book by Arthur Engel
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In our world ofgrowing technology, it is essential that students learn to work with and adapt to a variety of tools. The LCHS Math Department regularly utilizes graphing calculator technology to enhance lessons and provide more access to advanced mathematical thinking. We highly recommend that each student have his or her own graphing calculator for use during and outside of class, when deemed appropriate by his/her math teacher. Since we feel it is important for students to develop strong mental math and reasoning skills, there will be times when students are not permitted to use acalculator.
Our teachers usethe TI-83, TI-84 Plus, TI-84 Plus Silver Edition or the TI-Nspire (with TI-84 face plate) calculators. We recommend that students use one of these calculators so that our teachers will be able to help quickly trouble-shoot problems and provide consistent instruction on using the graphing calculator technology. All of these calculators are permitted on most standardized tests including theSATs, SOLs, and AP Exams.
Students taking AP Calculus AB, BC, or AP Statistics may want to purchase the TI-89 Titanium orthe TI-Nspire CAS because these calculators are equipped to deal with the advanced topics in these courses.
To find more information about these calculators, you may want to visit education.ti.com andclick on the "Products" tab. These calculators are available at most electronics stores, office supply stores, or can be found on eBay.
A limited number ofcalculators will be available for students who are financially unable to purchase their own calculator. There will be a $120 replacement fee charged to students if a calculator is lost or damaged.
Forms will be available through the math teachers during the first week of school for students wishing to check-out a calculator to use for the school year.
Calculators will be issued for the 2012-2013 school year on a first-come, first-served basis starting at 3:50 pm on Thursday, August 30 in the math wing hallway.
If you have anyquestions about getting a calculator for your student, please contact his orher math teacher or the Math Department Chair, Nicole Kezmarsky (Nicole.Kezmarsky@lcps.org).
HelpUs Get Cool Calculator Accessories with TI Points!!
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Do #1, 4, 7, 9, 12, 13, 14 from section 1.1.
Do #2, 5, 7, 10, 13, 14 from section 1.2.
Do #1, 3, 4, 7, 8, 9, 16, 20, 21, 22 from 1.3.
For practice only, do the quiz #1 handout.
Learn how to make a table of values on your
calculator. For the TI-82 and TI-83 calculators, you
enter a function using the [ Y= ] button,
set-up a table with the [ 2nd ] - [ TBLSET ] button, and then display
your table of values with the [ 2nd ] - [ TABLE ] button. The TI-85
cannot generate tables, so you will have to make your tables by hand.
The TI-86 can do tables, but you'll have to look in your manual to
see how to do this.
Monday's test will cover 2.1-2.4, 4.1-4.2.
See main course page for a more detailed list of topics.
Week 3
June 17 (M)
Test 2
June 18 (Tu)
Read 4.3-4.4 and 2.5-2.6. Do #1-30, 35, 37 from 4.3.
Do #3-26, 29 from 4.4.
Do #1-5, 8, 15, 16 from 2.5.
June 19 (W)
Here is all the homework and sections for Monday's test.
In 2.5, do #1-5, 8, 15, 16.
In 2.6, do #1-3, 6, 9-13 (also #16, 17, 21ab from 5.3).
In 4.1, do #34 and know basic derivative rules.
In 4.2, know basic derivative rules.
In 4.3, do #1-30, 34, 35, 37.
In 4.4, do #3-26, 29.
In 3.1, do #3-9.
June 20 (Th)
No new homework.
Monday's test will cover 2.5-2.6, 4.1-4.4, 3.1, as well as problems from 5.3.
See main course page for a more detailed list of topics.
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Standard Deviants Light Speed is a comprehensive video course designed to teach core
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Each module includes a video program plus a Digital Workbook that follows along with
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LIGHT SPEED ALGEBRA
This program introduces students to our friend, Algebra, the powerful super hero that is armed
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This series concentrates on the essentials of algebra plus provides a thorough breakdown of
difficult concepts using step-by-step explanations and visual examples.
THE POWERS AND FUNCTIONS OF ALGEBRA
For many students the study of algebra is similar to learning a new language, it can be very
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Jobs
Mathematics AS
Introduction to course
Mathematics is a popular choice with students; typically we have two hundred students studying AS Mathematics in the first year with over thirty of these opting to study Further Maths AS as well.
Course Details
You must enjoy Mathematics to consider it for an A Level subject; you should get a kick out of solving problems correctly and enjoy a challenge. In the first year, students study two Pure Maths modules (C1, C2) and Decision Maths (D1).
In the second year, you will study C3, C4 and Mechanics (M1). We follow the AQA syllabus.
Entry Requirements
In addition to the general entry requirements you are also required to have the following:
Where the course lead
Mathematics is essential if you want to study for a Mathematics degree and is often necessary for Physics, Engineering or Computing. It can also provide useful support for further studies in Biology, Chemistry, Finance, Business, Economics and Social Sciences.
An A and AS Level in Mathematics demonstrates that you have a level of numerical and problem solving skills which are well above average, making you particularly valued by employers and higher education establishments.
This course combines well with
Students doing A Level Maths study a wide variety of other subjects - the most popular being Economics and the Sciences. However, students studying Humanities and the Social Sciences are also well represented in Maths classes.
Course Assessment
3 x 1 and a half hour exams at AS
3 x 1 and a half hour exams at A2
Links
mathscareers.org (an excellent site for researching careers in maths and lots of exciting examples of how maths can be used in the real world)
What help is available?
Clearly most of your learning will take place inside the classroom, but as well as excellent teaching we also provide
Timetabled workshops for students who need extra help
Drop-in workshops for all students
Up-to-date textbooks
A range of resources, web-links and all assessment materials available on the college intra-net (moodle)
A good range of additional textbooks in the library
Revision, study guides and graphical calculators for sale
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No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units. less
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One reason for including certain material in the education of "all mathematicians" ... my example is complex analysis. You may end up teaching at a small college, where you teach all undergraduate math courses. Including complex analysis, since engineering and physics want their students learn it. And it is desirable that the instructor know more than just what is in the textbook.
Many times I have heard complaints of this kind... "My research is in graph theory so I will never need to know complex analysis, why do I have to waste time learning it?"
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MAT1102 Algebra & Calculus I
Review question
Calculus
What is the difference between the derivative function and the derivative at a point?
Given f(t), how can the first derivative f(t) be written in Leibniz notation? How about the second deriv
MAT1102 Algebra & Calculus I
Review question
Calculus
What is the difference between the derivative function and the derivative at a point?
Given f(t), how can the first derivative f'(t) be written in Leibniz notation? How about the second deriRelating coalgebraic notions of bisimulation
with applications to name-passing process calculi (extended abstract)
Sam Staton
Computer Laboratory, University of Cambridge
Abstract. A labelled transition system can be understood as a coalgebra for a
Math 486 Exam 3 Review Sheet
16 April 2008 This document is a preliminary review sheet. Since it is prepared well before the nal exam, it is possible that not all of the material on this review sheet will be covered on the nal exam. The nal exam is c
Chapter 2
Equational Logic
2.1
2.1.1
Syntax
Terms and Term Algebras
The natural logic of algebra is equational logic, whose propositions are universally quantied identities between terms built up from variables with operation symbols. For example
Mathematics TExES Competencies 8-12 DOMAIN INUMBER CONCEPTS Competency 001 The teacher understands the real number system and its structure, operations, algorithms, and representations. The beginning teacher: Understands the concepts of place value,
Abstract algebra
Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term abstract algebra is used to distinguish the field from "elementary algebra" or "high school alge
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Advanced Engineering Mathematics - 5th edition
Summary: Through four editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. ADVANCED ENGINEERING MATHEMATICS featuries a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts. And problem...show more sets incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight-parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Special Functions, Partial Differential Equations, Complex Analysis, and Historical Notes.
Benefits:
NEW! Throughout the text, students are invited to experiment with computations involving mathematical models and topics under discussion: for example, the effects of forcing terms and physical parameters on solution of wave and heat equations, and of filters on signal output.
NEW! Expanded treatment of special functions and orthogonal polynomials, with special attention to eigenfunction expansions and completeness of eigenfunctions leads to a discussion of the Haar wavelets.
NEW! New material on partial differential equations, including nonhomogenous heat and wave equations, the method of characteristics, and a chapter on Dirichlet and Neumann problems are included.
NEW! Expanded treatment of systems of linear and nonlinear ordinary differential equations and analysis of critical points and stability are included.
NEW! Expanded problem sets, including the introduction of sequences of problems that make use of such software packages such as MAPLE. Some problems also call on students to use computer analysis to explore relationships between solutions of mathematical models and the phenomena they model - just as they will in their careers.
NEW! More example problems are included throughout, particularly emphasizing computations based on the underlying theory.
Mathematical models of many phenomena are pursued in depth, with the objective of analyzing factors that influence behavior as well as predicting future behavior.
The computer plays a prominent role throughout the text. Computer graphics are used to display such concepts as direction field, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals.
Part IV: VECTOR ANALYSIS. 11. Vector Differential Calculus. Vector Functions of One Variable. Velocity, Acceleration, Curvature and Torsion. Tangential and Normal Components of Acceleration. Curvature As a Function of t. The Frenet Formulas. Vector Fields and Streamlines. The Gradient Field and Directional Derivatives. Level Surfaces, Tangent Planes and Normal Lines. Divergence and Curl. A Physical Interpretation of Divergence. A Physical Interpretation of Curl. 12. Vector Integral Calculus. Line Integrals. Line Integral With Respect to Arc Length. Green's Theorem. An Extension of Green's Theorem. Independence of Path and Potential Theory In the Plane. A More Critical Look at Theorem 12.5. Surfaces in 3- Space and Surface Integrals. Normal Vector to a Surface. The Tangent Plane to a Surface. Smooth and Piecewise Smooth Surfaces. Surface Integrals. Applications of Surface Integrals. Surface Area. Mass and Center of Mass of a Shell. Flux of a Vector Field Across a Surface. Preparation for the Integral Theorems of Gauss and Stokes. The Divergence Theorem of Gauss. Archimedes's Principle. The Heat Equation. The Divergence Theorem As A Conservation of Mass Principle. Green's Identities. The Integral Theorem of Stokes. An Interpretation of Curl. Potential Theory in 3- Space.
Part V: FOURIER ANALYSIS, ORTHOGONAL EXPANSIONS AND WAVELETS. 13. Fourier Series. Why Fourier Series? The Fourier Series of a Function. Even and Odd Functions. Convergence of Fourier Series. Convergence at the End Points. A Second Convergence Theorem. Partial Sums of Fourier Series. The Gibbs Phenomenon. Fourier Cosine and Sine Series. The Fourier Cosine Series of a Function. The Fourier Sine Series of a Function. Integration and Differentiation of Fourier Series. The Phase Angle Form of a Fourier Series. Complex Fourier Series and the Frequency Spectrum. Review of Complex Numbers. Complex Fourier Series. 14. The Fourier Integral and Fourier Transforms. The Fourier Integral. Fourier Cosine and Sine Integrals. The Complex Fourier Integral and the Fourier Transform. Additional Properties and Applications of the Fourier Transform. The Fourier Transform of a Derivative. Frequency Differentiation. The Fourier Transform of an Integral. Convolution. Filtering and the Dirac Delta Function. The Windowed Fourier Transform. The Shannon Sampling Theorem. Lowpass and Bandpass Filters. The Fourier Cosine and Sine Transforms. The Discrete Fourier Transform. Linearity and Periodicity. The Inverse N û Point DFT. DFT Approximation of Fourier Coefficients. Sampled Fourier Series. Approximation of a Fourier Transform by an N û Point DFT. Filtering. The Fast Fourier Transform. Computational Efficiency of the FFT. Use of the FFT in Analyzing Power Spectral Densities of Signals. Filtering Noise From a Signal. Analysis of the Tides in Morro Bay. 15. Special Functions, Orthogonal Expansions and Wavelets. Legendre Polynomials. A Generating Function for the Legendre Polynomials. A Recurrence Relation for the Legendre Polynomials. Orthogonality of the Legendre Polynomials. Fourier-Legendre Series. Computation of Fourier-Legendre Coefficients. Zeros of the Legendre Polynomials. Derivative and Integral Formulas for Pn(x). Bessel Functions. The Gamma Function. Bessel Functions of the First Kind and Solutions of Bessel's Equation. Bessel Functions of the Second Kind. Modified Bessel Functions. Some Applications of Bessel Functions. A Generating Function for Jn(x). An Integral Formula for Jn(x). A Recurrence Relation for Jv(x). Zeros of Jv(x). Fourier-Bessel Expansions. Fourier-Bessel Coefficients. Sturm-Liouville Theory and Eigenfunction Expansions. The Sturm-Liouville Problem. The Sturm-Liouville Theorem. Eigenfunction Expansions. Approximation In the Mean and Bessel's Inequality. Convergence in the Mean and Parseval's Theorem. Completeness of the Eigenfunctions. Orthogonal Polynomials. Chebyshev Polynomials. Laguerre Polynomials. Hermite Polynomials. Wavelets. The Idea Behind Wavelets. The Haar Wavelets. A Wavelet Expansion. Multiresolution Analysis With Haar Wavelets. General Construction of Wavelets and Multiresolution Analysis. Shannon Wavelets.
Part VI: PARTIAL DIFFERENTIAL EQUATIONS. 16. The Wave Equation. The Wave Equation and Initial and Boundary Condition. Fourier Series Solutions of the Wave Equation. Vibrating String with Given Initial Velocity and Zero Initial Displacement. Vibrating String With Initial Displacement and Velocity. Verification of Solutions. Transformation of Boundary Value Problems Involving the Wave Equation. Effects of Initial Condition and Constants on the Motion. Wave Motion Along Infinite and Semi-Infinite String. Fourier Transform Solution of Problems on Unbounded Domains. Characteristics and d'Alembert's Solution. A Nonhomogeneous Wave Equation. Forward and Backward Waves. Normal Modes of Vibration of a Circular Elastic Membrane. Vibrations of a Circular Elastic Membrane, Revisited. Vibrations of a Rectangular Membrane. 17. The Heat Equation. The Heat Equation and Initial and Boundary Conditions. Fourier Series Solutions of the Heat Equation. Ends of the Bar Kept at Temperature Zero. Temperature in a Bar With Insulated Ends. Temperature Distribution in a Bar With Radiating End. Transformations of Boundary Value Problems Involving the Heat Equation. A Nonhomogeneous Heat Equation. Effects of Boundary Conditions and Constants on Heat Conduction. Heat Conduction in Infinite Media. Heat Conduction in an Infinite Bar. Heat Conduction in a Semi-Infinite Bar. Integral Transform Methods for the Heat Equation in an Infinite Medium. Heat Conduction in an Infinite Cylinder. Heat Conduction in a Rectangular Plate. 18. The Potential Equation. Harmonic Functions and the Dirichlet Problem. Dirichlet Problem for a Rectangle. Dirichlet Problem for a Disk. Poisson's Integral Formula for the Disk. Dirichlet Problems in Unbounded Regions. Dirichlet Problem for the Upper Half Plane. Dirichlet Problem for the Right Quarter Plane. An Electrostatic Potential Problem. A Dirichlet Problem for a Cube. The Steady-State Heat Equation for a Solid Sphere. The Neumann Problem. A Neumann Problem for a Rectangle. A Neumann Problem for a Disk. A Neumann Problem for the Upper Half Plane. 19. Canonical Forms, Existence and Uniqueness of Solutions, and Well-Posed Problems. Canonical Forms. Existence and Uniqueness of Solutions. Well-Posed Problems.
Part VII: COMPLEX ANALYSIS. 20. Geometry and Arithmetic of Complex Numbers. Complex Numbers. The Complex Plane. Magnitude and Conjugate. Complex Division. Inequalities. Argument and Polar Form of a Complex Number. Ordering. Binomial Expansion of (z = w) n. Loci and Sets of Points in the Complex Plane. Distance. Circles and Disks. The Equation |z-a| = |z-b|. Other Loci. Interior Points, Boundary Points, and Open and Closed Sets. Limit Points. Complex Sequences. Subsequences. Compactness and the Bolzano-Weierstrass Theorem. 21. Complex Functions. Limits, Continuity and Derivatives. Limits. Continuity. The Derivative of a Complex Function. The Cauchy-Riemann Equations. Power Series. Series of Complex Numbers. Power Series. The Exponential and Trigonometric Functions. The Complex Logarithm. Powers. Integer Powers. z1/n for Positive Integer n. Rational Powers. Powers zw. 22. Complex Integration. Curves in the Plane. The Integral of a Complex Function. The Complex Integral in Terms of Real Integrals. Properties of Complex Integrals. Integrals of Series of Functions. Cauchy's Theorem. Proof of Cauchy's Theorem for a Special Case. Proof of Cauchy's Theorem for a Rectangle. Consequences of Cauchy's Theorem. Independence of Path. The Deformation Theorem. Cauchy's Integral Formula. Cauchy's Integral Formula for Higher Derivatives. Bounds on Derivatives and Liouville's Theorem. An Extended Deformation Theorem. 23. Series Representations of Functions. Power Series Representations. Isolated Zeros and the Identity Theorem. The Maximum Modulus Theorem. The Laurent Expansion. 24. Singularities and the Residue Theorem. Singularities. The Residue Theorem. Some Applications of the Residue Theorem. The Argument Principle. RouchTs Theorem. Summation of Real Series. An Inversion Formula for the Laplace Transform. Evaluation of Real Integrals. 25. Conformal Mappings.
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Everything you need to know to ace the math sections of the NEW SAT!. He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling ''Clueless'' approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and insider... more...
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