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I am studying for the Berkeley Math Tournament (BMT) and I was wondering if anyone had any ideas on what I should study to prepare. This is my first math competition and would like to have as much practice before hand as possible. Also, taking a look at last years competition there are a lot of problems that I am unsure of where to begin approaching them, if anyone has any references that would help me learn the ideas and mathematics behind the problem it would be greatly appreciated. Excuse my ignorance, but: Can you say a little more about the BMT: at what level of education are the participants? Is it geared for high school students, college undergrads, or...? – amWhyFeb 13 at 2:20 One obvious point that's probably already occurred to you: try to solve problems from last year's competition. Pay close attention to the types of mathematics that you need to solve them, and when you can't solve one, see what was used in the published solution. – Brian M. ScottFeb 13 at 2:32 1 Answer See the Art of Problem Solving - AoPS website: the link I've given is to the "resources" page with lots of articles geared toward high-caliber students, and those engaged in math competitions. But there are also many other links at AoPS that are relevant to your interests, so feel free to spend some time exploring articles/tutorials on topics covered in many math competitions, contest and test-taking strategies, a community forum, and links to other helpful resources (books, practice problems (many with solutions from other users), access to questions from earlier competitions, and more. For the main site, see AoPS. But practice is key: expose yourself to a variety of problems, try to team up with other interested students to have practice sessions, ask your instructors to supervise/advise...and (did I say practice?)
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More About This Textbook Overview Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics. Related Subjects Meet the Author Peter Cameron has taught mathematics at Oxford University and Queen Mary, University of London, with shorter spells at other institutions. He has received the Junior Whitehead Prize of the London Mathematical Society, and the Euler Medal of the Institute of Combinatorics and its Applications, and is currently chair of the British Combinatorial Committee
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MIT Course Number As Taught In Level Course Features Course Description The numerical methods, formulation and parameterizations used in models of the circulation of the atmosphere and ocean will be described in detail. Widely used numerical methods will be the focus but we will also review emerging concepts and new methods. The numerics underlying a hierarchy of models will be discussed, ranging from simple GFD models to the high-end GCMs. In the context of ocean GCMs, we will describe parameterization of geostrophic eddies, mixing and the surface and bottom boundary layers. In the atmosphere, we will review parameterizations of convection and large scale condensation, the planetary boundary layer and radiative transfer
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This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Professor Bruce H. Edwards of the University of Florida enriches these 36 lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts. Humans have been having fun and games with mathematics for thousands of years. Along the way, they've discovered the amazing utility of this field—in science, engineering, finance, games of chance, and many other aspects of life. This course of 24 half-hour lectures celebrates the sheer joy of math, taught by a mathematician who is literally a magician with numbers. Professor Arthur T. 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Edwards Immerse yourself in the unrivaled experience of learning—and grasping—calculus with Understanding Calculus: Problems, Solutions, and Tips. These 36 lectures cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. Award-winning Professor Bruce H. Edwards guides you through hundreds of examples and problems, each of which is designed to explain and reinforce the major concepts of this vital mathematical field. Whether you're a high-school student preparing for the challenges of higher math classes, an adult who needs a refresher in math to prepare for a new career, or someone who just wants to keep his or her mind active and sharp, there's no denying that a solid grasp of arithmetic and prealgebra is essential in today's world. In Professor James A. Sellers' engaging course, Mastering the Fundamentals of Mathematics, you learn all the key math topics you need to know. 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In the 36 intensively illustrated lectures of Mathematics Describing the Real World: Precalculus and Trigonometry, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more. The course also comes complete with a workbook featuring a wealth of additional explanations and problems. Save Up To $185 Prove It: The Art of Mathematical Argument Professor Bruce H. Edwards Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. But you don't have to imagine the exhilaration of constructing a proof—you can do it! Prove It: The Art of Mathematical Argument initiates you into this thrilling discipline in 24 lectures by Professor Bruce H. Edwards of the University of Florida. This course is suitable for everyone from high school students to the more math-savvy. Save Up To $175 High School Level—Geometry Professor James Noggle Professor Noggle's lectures on geometry are exceptionally clear and well organized. He has an evident love for the topic, and a real gift for conveying the elegance and precision of geometric concepts and demonstrations. You will learn how geometrical concepts link new theorems and ideas to previous ones. This helps you see geometry as a unified body of knowledge whose concepts build upon one another. Save Up To $185 Mastering Differential Equations: The Visual Method Professor Robert L. Devaney Make sense of differential equations with Professor Robert L. Devaney's Mastering Differential Equations: The Visual Method. These 24 visually engaging lectures cover first- and second-order differential equations, nonlinear systems, dynamical systems, iterated functions, and more. Whether you're a college student looking for a fresh perspective or a lifelong learner excited about mathematics, there's something for you to take away from this intriguing course. Save Up To $185 Meaning from Data: Statistics Made Clear Professor Michael Starbird Statistical information is truly everywhere. You can't look at a newspaper without seeing statistics on virtually every page. Meaning from Data: Statistics Made Clear is your introduction to a vitally important subject in today's data-driven society. In 24 half-hour lectures, which require no background in mathematics beyond basic algebra, you explore the principles and methods that underlie the study of statistics. Professor Michael Starbird puts his emphasis on the role of statistics in daily life: weather forecasts, business, and a host of other applications. Games People Play: Game Theory in Life, Business, and Beyond Professor Scott P. Stevens Game theory—the science of interactive, rational decision making—helps us understand how and why we make decisions. It also provides insights into human endeavors including biology, politics, and economics. In Games People Play: Game Theory in Life, Business, and Beyond, business consultant and award-winning Professor Scott P. Stevens helps you understand this profoundly important field. Throughout these 24 enlightening lectures, you explore the fundamentals of game theory in an engaging, comprehensible manner. You investigate the field's classic games, encounter its greatest minds, and discover its real world applications in arenas including corporate negotiations, foreign policy—and your everyday life. Save Up To $160 What Are the Chances? Probability Made Clear Professor Michael Starbird Learn how to understand the random factors behind almost everything—from the combinations of genes that produced you to the odds of how long you'll have to wait at a bus stop. In What Are the Chances? Probability Made Clear, award-winning Professor Michael Starbird makes the secret of numbers come alive for nonmathematicians. He picks intriguing, useful, and entertaining examples to illustrate the fundamental concepts of probability and teaches you how to apply probability to areas of your life ranging from physics to biology to finance; understand the nature of randomness and probabilistic reasoning; and much more.
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must-have textbook that millions in Latin America have used for their Algebra formation. This revised edition includes a CD-Rom with exercises that will help the student have a better understanding of equations, formulas, etc.This is the must-have textbook that millions in Latin America have used for their Algebra formation. This revised edition includes a CD-Rom with exercises that will help the student have a better understanding of equations, formulas, etc.Hide Description:Good. Ex-library book with stamps and markigns. Actual content...Good. Ex-library book with stamps and markigns. Actual content is clean. Good covers. Some small ink marks on top of the front cover. Inside has no writing or underlining
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More About This Textbook Overview Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming. Editorial Reviews From the Publisher From the reviews: "This gentle introduction to scientific computing aims to convey the basic ideas, principles and techniques of computational science to undergraduates in mathematics, science and engineering. … The real strength of the text is its adroit mix of analytical and numerical, theoretical and practical. … This is a top-notch book on scientific computing written with clarity … and a good sense of what students need to learn. It is among the best books in this area that I have seen." (William J. Satzer, The Mathematical Association of America, February, 2011) "The text flows nicely, and Tveito (Simula Research Laboratory, Norway) and colleagues thoroughly explain different subjects in meaningful steps. In addition to exercises at the end of each chapter, an instructive 'Projects' section allows readers to practice new concepts. … Overall, this textbook is a welcome addition to a small set of books currently available in scientific computing, an expanding area for undergraduate course development in many US colleges. Summing Up: Recommended. Lower-division undergraduates through researchers/faculty." (D. Papamichail, Choice, Vol. 48 (9), May, 2011) "This book is part of Springer's Texts in Computational Science and Engineering series, so it is written for students. … chapters more or less serve as a limited introduction to computational mathematics: they cover basic algorithms in numerical integration, initial-value problems for scalar ODEs, initial-value problems for two-component ODEs, rootfinding in one or two dimensions, and least squares approximations using constants, lines, and parabolas." (Toby Driscoll, SIAM Review, Vol. 53 (4), 2011) "In this appealing book the authors introduce to basic principles of numerical calculations which every engineer or scientist working with computers should be familiar with. … a very good selection of topics treated and presented important methods in a gentle style … ." (Rudolf Gorenflo, Zentralblatt MATH, Vol. 1220, 2011) Meet the Author Professor Aslak Tveito is the managing director of Simula Research Laboratory. His research is focused on computing the electrical activity in the heart. Tveito is the co-author of more than 60 papers published in international peer-reviewed journals, and one textbook introducing partial differential equations. Tveito has also edited four books published internationally. Professor Hans Petter Langtangen is the director of Center for Biomedical Computing, a Norwegian Center of Excellence at Simula Research Laboratory, and a professor of computer science at the University of Oslo. His research concerns numerical methods and software tools for continuum mechanical problems. Langtangen has published more than 40 journal papers, and more than 50 peer-reviewed contributions to conference proceedings and books. He is the author of three textbooks and an a co-editor of three books. Langtangen has been an active developer of open source and commercial software systems for computational sciences. He is a member of the European Academy of Sciences and serves on the editorial board of five leading international journals. Dr. Nielsen is a research scientist at Simula Research Laboratory where he investigates whether it is possible to compute the position and size of heart infarctions from ECG recordings. He has published a number of papers on computational mathematics and during his years at Norwegian Computing Center he solved many scientific computing problems for the Norwegian oil industry. The research interests of Professor Xing Cai center around parallel numerical methods and software for solving partial differential equations. He has more than 50 peer-reviewed publications in international journals and conference
Lots of real-world data, with descriptions of environmental and mathematical implications; stored in a variety of formats for easy download. Catalogued by mathematical topic and by environmental topiTeaCat is a dynamic mathematical application that aims to enable high school students to experiment with and to exercise a variety of mathematical topics. Even engineers may benefit of TeaCat for rath... More: lessons, discussions, ratings, reviews,... WCMGrapher is a free graphing application. It is designed to enable teachers to create graphs of functions, format the graphs, then copy and paste the graph into other applications. For example, yo... More: lessons, discussions, ratings, reviews,... Web Components for Mathematics (webcompmath or WCM) is a library used to create interactive graphing web applets for teaching mathematics. It is written in the Java programming language and is base... More: lessons, discussions, ratings, reviews,... Winplot is a general-purpose 2D/3D plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats. It allows for customizing and includes a data table which can bStudent model a loan they would like to take out. The only mathematical concepts required are addition and multiplication. Terminology and a few basic spreadsheet concepts need to be covered. More: lessons, discussions, ratings, reviews,... Students model a savings account and answer some thought-provoking questions. Addition and multiplication as well as a few spreadsheet concepts are all that is needed for students to use the model. More: lessons, discussions, ratings, reviews,... This collection of free worksheets provides practice in a variety of algebra topics, generating ten problems at a time for users to solve. Each worksheet is printable and comes with an answer key. To... More: lessons, discussions, ratings, reviews,... For systems of three linear equations in three variables, this Formula Solver program walk you through the steps for finding the solution using Cramer's Rule (also known as the Third Order Determinant... More: lessons, discussions, ratings, reviews,... Flash introduction to finding the equation of an ellipse centered on (0,0) and with its major axis on the x-axis. Students can use this Tab Tutor program to learn about the equation of this ellipse an
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However, to push forward the frontiers of the subject, or to apply it, one must have a solid understanding of its underlying intuition. Thus a study of classical differential geometry is warranted for someone who wants to do original research in the area as well as use it in applications, which are very extensive. Differential geometry is pervasive in physics and engineering, and has made its presence known in areas such as computer graphics and robotics. In this regard, the authors of this book have given students a fine book, and they emphasize right at the beginning that an undergraduate introduction to differential geometry is necessary in today's curriculum, and that such a course can be given for students with a background in calculus and linear algebra. They also do not hesitate to use diagrams, without sacrificing mathematical rigour. Too often books in differential geometry omit the use of diagrams, holding to the opinion that to do so would be a detriment to mathematical rigour. Much is to be gained by the reading and studying of this book, and after finishing it one will be on the right track to begin a study of modern differential geometry. Differential Geometry is one of the toughest subjects to break into for several reasons. There is a huge jump in the level of abstraction from basic analysis and algebra courses, and the notation is formidable to say the least. An ill-prepared student can begin reading Spivak Volume I or Warner's book and get very little out of it. This is, in fact, what happened to me. Only at the advice of a professor did I take an undergraduate diff. geometry course which used this book, and am I glad that I did. In short, here is a book which takes the key aspects of classical and modern differential geometry, and teaches them in the concrete setting of R^3. This has several advantages: (1) The student isn't lost in the abstraction immediately. When I took my first diff. geometry course, we spent the entire time taking derivatives in n-dimensional projective space and other equally abstract spaces. This book keeps it concrete, and supplements each idea with several worked out examples to help ground the student's intuition. (2) The book uses modern techniques when applicable. Just because this book teaches the material in a concrete/classical setting does not mean that its methods are outdated. The student will become very used to modern techniques, but applied here in easier settings than what you would find in a standard graduate leveled book. Hence, when the student eventually takes graduate leveled courses, he or she will come to see the definitions and techniques as natural extensions of those learned previously. (3) The student learns the classical theory first, which entirely motivates the modern theory. Going back to (2), this allows students to view the modern theory as a natural extension of the classical theory, and hence their intuition learned from this book is still applicable in the more abstract settings. Also, for arbitrary manifolds, our intuition comes entirely from surfaces in R^3. The fact that this book has a 100+ page chapter on surfaces alone makes it worth reading. The material covered in this book is expansive, and i think students will find that even in more advanced Riemannian geometry courses they will see material from this book still being taught. Hence, it will be a long time before a student completely outgrows this book. I've said only good things, but there is one thing that annoys me. This book drops the ball in providing intuition in several topics. For example, the book defines Christofell symbols as abstract sums of inner products. However, the point is that they provide the scalars for the coordinates of mixed partial derivatives in a tangent space. There is a theorem that implies this, but this intuition is never explicitly stated. In a book aimed at undergraduates, I feel that everything, including intuition, should be stated and highlighted. This has not been too bad of a hinderance for me, because a quick trip to the professor's office will often sort things out for me. However, any self-learners may get the wrong idea about how to thing about certain topics. This is not too bad of a problem, and for the most part this book does a good job at explaining and motivating topics, so I do not feel that any more than one star should be taken off. Prerequisites for reading: (1) Strong Linear Algebra background. And by this I do not mean computations in Lay, I mean theory in Axler or something comparable. Often times, change of bases are applied without being explicitly stated in the proofs, and you should be able to pick up on this immediately. (2) Analysis-both single variable and multiple variable. You do not need anything past the basics of multivariable differentiation and integration, i.e. no Stoke's theorem or differential forms are needed. (3) While not completely necessary, there are a few proofs which use the existence and uniqueness theorem of ordinary differential equations, so knowing this exhausts all possible prerequisites. I do no know ODE theory, and I am not having trouble understanding the book as a whole, so this prerequisite may be relaxed/forgotten.Read more › There are many differential geometry books out there. Some are very rigorous others not. This book walks the road in the middle. Intuition is developed in the first few chapters by discussing familiar surfaces in R^n, and then a discussion on more abstract manifolds follow. The book requires some very basic knowledge of linear algebra and some multivariate calculus knowledge. So basically every undergrad in the sciences should find this book easy to understand, and a good introduction to differential geometry.
Elementary Geometry - 3rd edition ISBN13:978-0471510024 ISBN10: 0471510025 This edition has also been released as: ISBN13: 978-0471537465 ISBN10: 0471537462 Summary: Although extensively revised, this new edition continues in the fine tradition of its predecessor. Major changes include : A notation that formalizes the distinction between equality and congruence and between line, ray and line segment; a completely rewritten chapter on mathematical logic with inclusion of truth tables and the logical basis for the discovery of non-Euclidean geometries ; expanded coverage of analytic geometry with more theorems discussed an...show mored proved with coordinate geometry; two distinct chapters on parallel lines and parallelograms ; a condensed chapter on numerical trigonometry; more problems; expansion of the section on surface areas and volume; and additional review exercises at the end of each chapter. Concise and logical, it will serve as an excellent review of high school geometry. ...show less 0471510046.67
Trigonometry: A Unit Circle Trigonometry. The Eighth Edition of this dependable text retains its best features-accuracy, precision, depth, strong student support, and abundant exercises, while substantially updating content and pedagogy. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus. A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics wit... MOREhin the context of real life using understandable, realistic applications consistent with the abilities of most readers.Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Chapter topics include Functions and Their Graphs; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Exponential and Logarithmic Functions; and more.For anyone interested in trigonometry.
mathematics at work - Achieve Mathematics At Work - Achieve mathematics at work series following up on the work of adp achieve has produced a series of mathematics at work brochures to examine how higher-level mathematics at work - achieve Shape of the Australian Curriculum Mathematics Shape Of The Australian Curriculum Mathematics 4 1 purpose 1 1 the shape of the australian curriculum mathematics will guide the writing of the australian mathematics curriculum k12 1 2 this paper has been shape of the australian curriculum mathematics Related Books About mathematics for economists pdf download Overview Intuitive Biostatistics is both an introduction and review of statistics. Compared to other books, it has: Breadth rather than depth. It is a guidebook, not a cookbook. Words rather than math. It has few equations. Explanations rather than recipes. This book presents few details of statistical... View detail Madelaine Hillyard is a world-famous heart surgeon at the top of her game. Her personal life is far less successful. A loving but overworked single mom, she is constantly at odds with her teenage daughter. At sixteen, Lina is confused, angry, and fast becoming a stranger to her mother—a rebel desperate... View detail Communication Sciences and Disorders: A Contemporary Perspective introduces students to the field in a clear and succinct manner that allows readers access to the most current theories, research, and practices through rich examples, detailed case studies and engaging anecdotes. It employs a
Pre-Algebra March 3, 2012 This course is designed to help students who have previously shown a weakness in the fundamentals of mathematics as well as to give all students a solid foundation in the fundamental concepts of Algebra. Pre-Algebra is very helpful to incoming freshmen by giving them a head start in their first year of high school mathematics.
Mathematics Department Mathematics traditionally has been the bedrock of a liberal arts education. The root of the word mathematics comes from the Greek "mathema," which means to know. At heart, mathematicians are people who are interested in knowing and understanding the world and universe around them. The Department of Mathematics at Washington & Jefferson College is composed of a student-centered group of faculty who are dedicated to the intellectual and mathematical growth of our students. Small classes (upper-level courses often have fewer than ten students) allow for individualized attention. Generous office hours and open door policies permit students to interact with faculty on demand. Often, student/faculty interaction goes beyond the classroom. A mathematics lounge creates a space where students can get to know their professors in an informal setting while sharing lunch or a snack. Spend time with us, and we will provide you an education that stands the test of time. You will graduate with the intellectual tools necessary to compete in a dynamic and changing world. You will be challenged and you will be proud of your intellectual achievements.
Each student is required to have a graphing calculator. The TI-83 is preferred but a TI-82 is acceptable. Although other calculators may have similar capabilities, I can't promise to be able to help with the operation of every calculator. Overview: One of the main objectives of this course is for you to understand the basic concepts of calculus well enough to know when, how, and why to apply them in real-world situations and to be able to interpret and communicate the results. To achieve this goal will require practice at a variety of numerical, graphical, and algebraic methods. You will also be expected to develop and practice your verbal and written communication skills. You will at times be expected to work in groups during class and will have ample opportunities to practice these skills. It is hoped that you will also find a group to work with outside of class. The preface of the book provides additional detail and insight into the methods you will encounter in this course. Page xii is particularly well-written but the entire preface is worth reading. Work Load: There will be in-class group work, daily reading and homework, 10-12 quizzes, 3 tests, and 1 final exam. You should expect to work at least 6-9 hours per week, outside of class. Grading: No make-ups will be given for any part of this course. However, your lowest test score and your two lowest quiz scores will be dropped. All students must take the final exam and the final exam score cannot be dropped. Quizzes: 20% (these will be based on the daily homework assignments) Test 1: 25% (Thursday, Feb. 15) Test 2: 25% (Thursday, Mar. 22) Test 3: 25% (Thursday, Apr. 19) Final Exam: 30% (Tuesday, May 8, 9:00 AM - 12:00 PM in LeConte 412) TOTAL: 100% (after lowest test score dropped) Final Grade: (I will round off to the nearest whole number percentage) A 90% - 100% B+ 87% - 89% B 80% - 86% C+ 77% - 79% C 70% - 76% D+ 67% - 69% D 60% - 66% F 0% - 59% Help is available: Working together on homework assignments is a great way to learn mathematics so I encourage this. You may also wish to use the Math Lab's free tutoring service. There are three locations: LeConte 101 Math Lab is open MTWTh from 11:00 AM - 5:30 PM, and F from 11:00 AM - 3:00 PM. Towers Area Math Lab is open MTWTh from 6:00 PM - 8:00 PM. Bates Area Math Lab is open MTWTh from 6:00 PM - 8:00 PM.
Book Search The concept of a proof is one of the key ideas—some would say the key idea—that sets mathematics apart from other disciplines. But students often have difficulties in understanding proofs and constructing their own proofs. Suitable for a variety of courses or for self-study, this text helps... Proofs, Structures and Applications, Third Edition Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is... Updated and expanded, Discrete Mathematics for New Technology, Second Edition provides a sympathetic and accessible introduction to discrete mathematics, including the core mathematics requirements for undergraduate computer science students. The approach is comprehensive yet maintains an... for New Technology In a comprehensive yet easy-to-follow manner, Discrete Mathematics for New Technology follows the progression from the basic mathematical concepts covered by the GCSE in the UK and by high-school algebra in the USA to the more sophisticated mathematical concepts examined in the latter stages of the... Published April 30th 1992
Notebook containing solutions to problems is available in CSULA Library. Call No. is 3042. Concepts and Key Words Lecture 1 Introduction Review of some basic concepts. Stress (at a point in a body). Stress is force per unit area, that is, intensity of distributed forces acting over a surface, real or imagined. A small rectangular parallelepiped (element) isolated from a loaded body. The rectangular stress components that act on this element: normal stresses and shear stresses. Subscript convention and direction convention for stress components. The stress matrix. Symmetry of the shear stresses. Six rectangular stress components define state of stress at a point in a body. Plane stress. Strain. Element under uniaxial stress. Corresponding normal strains. Linearly elastic material: Hooke's law; Poisson's ratio. Isotropic material. Strain-stress relations for uniaxial stress, biaxial stress, triaxial stress. Inverted equations. Introduction to the finite-element method. One-dimensional spring element: two node and one (spring) element axial system. Displacements of nodes. External forces applied at nodes. Isolated free body diagrams of nodes and (spring) element. Internal forces that act on element. Equilibrium equations for nodes and element. Internal force-node displacement relations for element. Element stiffness matrix, relates internal forces and displacements. System stiffness matrix, relates external forces and displacements. Case when a displacement is "applied" at one node, say 1, and an external force is applied at the other node, say 2. Determination of external force at node 1 (called reaction) and displacement at node 2, with the help of an added, very stiff ground spring at node 1. Lecture 4 Two-dimensional spring element. Example: a two-dimensional system of three noncollinear nodes connected by three springs. Application: plane truss problem. Pure bending of unsymmetrical Hookean beams. Out-of-plane bending moment is needed, in addition to in-plane bending moment, to produce bending in a plane not coincident with a principal centroidal axis of cross-section. Formula for bending stress stated in terms of principal centroidal axes of cross-section. Location of neutral axis. Transverse shear stresses revisited: the case of a beam with a circular cross section. Total shear stress over cross section at location of lateral stress-free surface acts tangent to lateral stress-free surface. Shear flow in Hookean beams with thin, open sections. Case of cantilevered beam with end load acting through "shear center" and parallel to principal axis of cross section. Under these conditions, beam does not twist. Shear stress is proportional to first moment with respect to neutral axis of cross section between free edge and exploratory cut where shear stress computed. Product of shear stress and local thickness called shear flow. Lecture 6 Application: symmetrical wide-flange beam. Shear stresses in web and flange. "Flow" interpretation of shear stresses. Shear center of thin-walled open-section Hookean beams. Example: cantilevered channel beam with end load that acts through shear center; therefore, no twist. Shear center is point on line of action of load about which the moment sum of the shear stresses over cross-section vanishes. If the faces of a cubical element are normal to the orthonormal eigenvectors of the stress matrix then only normal stresses act on these faces. The normal stresses are called principal stresses. Stress invariants: first, second, third. Total shear stress and direction on oblique surface of right-tetrahedron. Tensor transformation of strain matrix: "mathematical strain". "Engineering" strain. Equations of equilibrium. Generalized Hooke's law. Elastically homogeneous and isotropic material. Generalization of Hooke's law involves 36 constants in a 6 x 6 matrix [C]. Symmetry of [C] can be deduced from application of Castigliano's first theorem to strain energy per unit volume expressed as quadratic form in strains. Symmetry of [C] leaves 21 independent constants. Consequences of material symmetries on constants in [C] matrix. Assume stresses are given by taking certain partial derivatives of a scalar function of the lateral coordinates. Stresses satisfy equilibrium equations. Substitute stresses in the one governing stress compatibility equation to obtain biharmonic equation in the scalar function, now identified as Airy stress function. Another case, thin body in nearly plane stress state. Assume stresses and strains are nearly two-dimemsional. Assume again stresses given by Airy stress function. Substitute stresses in stress compatibility equation in lateral coordinates to obtain biharmonic equation in the Airy stress function. Other compatibility equations are not necessarily satisfied. Conclusion: plane strain and plane stress problems are essentially the same; can convert one solution into the other. Plane stress example: cantilever beam with uniform load. Boundary conditons. Trial polynomial solution to biharmonic equation; certain terms can be eliminated from consideration of boundary conditions. The determination of the unknown constant coefficients in polynomial from substitution into biharmonic equation and boundary conditions. Some stress boundary conditions cannot be satisfied pointwise but only as stress resultants. Comparison of calculated stress field with that from strength of materials. Lecture 18 Torsion of Prismatical Cylinders Cylinder of uniform cross-section. Assume one end fixed against rotation. Each cross-section rotates through angle (angle of twist) that is proportional to distance from fixed end. Assume angle of twist is small. Develop lateral components of displacement field in terms of angle of twist and position of particle relative to reference longitudinal axis. Assume longitudinal component of displacement field is function of lateral position coordinates only. This function is proportional to what is called the warping function. Resulting strain and stress fields. Enforcement of equilibrium equations leads to Laplace equation for the warping function. Enforcement of the lateral stress-free boundary conditons together with the Laplace equation forms a Neumann boundary value problem. Application: bar with elliptical cross section. Develop formula for torsional constant. Formula for maximum shear stress. The rectangular cross section case. Formulas for maximum shear stress and torsional constant in terms of ratio of two sides of rectangular cross section. The case of an elongated rectangular cross section. Approximate stress distribution. Extension to torsion of thin-walled open sections. Maximum shear stresses and torsional constants. The final exam will be open textbook. You will also be allowed to refer to three 8 1/2 x 11 in. sheets of notes during the exam.
Applied Calculus, Third Edition Geoffrey C. Berresford, Long Island University Andrew M. Rockett, Long Island University Basics of the TI-83 Basics of the TI-83 is a walkthrough of specific graphing calculator functions. You will learn how to: plot a function, change dimensions of the viewing rectangle, determine intercepts graphically and numerically, model data using regression, and compute factorials and permutations. Some resources on this page are in PDF format and require Adobe® Acrobat® Reader. You can download the free reader below!
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Mathematical Reasoning for Elementary principal goals of this text is to impart a positive attitude to those who aspire to be elementary or middle school teachers. With a positive attitude toward mathematics comes confidence and an increased willingness to learn the mathematical content, skills, and effective teaching techniques necessary to become a competent teacher of mathematics. To that end, the content and processes of mathematics are presented in an appealing and logical matter with three principal goals in mind: to develop positive attitudes towards mathematics a... MOREnd mathematics teaching, to develop mathematical knowledge and skills, and to develop students as competent mathematics teaching professionals. The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm readers with all the tools that they will need to become excellent elementary or middle school teachers. Thinking Critically. Sets and Whole Numbers. Numeration and Computation. Number Theory. Integers. Fractions and Rational Numbers. Decimals and Real Numbers. Algebraic Reasoning and Representation. Statistics: The Interpretation of Data. Probability. Geometric Figures. Measurement. Transformations, Symmetries, and Tilings. Congruence, Constructions, and Similarities. For all readers interested in mathematical reasoning for elementary teachers.
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More About This Textbook Overview Written for the Math for Liberal Arts course, TOPICS IN CONTEMPORARY MATHEMATICS helps students see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the text demonstrate how math relates to subjects—such as sociology, psychology, business, and technology—that generally interest students. This Enhanced Edition includes instant access to WebAssign, the most widely-used and reliable homework system. WebAssign presents over 500 problems, as well as links to relevant textbook sections, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly. Related Subjects Meet the Author Ignacio Bello attended the University of South Florida (USF), where he earned a B.A. and M.A. in Mathematics. He began teaching at USF in 1967, and in 1971 he became a member of the faculty and Coordinator of the Math and Sciences Department ay Hillsborough Community College (HCC). Professor Bello instituted the USF/HCC remedial program, which started with 17 students taking Intermediate Algebra and grew to more than 800 students with courses covering Developmental English, Reading, and Mathematics. In addition to Topics in Contemporary Mathematics, Professor Bello has written many other books that span the mathematics curriculum, many of which have been translated to Spanish. Professor Bello is featured in three television programs on the award-winning Education Channel. He helped create and develop the USF Mathematics department website, which serves as support for the Finite Math, College Algebra, Intermediate Algebra, Introductory Algebra, and CLAST classes at USF. Professor Bello is a member of the Mathematical Association of America (MAA) and the American Mathematical Association of Two-Year Colleges (AMATYC). He has given many presentations regarding the teaching of mathematics at the local, state, and national
358241 / ISBN-13: 9780534358242 Introductory Algebra: Equations and Graphs Yoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; ...Show synopsisYoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; and to engage students as active participants in the process of learning. Unlike other introductory algebra texts, Yoshiwara's INTRODUCTORY ALGEBRA, builds an intuitive framework for the future study of functions in intermediate algebra. This clearly differentiates Yoshiwara from standard introductory algebra texts. The text emphasizes the study of tables and graphs, and the concept of the variable is developed from that platform. Graphs are used extensively throughout the book to illustrate algebraic technique and to help students visualize relationships between variables. The numerous labeled web site by the authors believe that this skill must be learned through practice with pencil and paper.Hide synopsis ...Show more technique and to help students visualize relationships between variables. The numerous labelled website but the authors believe that this skill must be learned through practice with pencil and paper.Hide Description:New. Yoshiwara's INTRODUCTORY ALGEBRA was written with two...New. Yoshiwara's INTRODUCTORY ALGEBRA was written with two goals in mind: to present the skills of algebra in the context of modeling and problem solving; and to engage students as active participants in the process of learning. Unlike other introduct. Description:New. 0534358241 Premium Books are Brand New books direct from...New. 0534358241 Premium Books are Brand New books direct from the publisher sometimes at a discount. These books are NOT available for expedited shipping and may take up to 14 business days to receive. Description:New. 0534358241 *BRAND-NEW* FAST UPS shipping, so you'll...New. 0534358241
Discrete Mathemetics 9780618415380 0618415386 Summary: Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for studen...ts who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory. Ferland is the author of Discrete Mathemetics, published 2008 under ISBN 9780618415380 and 0618415386. Six hundred eighty seven Discrete Mathemetics textbooks are available for sale on ValoreBooks.com, one hundred twenty three used from the cheapest price of $110.18, or buy new starting at $111
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College Algebra: A Graphing Approach 9780618851881 0618851887 Summary: Part of the market-leading "Graphing Approach Series" by Larson, Hostetler, and Edwards, "College Algebra: A Graphing Approach," 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed.Continuing the series' empha...sis on student support, the Fifth Edition introduces "Prerequisite Skills Review." For selected examples throughout the text, the "Prerequisite Skills Review" directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace (see below for description) are referenced in every exercise set.The."New!" The "Nutshell Appendix" reviews the essentials of each function, discussed in the "Library of Functions" feature, and offers study capsules with properties, methods, and examples of the major concepts covered in the textbook. This appendix is an ideal study aid for students."New!" "Progressive Summaries" outline newly introduced topics every three chapters and contextualize them within the framework of the course."New!" "Make a Decision" exercises--extended modeling applications presented at the end of selectedexercise sets--give students the opportunity to apply the mathematical concepts and techniques they've learned to large sets of real data."Updated!" The "Library of Functions,"."Updated!" The "Chapter Summaries" have been updated to include the Key Terms and Key concepts that are covered in the chapter. These chapter summaries are an effective study aid because they provide a single point of reference for review."Updated!" The "Proofs of Selected Theorems" are now presented at the end of each chapter for easy reference.The Larson team provides an abundance of features that help students use technology to visualize and understand mathematical concepts. "Technology Tips" "Technology Support" notes appear throughout the text and refer students to the "Technology Support Appendix," where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. The "Technology Support"notes also direct students to the "Graphing Technology Guide," on the textbook's website, for keystroke support for numerous calculator models.Carefully positioned throughout the text, "Explorations" engage students in active discovery of mathematical concepts, strengthening critical thinking skills and helping them to develop an intuitive understanding of theoretical concepts."What You Should Learn" and "Why You Should Learn It" appears at the beginning of each chapter and section, offering students a succinct list of the concepts they will soon encounter. Additionally, this fe Larson, Ron is the author of College Algebra: A Graphing Approach, published 2007 under ISBN 9780618851881 and 0618851887. Three hundred eighty one College Algebra: A Graphing Approach textbooks are available for sale on ValoreBooks.com, one hundred forty two used from the cheapest price of $0.01, or buy new starting at $34
This updated 8th edition of Practical Problems in Mathematics for Carpenters is composed of very short units that begin with a brief explanation of the math principle being covered, followed by straightforward explanations and examples that are worked out in detail so you can see first-hand how to perform the given functions. Discontinued Item. Limited Availability. This widely used text/workbook, teaches the practical mathematics essential to the building construction and carpentry trades. The book features short units that begin with a brief explanation of an important math principle followed by straightforward explanations and examples that are worked out in detail so you can see first-hand how to perform the functions involved. Basic mathematical problems relevant to the construction trade are accompanied by clear-cut illustrations and together give you the opportunity to apply and practice math principles common to carpentry. Features: Based on realistic carpentry problems, including modern construction materials and practices. Includes integrated coverage of simple 4-function calculator use in solving math problems. Easy-to-understand explanations for all the math principles carpenters are likely to encounter in the field. From the Preface Practical Problems in Mathematics for Carpenters is part of a series of Practical Problems books, each focusing on a particular craft or occupation. Each of these books is made up of short units with a brief explanation of a mathematical principle followed by problems involving the user in the math principle as it applies to the particular occupation. This time-tested approach has been found to help the student build an understanding of the necessary mathematics and develop vocabulary for the trade. Use of Practical Problems in Mathematics for Carpenters before or with the study of carpentry will help the student succeed in the study of his or her core carpentry textbook. Practical Problems in Mathematics for Carpenters uses a step-by-step approach, beginning with the most basic arithmetic, so no student will be left behind. Many students will not need to study the first few units and work the problems in them, but the instructor is encouraged to provide opportunities for all students to use these basic units to build a foundation for the rest of the course. Examples are included with the explanations of basic principles. By reading the explanation of the principle and finding where each principle or operation is used in the examples, you will be prepared to solve all of the problems in the unit. Changes in the eighth edition of Practical Problems in Mathematics for Carpenters include updating construction practices to make the book more relevant to today's carpenters. A few errors that existed in the seventh edition have been corrected in this edition. About the Authors Mark W Huth brings many years of experience in the industry to this book, having worked as a carpenter, contractor, and a building construction teacher. His career has allowed him to consult with hundreds of construction educators in high schools, colleges, and universities. Mark has written several other construction titles, including Understanding Construction Drawings. Harry Huth's experience as a high school mathematics teacher and his decades as a roofer and cabinetmaker prepared him to help students overcome their fear of mathematics and succeed in this fundamental area of study. As a cabinetmaker, he had to solve all kinds of mathematical problems, and his knowledge is apparent in Practical Problems in Mathematics for Carpenters.
2013 Nrp Study Guide 2013 CRCT Study Guide for 8th Grade - Cobb County School District. Jan 8, 2013 Reading. Reading Skills and Vocabulary Acquisition Economics The chapters of this guide are organized by subject. an additional tool for student practice. The. 5 Which event creates the MOST change in the cat? Jan 8, 2013 Reading. Reading Skills and Vocabulary Acquisition Economics The chapters of this guide are organized by subject. an additional tool for student practice. The. 5 Which event creates the MOST change in the cat? Please note that some test questions are taken from the Case Book. PLAY: The offensive coach protests that the red and blue glove the pitcher is using is not legal. Players not listed on a lineup card as substitutes are ineligible to play. a . Source Material: A Raisin in the Sun by Lorraine Hansberry. 7. 2. Did you find the Study Guide useful in preparing your class for the play and/or in. educators and group leaders take the opportunity to read the script of Clybourne Park variable calculus and their applications. It lays a foundation for a Contemporary Linear Algebra, (Anton and Busby) and Calculus, 8th edition. (Anton, Bivens and Davis). They are available new at. Identical solutions will be immediately It presents selected topics in algebra and calculus and their applications [1] Calculus: Early Transcendentals, 8th or 10th Edition, by H. Anton, I. Bivens, S. Davis (Wiley). discussing assignments and methods of solution with other students. Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners.
Spectrum Math, 2007 Edition, Grade K 1 2 3 4 5 7 8 Retail Price: $9.95 CBD Price: $6.89 Buy 32 Algebra math skills. This workbook features drill practices, chapter pre-tests, chapter post-tests, mid-book tests, and a final. Help students become more familiar with a testing environment, and provide practice with both problem-solving and analytical algebra exercises. An assignment record sheet, record of test scores sheet and answer key are included. Spectrum Geometry, Grades 6-8 Retail Price: $9.95 CBD Price: $6.89 Buy 36 Data Analysis & Probability operations, ratios, measures of central tendency, graph interpretation, probability, and other important aspects of understanding probability. The variety of activities also helps extend problem-solving and analytical abilities. 128 perforated pages, softcover. Grades 6-8. Spectrum Measurement, Grades 6-8 Retail Price: $9.95 CBD Price: $6.89 Buy 48 customary and metric measurements, ratios and proportions, percents and rates, volume, angles, and more. The variety of activities also helps extend problem-solving and analytical abilities. 128 perforated pages, softcover. Grades 6-8.
Beginning Algebra accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Earlier coverage of the Order of Arithmetic Operati... MOREons--now section 1.5 so that operations is now covered together before Introduction to Algebra. The discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. Section 4.3 now offers a more thorough introduction to polynomials, with the addition of new terminology at the beginning of the section and a new lesson on evaluating polynomials at the end. Revised Ch. 7 on Graphing and Functions includes new coverage of the rectangular coordinate system and slope. The coverage of the rectangular coordinate system in Chapter 7 has been improved for greater clarity. John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. They have carefully crafted their texts to support students in this course by staying with them every step of the way. Tobey and Slater... With you every step of the way. This 6th edtion of Beginning Algebra is appropriate for a 1-sem course in appropriate for a 1-sem course in Introductory, Beginning or Elementary Algebra where a solid foundation in algebraic skills and reasoning is being built for those students who have little or no previous experience with the topice. The utlimate goal of this text is to effectively prepare students to transition to Intermediate Algebra. One of the hallmark characteristics of B eginning Algebra 6e that makes the text easy to learn from is the building-block organization. Each section is written to stand on its own, and each homework set is completely self-testing. Beginning Algebra 6e is a worktext, meaning the design is open and friendly with wide margins so can you can encourage your students to take notes and work exercises right on the text page. Also with worktexts, images/visuals are used more frequently to convey the math concept so there are fewer words and less text for the student to read.
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Precalculus : Functions and Graph detailed solutions for odd-numbered exercises. The Ninth Edition of Swokowski Cole's highly respected precalculus text retains the elements that have made it so popular with instructors and students alike; the time-tested exercise sets feature a variety of applications; its exposition is clear; its un
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MicroComputers and Mathematics - J. W. Bruce - Hardcover 9780521375153 ISBN: 0521375150 Publisher: Cambridge University Press Summary: The interaction between computer mathematic...s. The authors cover topics such as number theory, approximate solutions, differential equations and iterative processes, with each chapter self-contained. Many exercises and projects are included giving ready made material for demonstrating mathematical ideas. Only a fundamental knowledge of mathematics is assumed and programming is restricted to 'basic BASIC' which will be understood by any microcomputer. The book may be used as a textbook for algorithmic mathematics at several levels, with all the topics covered appearing in any undergraduate mathematics course. Bruce, J. W. is the author of MicroComputers and Mathematics - J. W. Bruce - Hardcover, published under ISBN 9780521375153 and 0521375150. Eleven MicroComputers and Mathematics - J. W. Bruce - Hardcover textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $0.01, or buy new starting at $3,262.80
books.google.com - Easy Learning GCSE Maths Revision Guide for Edexcel A includes revision content with highlighted grade levels so that students know exactly which grade they are working at, making revising for GCSE Maths easy. ·Easy to use - clear and comprehensive structure and design ·Easy to revise - colour-coded... Maths Revision Guide for Edexcel A
work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Here in this volume, the authors have again confined their attention to varieties defined on a ground field without characteristic. In order to familiarize the reader with the different techniques available to algebraic geometers, they have not confined themselves to one method and on occasion have deliberately used more advanced methods where elementary ones would serve, when by so doing it has been possible to illustrate the power of the more advanced techniques, such as valuation theory. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed. less
Do Two Halves Really Make a Whole? Really, there is no such thing as Algebra 1 and Algebra 2. something to our children. Will it be of any more value than the material goods we have acquired? While it may be somewhat narrow in perspective, here is something to consider. As you educate your students, can you say they are involved in concept development, or are they learning passively? Are they figuring things out for themselves, or are they learning tricks and shortcuts? Do they see the logic in what they are learning, or are they just memorizing information for a test? Are they analyzing their mistakes to find the reasons why they answered incorrectly, or are they just accepting their fate and recording a grade? A legacy can mean many things, but helping our children learn to think may be one of the longest-lasting tools we can bequeath to our children. Of course, we need to carefully consider the educational materials we use to teach our children, and those materials need to be developed logically. Unfortunately, traditional mathematics instruction is often driven by programs that are developed topically instead of logically. As we cover the traditional scope and sequence of algebra, I trust you will receive food for thought as you strive to leave an educational legacy to your child. "Do two halves really make a whole?" seems like such a simple question, but is the answer that obvious? Not when it comes to high school algebra! And I'm not talking about some new way to add algebraic fractions. I'm referring to the age-old practice of teaching two years of algebra in high school, which presumably makes up a complete algebra course. They may have been called Algebra 1 and 2, or Beginning Algebra and Advanced Algebra. In either case, the implication was that each comprised one-half of a complete algebra course. However, if you look at the table of contents in any "second-year algebra" book, you will find that at least 50 percent of the book is a repeat of "first-year algebra." So really, there is no such thing as Algebra 1 and Algebra 2. These are courses (or names for courses) that came about as a result of school scheduling. Many years ago, when it was the norm to require only two math credits to graduate from high school, a study of algebra was a natural beginning credit. Of course, since it was generally taught "mechanically," utilizing many formulas and rules, a lot of practice and repetition was involved and, in fact, the study was not even completed in one year. So, for another math credit, geometry was taught for a year. It was considered "another discipline," involving a significant amount of logical reasoning and proof, and it gave students "another math experience." That took care of the required credits. Then, the next year, students interested in going further in their study of mathematics were offered the opportunity to continue, and finish, their study of algebra. Of course, because of the "procedural" way it was taught initially, students simply didn't remember much of that first year. So, they started over, re-studying many of the same things. This time, however, it was called Advanced Algebra. Something of a contradiction, don't you think? In fact, the word "advanced" is a relative term anyway. Chapter 2 of an algebra book is "advanced" compared to Chapter 1, isn't it? This has been perpetuated through the years, primarily because of that traditional implementation. When you try to memorize rules, formulas, tricks and shortcuts without really knowing why they work, it will take a lot of drill and review just to remember the material for a test. Yet, even today, that approach is often considered to be the "normal way" to teach algebra. Therefore, I suggest that one of the most fragmenting things we have done in mathematics education is to forcibly insert a geometry course into the middle of an algebra course. Algebra is a single, "complete" course, divided only by concept areas. It is the study of relations (equations and inequalities), and it develops by degrees (as defined by the exponents). It begins, very logically, with a study of first-degree relations (all of the exponents are "1"), and continues to develop by exploring other types of exponents. Included are higher-order relations (with integer exponents), rational-degree relations (with fractions as exponents) and literal-degree relations (when the exponents are variables, or "letters"). As such, algebra is the basic language of all upper-level mathematics courses, including geometry. Not only is geometry not a prerequisite for advanced algebra (whatever that is supposed to be), but you really need a good understanding of algebra as a complete course before you can fully understand a complete geometry course. That means there is a disadvantage, from the viewpoints of instruction and subject integrity, when you study geometry in the middle of an algebra course. The analogy may be somewhat over-simplified, but it is a little like beginning to learn English, and before reaching a reasonable level of mastery in the structure and syntax of the language, being introduced to a study of classic literature. They are just not ready for that yet. Of course, all this would be irrelevant if algebra were taught analytically, without dependence on rules and shortcuts. If students were taught the "why" of algebraic principles, less repetition and practice would be necessary, and algebra could be studied in one school year. Then, the two "halves" would truly make a "whole." Thomas Clark is the president of VideoText Interactive and the author of Algebra: A Complete Course and Geometry: A Complete Course. His Convention workshops will go into greater detail concerning the effective teaching of mathematics. For more information, visit
Book summary Difference equations, second edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.* phase plane analysis for systems of two linear equations* use of equations of variation to approximate solutions* fundamental matrices and floquet theory for periodic systems* lasalle invariance theorem* additional applications: secant line method, bison problem, juvenile-adult population model, probability theory* appendix on the use of mathematica for analyzing difference equaitons* exponential generating functions* many new examples and exercises [via]
Elementary Number Theory 9780073051888 ISBN: 0073051888 Edition: 6 Pub Date: 2005 Publisher: McGraw-Hill College Summary: Elementary Number Theory, Sixth Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elemen...tary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history. Burton, David M. is the author of Elementary Number Theory, published 2005 under ISBN 9780073051888 and 0073051888. Two hundred thirteen Elementary Number Theory textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $44.95, or buy new starting at $160.62
Waverley TrigonometryHigh school calculus covers the topics covered in the first two semesters of college calculus discipline and introduces you to the most fundamental concepts in the subject so you can answer questions such as these two and many more. I took AP calculus (BC level) when I was a senior in high schoo...
Key to Algebra This series of ten workbooks is equivalent to a complete first year algebra course, although less difficult than most. Titles of each book indicate topics covered: Operations on Integers; Variables, Terms and Expressions; Equations; Polynomials; Rational Numbers; Multiplying and Dividing Rational Expressions; Adding and Subtracting Rational Expressions; Graphs; Systems of Equations; and, Square Roots and Quadratic Equations. The worktext format provides instruction, examples, and room for problem solving, all within each workbook. Word problems help students understand life applications for algebra. As in the Key to Geometry series, much of the time students "discover" mathematical principles through problem solving activities with presentation of the rules following. This is in contrast to most algebra programs which teach rules first, with application practice following. Review takes place at the end of each book. Reproducible tests are available. Answers and Notes come in three separate books: one covering Books 1-4, one for Books 5-7, and one for Books 8-10. Like the other Key series, the books are black and white, consumable workbooks. They have large print and fewer exercises per page than most standard textbooks, so they are unintimidating. Because they are easy to use and understand, these books are especially good for both students and parents who are weak in math. While Key to Algebra can be a full, first-year algebra course, it can also be used for review or as a gentle introduction, possibly using only the first seven books before a student begins a rigorous algebra course. Students who plan to go on to an Algebra II course should probably choose a more rigorous first year course. Pricing All prices are provided for comparison only and are subject to change. Click on prices to verify their accuracy
Mathematica in the Classroom Classroom Chemistry Simulations At Imperial College, staff from the mathematics and chemistry departments have set up computer-based "Mathematics Laboratories" for first year chemistry undergraduates. We've provided several types of activity in these laboratories, but one of the most important kinds involves students' setting up and studying models and simulations of chemical conditions and processes. Dedicated simulation software exists for this sort of thing, much of it offering a lot of presentational sophistication and dynamic interactivity. But actually, all our simulations are implemented entirely in Mathematica; moreover, our presentation style is simple and stark in the extreme. Phil Ramsden, a Mathematica user and educator since the days of Version 1.0, serves on the Program Committee of the International Mathematica Symposium. At Imperial College in London, England, he is the manager of the METRIC Project, which writes and runs Mathematica-based courses. In his spare time he does a little math.
The Higher Arithmetic: An Introduction to the Theory of Numbers Now into its Eighth edition, The Higher Arithmetic introduces the classic concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers The theory of numbers is considered to be the purest branch of pure mathematics and is also one of the most highly active and engaging areas of mathematics today. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers & number theory, and primality testing. Written to be accessible to the general reader, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly. Now with updated ACLS algorithms An Introduction to Clinical Emergency Medicine is a much-needed resource for individuals practicing in this challenging field. It takes a novel approach, describing ...
Introduction Elementary algebra is concerned with certain simple functions such as addition and multiplication, with the development of notation for their use, and with the treatment of properties of these functions (such as commutativity) and of relations among them. This text continues the treatment of functions, but with more emphasis on their properties and their applications, and introduces the so-called elementary functions which form the basis for most work in the applications of mathematics. The elementary functions include the logarithm, antilogarithm, and the circular (also called trigonometric) and the hyperbolic functions. The present treatment of elementary functions differs from most traditional texts in three major respects. Firstly, each function introduced is defined explicitly in terms of known functions so that means are provided for the evaluation of each function introduced. This contrasts with the common definition of logarithms and trigonometric functions in terms of tables alone. Secondly, the treatment of each function is based largely on the slope of the function, and upon the related solution of an addition formula for the function. Thirdly, this text is based on the notation and the treatment of algebra presented in Reference 1. The text includes a summary and review of the notation; most of this review appears in this chapter and the rest is interspersed as needed. Any reader familiar with the material of algebra but not with the notation should find the text and exercises of this chapter an adequate introduction. The simplicity and precision of the notation permits an algorithmic treatment of the material. In particular, every expression in the text can be executed directly by simply typing it on an appropriate computer terminal. The use of a computer is not essential, but it can be useful in exercises and other explorations of the functions treated. Suggestions for the use of an APL computer may be found in Section 1.4, in Chapter 10, and in Appendix C of Reference 1. Further information about the computer may be found in References 2-4. The serious student should treat the exercises as an integral part of the text. The point at which each group of exercises can be attempted is indicated by a marginal note consisting of a domino (⌹) followed by the number of the first exercise in the group. The groups are separated by horizontal lines. The inclusion of too many simple exercises may bore the quick student, but their exclusion may leave unbridgeable gaps in the experience of some. The student should therefore learn to use discretion in the doing of exercises, ranging ahead and skipping detail, but being prepared to return to do earlier exercises whenever unintelligible difficulties arise in later ones. The most serious difficulty most students find with this approach is psychological; one must learn to treat exercises as a potential source of light and delight rather than as a capriciously imposed drudgery.
This Mathematics Dictionary is a comprehensive dictionary with suggestions of about thousands of internet related terms and abbreviations.Learn about the Mathematics terms and much more.Mathematics Dictionary is content all maths related Keyword description,which is used in all stream. Math/Maths Dictionary is a set of daily brain training exercises and math drills designed to enhance mental arithmetic. we provide the facility of advance search in our Management dictionary. which helped you all to seach your need. Feature: Quick dynamic search of words while you type Filters to help you locate the word you are searching for. tags: math guide, maths help, mathematics, maths book, formulas book
QuickMath is an automated service for answering common math problems over the internet. ... see more QuickMath is an automated service for answering common math problems over the internet. Think of it as an online calculator that solves equations and does all sorts of algebra and calculus problems - instantly and automatically! When you submit a question to QuickMath, it is processed by Mathematica, the largest and most powerful computer algebra package available today. The answer is then sent back to you and displayed right there on your browser, usually within a couple of seconds. Best of all, QuickMath is 100% free! The TIMSS-R Video Study is a cross-national study of eighth-grade classroom mathematics and science teaching. The study... see more The TIMSS-R Video Study is a cross-national study of eighth-grade classroom mathematics and science teaching. The study involves videotaping and analyzing teaching practices in more than onethousand classrooms in various countries. Links at this site provide information about the study and the tools used. A tool of interest to educational researchers is called vPrism. vPrism software for Mac OS that makes it easy to turn video into information that you can use: for research, for training, or presentations. vPrism allows you to easily: (1) Archive and organize your digital video files (2) Transcribe and annotate your video (3) Define and mark codes (4) Search and retrieve video using text or codes (5) Export event codes for statistical analysis (6) Prepare cliplists for presentations and discussions (7) Export for presentations to award-winning VideoVisor Pro software. It is useful as a teacher training tool as well as a research tool. vPrism is exclusively sold by LessonLab Inc. at a price of $995. Would anyone using this software please add an assignment so that we can establish a virtual vPrism user's group?The subject introduces the principles of ocean surface waves and their interactions with ships, offshore platforms and... see more The subject introduces the principles of ocean surface waves and their interactions with ships, offshore platforms and advanced marine vehicles. Surface wave theory is developed for linear and nonlinear deterministic and random waves excited by the environment, ships, or floating structures. Following the development of the physics and mathematics of surface waves, several applications from the field of naval architecture and offshore engineering are addressed. They include the ship Kelvin wave pattern and wave resistance, the interaction of surface waves with floating bodies, the seakeeping of ships high-speed vessels and offshore platforms, the evaluation of the drift forces and other nonlinear wave effects responsible for the slow-drift responses of compliant offshore platforms and their mooring systems designed for hydrocarbon recovery from large water depths. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.022. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.24. This is the seminal article describing C. E. Shannon's mathematical model of Communication, originally printed in the Bell... see more This is the seminal article describing C. E. Shannon's mathematical model of Communication, originally printed in the Bell Systems Technical Journal in 1948. This is the original source for the standard Source-Message-Channel-Receiver (SMCR) model of communication frequently used in the analysis of speech and media communication. Speech students will be surprised by the amount of math in this landmark work in their field. A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for... see more A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.The material and its presentation are pretty stripped-down and it will probably be desirable for the instructor to supply further hints from time to time or to let the students consult other sources. Various concepts and and topics that are often covered in introductory mathematical logic or computability courses are given very short shrift or omitted entirely, among them normal forms, definability, and model theory. This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to... see more This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to read on their own to refresh or clarify what they learned in class. This text is designed for use with the "Advanced Algebra II: Homework and Activities" ( and the "Advanced Algebra II: Teacher's Guide" ( collections to make up the entire course.
and Study aids2013-12-09T23:18:49Student Essentials: Critical Thinking Hills practical and easy-to-use guide allows students to master the essentials of critical thinking in just one hour. With advice, useful checklists and exercises to help students develop and apply core critical thinking skills. From constructing s...112 pages187 KB5.99McGraw-Hill's Math Grade 6 Editors students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills!McGraw-Hill's Math Grade 6 helps your middle-school student learn and practice basic math skills he or she will need in the classroom and on ...160 pages11.4 MB8.29Statistics Hacks: Tips & Tools for Measuring the World and Beating the Odds Frey Media2008-07-13Want to calculate the probability that an event will happen? Be able to spot fake data? Prove beyond doubt whether one thing causes another? Or learn to be a better gambler? 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A revision of McGraw-Hill's leading calculus text for the 3-semester sequence taken primarily by math, engineering, and science majors. The revision is substantial and has been influenced by students, instructors in physics, engineering, and mathematics, and participants in the national debate on the future of calculus. Revision focused on these key areas: Upgrading graphics and design, expanding range of problem sets, increasing motivation, strengthening multi-variable chapters, and building a stronger support package. Table of Contents Calculus and Analytic Geometry 1. An Overview of Calculus. 1.1 The Derivative 1.2 The Integral 1.3 Survey of the Text 2. Functions, Limits, and Continuity. 2.1 Functions 2.2 Composite Functions 2.3 The Limit of a Function 2.4 Computations of Limits 2.5 Some Tools for Graphing 2.6 A Review of Trigonometry 2.7 The Limit of (sin ō)/ō as ō Approaches 0 2.8 Continuous Functions 2.9 Precise Definitions of "lim(x->infinity)f(x)=infinity" and "lim(x->infinity)f(x)=L" 2.10 Precise Definition of "lim(x->a)f(x)=L" 2.S Summary 3. The Derivative. 3.1 Four Problems with One Theme 3.2 The Derivative 3.3 The Derivative and Continuity 3.4 The Derivative of the Sum, Difference, Product, and Quotient 3.5 The Derivatives of the Trigonometric Functions 3.6 The Derivative of a Composite Function 3.S Summary 4. Applications of the Derivative. 4.1 Three Theorems about the Derivative 4.2 The First Derivative and Graphing 4.3 Motion and the Second Derivative 4.4 Related Rates 4.5 The Second Derivative and Graphing 4.6 Newton's Method for Solving an Equation 4.7 Applied Maximum and Minimum Problems 4.9 The Differential and Linearization 4.10 The Second Derivative and Growth of a Function 4.S Summary 5. The Definite Integral. 5.1 Estimates in Four Problems 5.2 Summation Notation and Approximating Sums 5.3 The Definite Integral 5.4 Estimating the Definite Integral 5.5 Properties of the Antiderivative and the Definite Integral 5.6 Background for the Fundamental Theorems of Calculus 5.7 The Fundamental Theorems of Calculus 5.S Summary 6. Topics in Differential Calculus. 6.1 Logarithms 6.2 The Number e 6.3 The Derivative of a Logarithmic Function 6.4 One-to-One Functions and Their Inverses 6.5 The Derivative of b^x 6.6 The Derivatives of the Inverse Trigonometric Functions 6.7 The Differential Equation of Natural Growth and Decay 6.8 l'Hopital's Rule 6.9 The Hyperbolic Functions and Their Inverses 6.S Summary 7. Computing Antiderivatives. 7.1 Shortcuts, Integral Tables, and Machines 7.2 The Substitution Method 7.3 Integration by Parts 7.4 How to Integrate Certain Rational Functions 7.5 Integration of Rational Functions by Partial Fractions 7.6 Special Techniques 7.7 What to Do in the Face of an Integral 7.S Summary 8. Applications of the Definite Integral. 8.1 Computing Area by Parallel Cross Sections 8.2 Some Pointers on Drawing 8.3 Setting Up a Definite Integral 8.4 Computing Volumes 8.5 The Shell Method 8.6 The Centroid of a Plane Region 8.7 Work 8.8 Improper Integrals 8.S Summary 9. Plane Curves and Polar Coordinates. 9.1 Polar Coordinates 9.2 Area in Polar Coordinates 9.3 Parametric Equations 9.4 Arc Length and Speed on a Curve 9.5 The Area of a Surface of Revolution 9.6 Curvature 9.7 The Reflection Properties of the Conic Sections 9.S Summary 10. Series. 10.1 An Informal Introduction to Series 10.2 Sequences 10.3 Series 10.4 The Integral Test 10.5 Comparison Tests 10.6 Ratio Tests 10.7 Tests for Series with Both Positive and Negative Terms 10.S Summary 11. Power Series and Complex Numbers. 11.1 Taylor Series 11.2 The Error in Taylor Series 11.3 Why the Error in Taylor Series Is Controlled by a Derivative 11.4 Power Series and Radius of Convergence 11.5 Manipulating Power Series 11.6 Complex Numbers 11.7 The Relation between the Exponential and the Trigonometric Functions 11.S Summary 12. Vectors. 12.1 The Algebra of Vectors 12.2 Projections 12.3 The Dot Product of Two Vectors 12.4 Lines and Planes 12.5 Determinants 12.6 The Cross Product of Two Vectors 12.7 More on Lines and Planes 12.S Summary 13. The Derivative of a Vector Function. 13.1 The Derivative of a Vector Function 13.2 Properties of the Derivative of a Vector Function 13.3 The Acceleration Vector 13.4 The Components of Acceleration 13.5 Newton's Law Implies Kepler's Laws 13.S Summary 14. Partial Derivatives. 14.1 Graphs 14.2 Quadratic Surfaces 14.3 Functions and Their Level Curves 14.4 Limits and Continuity 14.5 Partial Derivatives 14.6 The Chain Rule 14.7 Directional Derivatives and the Gradient 14.8 Normals and the Tangent Plane 14.9 Critical Points and Extrema 14.10 Lagrange Multipliers 14.11 The Chain Rule Revisited 14.S Summary 15. Definite Integrals over Plane and Solid Regions. 15.1 The Definite Integral of a Function over a Region in the Plane 15.2 Computing \|R f(P) dA Using Rectangular Coordinates 15.3 Moments and Centers of Mass 15.4 Computing \|R f(P) dA Using Polar Coordinates 15.5 The Definite Integral of a Function over a Region in Space 15.6 Computing \|R f(P) dV Using Cylindrical Coordinates 15.7 Computing \|R f(P) dV Using Spherical Coordinates 15.S Summary 16. Green's Theorem. 16.1 Vector and Scalar Fields 16.2 Line Integrals 16.3 Four Applications of Line Integrals 16.4 Green's Theorem 16.5 Applications of Green's Theorem 16.6 Conservative Vector Fields 16.S Summary 17. The Divergence Theorem and Stokes' Theorem. 17.1 Surface Integrals 17.2 The Divergence Theorem 17.3 Stokes' Theorem 17.4 Applications of Stokes' Theorem 17.S Summary Appendices: A. Real Numbers. B. Graphs and Lines. C. Topics in Algebra. D. Exponents. E. Mathematical Induction. F. The Converse of a Statement. G. Conic Sections. H. Logarithms and Exponentials Defined through Calculus. I. The Taylor Series for f(x,y). J. Theory of Limits. K. The Interchange of Limits. L. The Jacobian. M. Linear Differential Equations with Constant Coefficients. Answers to Selected Odd-Numbered Problems and to Guide Quizzes List of Symbols Index
I am going to college now. As math has always been my weakness, I purchased the course material in advance. I am plan on learning a handful of chapters before the classes begin. Any kind of pointers would be highly appreciated that could assist me to start studying middle school math with pizzazz! book d answers myself. It's true , there are programs that can help you with homework. I think there are several ones that help you solve math problems, but I believe that Algebrator stands out amongst them. I used the program when I was a student in Algebra 2 for helping me with middle school math with pizzazz! book d answers, and it always helped me out since then. Step by step I understood all the topics, and soon I was able to solve the most challenging of the tasks on my own. Don't worry; you won't have any problem using it. It was made for students, so it's simple to use. Basically you just have to type in the topic nothing more .Of course you should use it to learn math, not just copy the answers, because you won't improve that way. It would really be nice if you could let us know about a software that can offer both. If you could get us a home tutoring software that would give a step-by-step solution to our problem, it would really be great. Please let us know the genuine links from where we can get the tool. Algebrator is a very great software and is definitely worth a try. You will also find several interesting stuff there. I use it as reference software for my math problems and can say that it has made learning math more fun.
Annotations for Figuring Out Geometry Baker & Taylor Explains the basic principles of geometry with step-by-step instructions on topics such as angles, area, volume, and polygons. ---------------------- Baker & Taylor This set of remedial math books for struggling math students provides step-by-step lessons to the basics of math, including fractions, decimals, percents, ratios, and more.
With more than 100 built-in functions, forms to enter matrix and list data, SCalc calculates matrix inversions, LU (QR) decompositions, definite integrals, derivatives and zeros of simple functions. Solve a system of linear equations using QRS operation. Draw 15 graphs/plots, compute 10 commands. Switch to increasingly complex layouts, solve equations and compute special functions.Draw parametric, cartesian and polar graphs. Zoom in and zoom out with a display of scale and zoom level used. Track graph functions. Stretch and compact graphs along the y-axis. Compute commands like integrations, derivatives, maxima and minima along with drawings of results on the graphics screen. Also obtain samples of x-y data of graphs or functions. Using x-y data, curve-fit and plot. Use 3 choice backgrounds and draw with a selection of colors. Compute list functions, exponential functions, statistical, and various special functions. Define your own functions and variables, store them on external SD card and reload them back into internal memory. Do multiple conversions between primary units. Compute properties of simple geometric figures. Install or move the application to an SD card.Choose any previous command from a history list. Read the built-in function list -- upon long pressing the result -- and the helpful summary information to bring the function into input. Use help to determine valid values for the parameters for built-in functions.With recent improvements, swipe left and swipe right on the special function keys to find the keys you want easily. Position the coordinate lines precisely with left and right arrow controls on the graph screen. Find the scale and zoom level upon touch in a floating window display. Pinch with two fingers to zoom in and zoom out of the graphs. To find zero, repeatedly touch the result (R button) on graphics screen. If possible, you can find different zeros each time within a given range.With SCalc , you do not need to visit a help website or usage manual as plenty of easy to read instructions are provided with every step of calculation. These help messages can be turned off once you are familiar with the usage. When there is an error in the input, SCalc highlights the exact location of error in the input. Care has been taken in the design of the interface, so users with or without a keyboard can get the same functionality and ease of use.To use international versions, set the input language for on screen keyboard to be
The shape of content : creative writing in mathematics and science( Book ) 3 editions published in 2008 in English and held by 117 libraries worldwide "This book is a collection of creative pieces--poems, short stories, essays, play excerpts--that give shape to mathematical and scientific content. It portrays by example how various people work creatively with ideas from mathematics and other sciences."--BOOK JACKET.Calculus film project( Visual ) 2 editions published between 1992 and 2008 in English and held by 40 libraries worldwide Collection of short animated films about calculus ranging from informal to detailed investigations. MAA calculus films( Visual ) 1 edition published in 1993 in English and held by 19 libraries worldwide Pt. 2 (ca. 52 min.). Presents Newton's method as representative of an iterative procedure; defines the definite integral using Riemann sums; demonstrates the fundamental theorem of calculus, showing the functions F(x) and f(x) graphed simultaneously on separate sets of axes to illustrate that F'(x) = f(x); defines area in terms of the calculus. Pt. 3 (ca. 53 min.). Discusses areas under curves with emphasis on the graphs of continuous and monotone functions; illustrates the definite integral by the method of upper and lower sums; explains that the volume of an urn-like solid can be expressed with a definite integral; explains that the volume of a torus can be expressed as a definite integral using the shell method. Science for good or ill by Chandler Davis( Book ) 2 editions published between 1989 and 1990 in English and held by 9 libraries worldwide The geometric vein( Book ) 1 edition published in 1981 in English and held by 9 libraries worldwide Keeping in mind the McCarthy era at the University of Michigan( Visual ) 4 editions published in 2000 in English and held by 2 libraries worldwide A documentary about three faculty members--Clement Markert, Mark Nickerson, and Chandler Davis--forced to leave the University of Michigan because of alleged affiliations with the Communist Party. Caroms( Visual ) in English and held by 1 library worldwide Shows the relationship between a carom and a reflection, and uses this principle to solve elementary geometric inequalities leading up to an exploration of Fagnano's problem: to find a triangle of minimum perimeter that can be inscribed in a given acute-angled triangle. Features mathematician Chandler Davis. Dance of the shells( Visual ) 1 edition published in 2002 in English and held by 1 library worldwide Entrant in the Dance Films Association's 31st annual Dance on Camera Festival 2003. Videodance work.
has penciled notes and math problems in a few drill...Good. Book has penciled notes and math problems in a few drill sections. Overall, text is clean, and the book is still usable
447 San Ysidro statistics and SPSS algebra 1, algebra 2 and calculus
FOR PARENTS FOR STAFF MATHEMATICS DEPARTMENT Click on your teacher's name to access his or her website. The Sachem Mathematics Department is committed to providing meaningful courses designed to motivate and encourage mathematical and critical thinking. The mathematics courses offered will not only aid in development of conceptual understanding of mathematics, but will increase problem solving skills and enhance students' abilities to communicate and reason mathematically. To view a description of all course offerings, please view the Guidance Handbook.
designedGet the Math is designed to help students understand real-world applications of Algebra I. Interrelated video segments and interactive tools support student learning of algebraic concepts related to music, fashion, videogames, restaurants, basketball, and special effects
Synopses & Reviews Publisher Comments: The classic Mathematics for Engineers and Scientists covers in detail all mathematical requirements common to first year engineering students of every discipline. It includes numerous illustrative worked examples and extensive problem sets at the end of each chapter, with answers to odd-numbered questions provided at the end of the book. In this sixth edition, the level of rigor has been lowered to cater to the needs of incoming engineering students. Students are encouraged to make use of computer algebra packages, primarily MAPLE and MATLAB. The author has included a new chapter on double integrals, and incorporated many new applications and examples
Prealgebra and Introductory Algebra (Paper) - 3rd edition Summary: Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra& Introductory Algebra, Third Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for20.84VeryGood SellBackYourBook Aurora, ILGood SellBackYourBook Aurora, IL 0321644905 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Solutions manual (available only to teachers) Marc Frantz holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University. He teaches mathematics at Indiana University, Bloomington where he is a research associate. Annalisa Crannell is professor of mathematics at Franklin & Marshall College. She is the coauthor of Writing Projects for Mathematics Courses.
Mathematics for Physics 9780199289295 ISBN: 0199289298 Pub Date: 2007 Publisher: Oxford University Press, Incorporated Summary: Mathematics is the essential language of science. It enables us to describe abstract physical concepts, and to apply these concepts in practical ways. Yet mathematical skills and concepts are an aspect of physics that many students fear the most. Mathematics for Physics recognizes the challenges faced by students in equipping themselves with the maths skills necessary to gain a full understanding of physics. Working ...from basic yet fundamental principles, the book builds the students' confidence by leading them through the subject in a steady, progressive way. As its primary aim, Mathematics for Physics shows the relevance of mathematics to the study of physics. Its unique approach demonstrates the application of mathematical concepts alongside the development of the mathematical theory. This stimulating and motivating approach helps students to master the maths and see its application in the context of physics in one seamless learning experience. Mathematics is a subject mastered most readily through active learning. Mathematics for Physics features both print and online support, with many in-text exercises and end-of-chapter problems, and web-based computer programs, to both stimulate learning and build understanding. Mathematics for Physics is the perfect introduction to the essential mathematical concepts which all physics students should master. Woolfson, Michael M. is the author of Mathematics for Physics, published 2007 under ISBN 9780199289295 and 0199289298. One hundred ninety two Mathematics for Physics textbooks are available for sale on ValoreBooks.com, five used from the cheapest price of $36.10, or buy new starting at $61.12
Beginning Algebra is an insightful text written by instructors who have firsthand experience with developmental mathematics. The text places an emphasis on graphing and exercises that are infused with review. Applications found in the exercise sets are based on real-world data, which helps to promote student in mathematics and, in turn, may serve to motivate and engage them more effectively.
Lisbon and the Algarve" Rick finds salty sailors' quarters and Fado singers mixed with architecture from Portugal's days as a world power.G 11:00 pm Learning Math: Patterns, Functions & Algebra"Linear Functions and Slope" Explore linear relationships by looking at lines and slopes. Using computer spreadsheets, examine dynamic dependence and linear relationships and learn to recognize linear relationships expressed in tables, equations, and graphs. Also, explore the role of slope and dependent and independent variables in graphs of linear relationships, and the relationship of rates to slopes and equations.G 11:30 pm Learning Math: Patterns, Functions & Algebra"Solving Equations" Look at different strategies for solving equations. Topics include the different meanings attributed to the equal sign and the strengths and limitations of different models for solving equations. Explore the connection between equality and balance, and practice solving equations by balancing, working backwards, and inverting operations.G
Basic Math and Pre-Algebra - 2nd edition Delivers the appropriate amount of expert coverage on basic math topics for consumers who need a supplement to a beginning basic math text or class; who need to prepare for exams; or who need to brush up on the fundamentals of basic math Chapter Check-In gives readers an overview of what they'll learn in the chapter Chapter Check-Out reviews the chapter to enforce the items learned and help with comprehensio...show moren Review section is a summary test on all chapter topics in the book -- great tool for teachers and students Resource Center directs reader to additional information available for the subject such as books and websites 500 practice questions available online at CliffsNotes.com and directly ties to each chapter in the book
Course Materials: You need at least an 1-inch looseleaf binder and looseleaf paper on which to take notes and to do written assignments. You may take notes in ink, but you should usepencil for classwork and homework. You will need your textbook every day. Textbooks: You will be issued a mathematics textbook. You are responsible for keeping it in good condition. If you lose your textbook during the year, you must get another book within two (2) school days. Notebooks: Two notebook tests will be given each nine weeks. In order to receive the best grade possible, take down all bell work, class notes and examples; and follow this with the homework assignments (labeled with the date it was assigned, textbook page number and problem numbers). Any handouts should be dated and placed in the notebook immediately. Notebook tests are 100 points each. Tests: Tests will consist of selected material from notes and other written work from a unit. All tests are 100 points each and are announced two (2) class days in advance of the date the test is given. Tests will be graded within two (2) class days after the test date. A student may make test corrections on any test to earn back 50% of points missed. Quizzes: Quizzes may be given more than once per week. They will cover important material from your notes. Quizzes may vary in point value, but are usually 20-25 points each. Bell Work/Writing Assignments: Students are expected to come into the classroom and to begin the posted bell work or writing assignments immediately. Students have only 5-7 minutes to complete bell work. Occasionally, these will be collected and checked for completeness according to the daily work rubric. Bell work assignments are 5 points each. Daily Work: Classwork or homework will be assigned every day. It will include written work from your textbook, handouts, or problems given in class. Classwork or homework will be checked according to the following rubric: 5 – all problems attempted and necessary work shown 4 – at least two-thirds of all problems attempted and necessary work shown 3 – at least one-third of all problems attempted and necessary work shown 0 – less than one-third of all problems attempted Homework is to be done independently. Homework that is obviously copied will result in a grade of 0 for the persons involved. Call 326-7542 if you need an assignment. Partners: You will be assigned a partner who will sit near you and will work with you on assignments during class. If you have any problems working with your partner, please let Mrs. Hart know. Make-up Work: Keep up with your absences from class so that you will not exceed the limit for unexcused absences. When you return, get all notes and assignments from Mrs. Hart within five (5) school days. It is your responsibility to make sure that you get all make-up work. All make-up daily work must be submitted the day you return to class, unless other arrangements have been made with Mrs. Hart. Tests or quizzes must be made up within ten (10) school days after your return to class. Tutoring: Please ask Mrs. Hart for tutoring when you do not understand the material covered in class. She is available for tutoring during the first 10 minutes of lunch unless she must serve duty. She is also available for tutoring after school on Mondays, Wednesdays, and Thursdays unless she is required to attend a meeting. Progress Reports: Progress reports will be issued by your homeroom teacher twelve (12) times this year. These reports will contain only your current grade for all of your classes. Parents/guardians may check grades at any time using the Parent Portal. Report Cards: Report cards will be issued November 1, January 24, April 9 and June 5. Please have your parent/guardian sign the first three report cards and show them to Mrs. Hart for extra bonus points. Parent/Teacher Conferences: Parent/teacher conferences are September 20 (4 – 7 pm), September 21 (8 am – noon), February 14 (4 - 7 pm), and February 15 (8 am - noon). If parents/guardians must contact Mrs. Hart at any other time, she can be reached in her classroom (326-7542) during her planning period from 9:00 until 9:50 (9:10 until 10:00 on homeroom days) or after school. Contact her by e-mail using dedrah@darlington.k12.sc.us. Planning Period: Mrs. Hart's planning period is 2nd period (9:00-9:50 most days; 9:10-10:00 on days with homeroom). Behavioral Expectations: You are expected to Follow teacher instructions the first time they are given. Raise your hand before you talk, walk, or touch something that does not belong to you. Use respect (not "shut up" or name-calling) when speaking to others. Leave gum, candy, food or drinks outside the classroom. Follow Darlington County School District Discipline Code and Lamar High School policies. Consequences For Violations Of Behavioral Expectations: 1st offense – Name on the chalkboard and loss of bonus point. 2nd offense – Check by your name and 15-minute detention after school. 3rd offense – Second check by your name, parent contact and referral to administration. Rewards For Following Behavioral Expectations: Bonus point for each day. Homework Pass for five consecutive bonus points. Bonus Points: Bonus points are awarded daily for class participation and acceptable behavior. Examples of acceptable behavior are being on time for class, being in assigned seat, following teacher instructions the first time they are given, having all required materials, completing assignments, dressing properly, staying on assigned tasks, displaying a positive attitude, and following all rules and procedures. Points may not be awarded because of unexcused tardies to class, leaving class on your own initiative, failing to bring course materials to class, failing to do assignments, wearing questionable clothing requiring administration to check for dress code violation, breaking a rule, getting off subject, or failing to follow procedures. Work for Other Classes: Mrs. Hart reserves the right to collect and destroy any work from another class that she sees during the class period. Absences, Tardies, and Hall Passes: School policies will be followed with respect to these procedures. Parents/guardians may check student attendance at any time using the Parent Portal. Restroom Privileges: A student will not be allowed to use the restroom during the first 20 minutes of class. Otherwise, Mrs. Hart will follow the Lamar High School hall pass procedure. Off-Limits Areas: Mrs. Hart's desk area (including filing cabinets and shelves), cabinets, and tables are off-limits at all times. The classroom telephone can be used after school hours with Mrs. Hart's permission.
*SKILL REVIEW -- if available . Practice Placement Test Pre-Algebra Take the Practice Placement Test, then --after you receive your results-- use this guide to locate the ... South Carolina Mathematics Standards for Algebra 1; Prerequisite skill practice is provided on Study Guide pages and in the Mixed Review section of every lesson to better ... Why Course Hero? Used Course Hero for the first time yesterday and I cannot wait to use it again. I was extremely confused on my accounting test and how to read the FASB ... Our Archives Feel free to browse our math homework solutions archives. If you have an assignment that is similar to one in our archives feel free to request a price ... Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math ... u0022The homework system in MathXL is a fantastic way to facilitate student engagement with the course material in a classroom. I have noticed a distinct improvement in my ... The Tobey/Slater series builds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical building block organization ...
Builds on the author's tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' ...Show synopsisBuilds on the author's tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' proficiency and conceptual understanding of algebra. This text continues coverage and integration of geometry in examples and exercises 610
College Algebra 9780073312620 ISBN: 0073312622 Edition: 8 Pub Date: 2007 Publisher: McGraw-Hill College Summary: The Barnett, Ziegler, Byleen College Algebra series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and problem solving rather than mathematical theory. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, the students and instructors will find E...xplore-Discuss boxes which encourage students to think critically about mathematically concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. Barnett, Raymond A. is the author of College Algebra, published 2007 under ISBN 9780073312620 and 0073312622. Thirty six College Algebra textbooks are available for sale on ValoreBooks.com, nineteen used from the cheapest price of $103.45, or buy new starting at $235.68
fifth edition of Essential MATLAB for Engineers and Scientists provides a concise, balanced overview of MATLAB's functionality that facilitates independent learning, with coverage of both the fundamentals and applications. The essentials of MATLAB are illustrated throughout, featuring complete coverage of the software's windows and menus. Program design and algorithm development are presented clearly and intuitively, along with many examples from a wide range of familiar scientific and engineering areas. This is an ideal book for a first course on MATLAB or for an engineering problem-solving course using MATLAB, as well as a self-learning tutorial for professionals and students expected to learn and apply MATLAB.Updated with the features of MATLAB R2012bExpanded discussion of writing functions and scriptsRevised and expanded Part II: ApplicationsExpanded section on GUIsMore exercises and examples throughoutCompanion website for students providing M-files used within the book and selected solutions to end-of-chapter problems
partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation. Its modular structure makes the book suitable for a variety of uses and users Homework sets are available from Appendix provides material that is usually covered in mathematical analysis courses (e.g. the Lebesgue integral) but is often unfamiliar to the applied mathematician Reviews & endorsements "This carefully written book by a well-known expert in the area is also an excellent guide to the present literature, recommended as well to graduate students as to experts in the area. This volume will help the reader in getting acquainted with some mathematical aspects of the modern theory of linear and non-linear phenomena arising in relevant applications to mathematical physics." Zentralblatt MATH "This is a really wonderful book. It offers an amazing variety of information, well condensed but nevertheless very clear and easily understandable. It can be used just for learning mathematics, its notions and insights, yet the advanced reader discovers new, unexpected material over and over again, becoming up to date in a broader field, learning special methods, or using the book as an excellent manual when solving problems and exercises. The author has succeeded in creating a new, highly innovative kind of textbook. This most valuable modern book hardly needs recommendation, since it captures the reader as soon as she or he starts reading. We shall soon find it in reference lists. The author deserves the highest praise for this wonderful intellectual gift to the community. It certainly involved a huge amount of work combined with an expert's broad knowledge." Siegfried Grossmann, Journal of Fluid Mechanics "This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together." Laura K. Gross, Bridgewater State University for SIAM ReviewAndrea Prosperetti, The Johns Hopkins University and University of Twente Andrea Prosperetti is the Charles A. Miller, Jr Professor in the Department of Mechanical Engineering at the Johns Hopkins University. He also holds the Berkhoff Chair in the Department of Applied Sciences at the University of Twente in the Netherlands
More About This Textbook Overview Work more effectively and check solutions as you go along with the text! This Student Solutions Manual that is designed to accompany Anton's Calculus: Late Transcendentals, Single Variable, 8th edition provides students with detailed solutions to odd-numbered exercises from the text. Designed for the freshman/sophomoreBe Prepared This book can be helpfull for anyone taking calculus I & II, however, be prepared for many contradictions to the textbook, even incorrect answers and/or the use of wrong identities, including different, albeit correct answers that dont match the textbook. This makes at home problem solving frustrating and very difficult at times. If you are the type of person that likes to be able to follow all of the steps to get to the answer, consider that this book leaves out alot of steps that can be very helpfull, making you to really have to think about how to go about it. Maybe in the long run that is better for you, but it is still frustrating. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
First Book in Algebra Description: "A First Book in Algebra" will give you the confidence to tackle mathematical, science or social research problems using the power of algebra. Contains extensive worked examples and over 1400 exercises - with answers of course!First published overMore... "A First Book in Algebra" will give you the confidence to tackle mathematical, science or social research problems using the power of algebra. Contains extensive worked examples and over 1400 exercises - with answers of course!First published over 100 years ago, this volume remains the definitive guide to applying elementary algebra to real-world problems, whether for everyday use or exam preparation
books.google.com of the mathematical theory of multi-frequency oscillations
Linear Systems Publisher Review: Mathematical program for university students. Linear Systems gives a complete, step-by-step solution of the following problem: Given a 2x2 linear system (two equations, two variables) or 2x3, or 3x2, or 3x3, or 3x4, or 4x3, or 4x4 linear system. Find its solution set by using the Gauss-Jordan elimination method. The program is designed for university students and professors. Linear Systems' 1.02 is Mathematics software design by Dekov Software. It runs on following operating system: Windows 95/98/Me/NT/2000/XP Linear Systems 1.02 has been tested by the Soft32Download and it has been awarded with the "5 Stars Award" based in this criteria: user interface, features and price/value.
Introduction to Modern Analysis Shmuel Kantorovitz This text provides a comprehensive course in Modern Analysis. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters apply theory to applications in Probability Theory and Partial Differential Equations.
path to conquering the math skills essential for nursing success...and reducing the anxieties math often induces! Step by step, skill by skill...students progress from simple to complex calculations, building their proficiencies and testing it along the way. It's perfect for course review and quick reference
Programs in the Department of Mathematical Sciences 150 - Mathematics - BA 1. Students will demonstrate a conceptual understanding of and procedural facility with basic calculus concepts. 2. Students will apply concepts from algebra, geometry, and trigonometry in solving problems involving calculus. 3. Students will use the principles of multiple variable calculus. 4. Students will apply basic set operations. 5. Students will apply basic propositional and predicate logic. 6. Students will use the concepts of relation and equivalence relation. 7. Students will apply fundamental ideas of linear algebra. 8. Students will demonstrate competency with ordinary differential equations and their applications. 9. Students will apply the concept of sequence and infinite series. 10. Students will apply major concepts of abstract algebra. 11. Students will analyze functions of one or more variables. 12. Students will develop and evaluate mathematical arguments and proofs. 13. Students will select and use various types of reasoning and methods of proof. 14. Students will solve application problems that arise in mathematics and those involving mathematics and other contexts. 15. Students will select, apply and translate among mathematical representations to solve problems. 16. Students will communicate mathematical thinking coherently and clearly to peers, faculty and others. 17. Students will use the language of mathematics to express ideas precisely. 18. Students will use knowledge of mathematics to select and use appropriate technological tools, such as, but not limited to, graphing calculators or computer algebra systems (e.g. Mathematica and MATLAB). 19. Students will solve problems using an object oriented programming language and its corresponding operating system.
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as - via extended case studies - carrying out some of these... more... A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools... more... Learn how to develop your reasoning skills and how to write well-reasoned proofs Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques... more...... more...
News Detail Kent State Dedicates New Math Emporium on Sept. 13 Posted Sep. 7, 2011 New state-of-the art learning center equips college students with math skills needed for academic success Members of the Kent State University community will gather Sept. 13 at 4 p.m. to celebrate the opening of the new Kent State University Math Emporium, a state-of-the-art computerized learning center designed to help students learn math. Located on the second floor of the Kent State University Library, the Math Emporium launched this fall with the start of classes on Aug. 29. The introduction of the Math Emporium is an example of how Kent State is dedicated to the success of its students. Basic math skills are an essential foundation for many courses of study and necessary for students' overall academic success in college. "The university has developed a specialized learning experience to equip students with the mathematical knowledge they will need on their path to graduation,†said Robert G. Frank, Kent State provost and senior vice president for academic affairs. "The students will learn math by interacting with a team of instructors and the web-based math software called ALEKS. The Math Emporium promises to make a significant impact on our first-year retention. For some students, it will give them confidence in their math skills to pursue careers that require math, such as nursing and finance.â€ At the Math Emporium, students will learn through an innovative, engaging and easy-to-use program designed to help them become comfortable and proficient in basic mathematics. The Math Emporium serves as the classroom for four classes: Basic Algebra 1, 2, 3 and 4. Prior to the beginning of school, students take a placement assessment to determine which math courses they need. Students who need additional math preparation to succeed in college will be matched with the appropriate course of study in the Math Emporium. "Students will focus on learning exactly what they need to know at their own pace while their instructional team provides individualized coaching,†said Andrew Tonge, chair of the Department of Mathematical Sciences at Kent State. "The Math Emporium uses an adaptive software program, ALEKS, to determine what students already know. It then offers each student an individualized choice of paths forward. This enables them to complete the curriculum efficiently by always studying only material they are ready to learn. All students can then manage their study time to focus on actively learning precisely the information they need, with the aid of online help tools and an interactive e-book, together with one-on-one assistance from an instructional team.â€ The lead professor and the instructional team at the Math Emporium function as coaches, providing in-depth personalized teaching and support. Periodically, each student takes a progress assessment to check that they have fully understood the information they recently studied. Any material that has not been properly mastered is reassigned as part of the future study plan. At the end of the course, a comprehensive assessment determines the grade. This ensures students have a sufficiently rigorous grounding to have good prospects for success in subsequent courses. "The Math Emporium's potential effect on student success is very exciting,†Frank said. "In addition to this Math Emporium on our Kent Campus, we will have similar facilities on our Regional Campuses.â€ The Math Emporium features state-of-the-art technology with 247 computer stations in an 11,154-square-foot space. The facility also features bright, vibrant colors and comfortable furniture, making it an attractive and appealing environment. The Math Emporium is staffed from 7:30 a.m. to 9 p.m. Monday through Thursday; 7:30 a.m. to 6 p.m. on Friday; 10 a.m. to 6 p.m. on Saturday; and 12 p.m. to 8 p.m. on Sunday. Students also can access the program from any web browser. Media Note: Members of the media are welcome to attend and cover the dedication of the Kent State University Math Emporium on Sept. 13 at 4 p.m. The Math Emporium is located on the second floor of the Kent State University Library. Parking is available in the Kent Student Center Visitor Lot. Photo Caption: The Kent State University Math Emporium is a new state-of-the-art learning center that equips students with the mathematical knowledge they will need on their path to graduation.
instructional design supports the investigative approach to introduce a lesson while developing students' abilities to reason mathematically and communicate their thinking While the focus of the course is on expanding knowledge of functions, students will achieve an extended knowledge base on exponential and logarithmic functions, trigonometric functions, polynomial and rational functions, and characteristics of functions
The Mathematics that Every Secondary School Math Teacher Needs to Know knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the mathematical insight they need to engage their students in learning mathematics in a multifaceted way that i... MOREs interesting, developmental, connected, deep, understandable, and often, surprising and entertaining.Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT":M Multiple Approaches/RepresentationsA Applications to Real LifeT TechnologyH HistoryN Nature of Mathematics: Reasoning and ProofS Solving ProblemsI Interlinking Concepts: ConnectionsG Grade LevelsH Honing of Mathematical SkillsT Typical ErrorsThis text is ideally suited for a capstone mathematics course in a secondary mathematics certification program, is appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers. This clear, interactive, learner-centered text and resource will help pre-service and in-service secondary mathematics teachers gain the deep mathematical insight they need to teach their students in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining.
This unit explores a real-world system – the Great Lakes – where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained. Just as we usually take for granted the basic arithmetical operations with real numbers, so we usually assume that, given any positive real number a, there is a unique positive real number b = such that b2 = a. We now discuss the justification This unit is from our archive and is an adapted extract from Complex analysis (M33 want you now to follow a worshipper on a 'pilgrimage in miniature' around Dakshineswar temple on the outskirts of Calcutta. Before you read further, please study carefully the plan of Dakshineswar temple in Figure 14Databases are one of the more enduring software engineering artefacts; it is not uncommon to find database implementations whose use can be traced back for 15 years or more. Consequently, maintenance of the database is a key issue. Maintenance can take three main forms: Operational maintenance, where the performance of the database is monitored. If it falls below some acceptable standard, then reorganisation of the database, usuall OU PGCE has been developed by The Open University and its partner schools to provide an innovative, student-teacher centred approach to initial teacher education. We aim to build on the skills, knowledge and experience that student teachers bring to the profession, and then to prepare them for a career in teaching. The course leads to the award of PGCE, and Qualified Teacher Status (QTS) conferred by the appropriate statutory body. Working with a Partner Schools Network, the OU PGCE prov joining a learned society or professional organisation. They can be very useful for conference bulletins as well as in-house publications, often included in the subscription. Don't forget to ask about student rates. Try looking for the websites of learned societies associated with your subject area (e.g. The Royal Society, the Institute of Electrical language is a complex communication system that allows the generation of infinitely many different messages by combining the basic sounds (phonemes) into words, and combining the words into larger units called sentences. The way the sounds combine is governed by phonological rules, and the way the words combine is governed by syntactic rules. Phonemes can be divided into the vowels, which are made by vibration of the vocal folds, and consonants, which are abrupt sounds made by bri
the difference is, the TI-89 is only rated up to pre-calc but has engineering capacities wheras the TI-inspire has calculus capabilities but is not rated for engineering. I don;t know if it would be better to have engineering or calculus under its list of capabilities. And if all calculators are the same, then why is it that you can't graph with a TI-30 but you can with a TI-92?Trigonometry, some pretty good stat analysis, numeric multi-variable single-equation solver, numeric derivatives and integrals are included in most of the recent TI models. (the syntax for the last ones and the computation time are terrible, but that's another subject). I guess there is some formal calculus (ie instead of computing an approx of the derivative / integral /etc. it gives you the mathematical form of it) in the new models, but I never tried it so I can't say. After a quick internet search, I realized some of my comrades had a TI-89, so I can guarantee you it works with the features I mentioned. EDIT : including some formal calculus. I don't know about the N-spire, but it just looks to me like more expensive for similar functionalities plus a good look, which is not what most engineering students want. I am not much more advanced by your definition of pre-calculus. Sorry, but I am no American and I cannot guess what you mean by 'advanced math' especially after naming trigo etc. in another part. And anyways, I have to warn you : if you want to get to engineering, you will need more computing power than a calculator, you will need to learn 'real' programming not guess what you mean by that. "Algebra" is a large subject, from kids understanding theorems like "the sum of two odd numbers is an even numbers" to recent cutting-edge research in maths. And I don't think I am particularly stupid by not understanding the subtle difference between "algebra1" and "algebra2" on the basis of what you wrote. Make the effort to write so that I can understand it. If you told me "it includes matrices products and diagonalization, arithmetic congruences, basic algorithmic, etc." I would understand
Elements of Modern Algebra - 6th edition Summary: Helping to make the study of modern algebra more accessible, this text gradually introduces and develops concepts through helpful features that provide guidance on the techniques of proof construction and logic analysis. The text develops mathematical maturity for students by presenting the material in a theorem-proof format, with definitions and major results easily located through a user-friendly format. The treatment is rigorous and self-contained, in keeping with...show more the objectives of training the student in the techniques of algebra and of providing a bridge to higher-level mathematical courses. Benefits: NEW! The text and examples have been carefully refined for clarity and ease of understanding. Biographical sketches of mathematicians who have influenced the development of the material are included to provide insight into the historical development of mathematics. A summary of key words and phrases at the end of each chapter provides a valuable overview of the chapter. An abundance of examples develop students' intuition. A list of special notations used in the book and the group tables for the most common examples are on the endpapers for quick and easy reference. NEW! Homework problems have been added, revised, and improved. NEW! The coverage of binary operations and permutations and inverses has been split into two sections in Chapter 1. NEW! An optional section on the solution of cubic and quartic equations by formulas appears in Chapter 8. Descriptive labels and titles are placed on definitions and theorems to indicate their content and relevance. Strategy boxes are included to give guidance and explanation about techniques of proof. This feature forms a component of the bridge that enables students to become more proficient in their poof construction skills. Symbolic marginal notes are used to help students analyze the logic in the proofs of theorems without interrupting the natural flow of the proof. A reference system provides guideposts to continuations and interconnections of exercises throughout the text. An appendix on the basics of logic and methods of proof is included to assist students with a weak background in logic. The Field of Real Numbers. Complex Numbers and Quaternions. De Moivre's Theorem and Roots of Complex Numbers. Key Words and Phrases. A Pioneer in Mathematics: William Rowan Hamilton. 8. POLYNOMIALS. Polynomials over a Ring. Divisibility and Greatest Common Divisor. Factorization in F[x]. Zeros of a Polynomial. Solutions of Cubic and Quartic Equations by Formulas (Optional). Algebraic Extensions of a Field. Key Words and Phrases. A Pioneer in Mathematics: Carl Friedrich Gauss. Shows some signs of wear, and may have some markings on the inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy! $12$63.45 +$3.99 s/h Good eCampus.com Lexington, KY May contain some highlighting. Supplemental materials may not be included. We select best copy available. - 6th Edition - Hardcover - ISBN 9780534402648
Forget the jargon. Forget the anxiety. Just remember the math. In this age of cheap calculators and powerful spreadsheets, who needs to know math? The answer is: everyone. Math is all around us. We confront it shopping in the supermarket, paying our bills, checking the sports stats, and working at our jobs. It is also one of the most fascinating-and... more... Towards the end of the nineteenth century, Frege gave us the abstraction principles and the general notion of functions. Self-application of functions was at the heart of Russell's paradox. This led Russell to introduce type theory in order to avoid the paradox. Since, the twentieth century has seen an amazing number of theories concerned with types... more... Numerical Modeling of Water Waves, Second Edition covers all aspects of this subject, from the basic fluid dynamics and the simplest models to the latest and most complex, including the first-ever description of techniques for modeling wave generation by explosions, projectile impacts, asteroids, and impact landslides. The book comes packaged with... more... The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problems. Typically, such problems are expressed in terms of differential equations which contain at least one small parameter, and they can arise in many fields: fluid mechanics, particle physics, and combustion... more... Rod structures are widely used in modern engineering. These are bars, beams, frames and trusses of structures, gridwork, network, framework and other constructions. Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics... more... This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows, and certain integrable systems. The subjects are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. more...
15 Total Time: 4h 27m Use: Watch Online & Download Access Period: Unlimited Created At: 07/29/2009 Last Updated At: 04/18/2011 The most common applications of differentiation and derivatives are uses in position/velocity/acceleration, related rate problems, linear approximation, and related rates. In this 15-lesson series, we'll go through each of these applications. We'll start with a couple lessons on calculus word problems calling for you to differentiate a position or velocity function in order to come up with either velocity (instantaneous rate of change in position) or acceleration (instantaneous rate of change in velocity). Then, we'll have three lessons on linear approximation, Newton's method, highe-order derivatives, and using the tangent line in linear approximation. Related rate problems involve using a known rate of change to find an associated rate of change. The three steps to problem solving are understanding what you want, determining what you know, and finding a connection between the two. We'll have five lessons that teach you how to approach and solve related rate problems. Last, we'll learn about the relationship between slope and optimization. On an interval, the sign of the derivative of a function indicates whether that function is increasing or decreasing. Values that make the derivative of a function equal to 0 are candidates for the location of maxima and minima of the function. Once we master this concept, we'll look at several word problems that ask us to use derivatives to optimizeProf Burger does it again!! Video is so helpful....this is a topic I have struggled on. Clear, easy to understand and best of all you will remember this going into the test! Below are the descriptions for each of the lessons included in the series: Calculus: Acceleration and the Derivative Solve Distance & Velocity Word Problems Higher-Order Derivatives, Linear Approx In this lesson, we learn about multiple derivatives and tangent line approximations for these. Higher-order derivatives are results of taking the derivative more than once. Where the derivative of x^4 is 4x^3. The second derivative of the original x^4 would be the derivative of the derivative, which is 12x^2. You can also calculate third and fourth derivatives and so on... This lesson will walk you through what notation (Leibniz notation) denotes higher-order derivatives (d^2y/dx^2) or with multiple prime sympols for f(x) derivatives. Derivatives can allow you to approximate values of complicated functions near values you know. For example, in this video, you will see Professor Burger approximate the square root of 4.1 by using derivatives and the knowledge that the square root of 4 is equal to 2 (a very close point on the function's graph). Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hôp Using Tangent Line Approximation Formula Newton's Method Pebble analysis Ladder Baseball Blimp Math Anxiety Theory Connection Between Slope & Optimization Fence Box Can professional Wire-Cutting
at the majority of universities both in this country and abroad use the first number to designate level. First year courses are 100, second year 200 and so on. Graduate courses or dual enrolled courses are typically 500 level. Quote: And when used in relation to mathematics, ironically, means the exact opposite. Proof? Quote: Regardless, I can only guess about the nature of your courses, they don't sound like anything serious. But that is irrelevant to the general issue here, namely, that engineering, physics, etc students don't even come close to satisfying the requirements for a mathematics degree. Heck, they are far from the minor as well. This was just as true 15 years ago as it is today. Mathematics programs haven't changed much. As so often on this forum, you are wrong. These were graduate level courses (seniors at RU typically take the classes with the grad students). And I have met all of the requirements for a BA in mathematics as well as my two other BS degrees at RU. Quote: As I linked to earlier, the introductory sequence of mathematics courses includes linear algebra and differential equations. Are these subjects limited to basic courses? No..... There is no "Bayesian math"....... 15 years ago the Bayesian analysis was run by the math department and had a math course code number. It maybe run by the stats department now but it is a very real course. At the undergrad level the introductory sequence (Calculus, linear algebra, differential eq) is all that is required of engineering students. Certainly at the grad level engineering students may take some additional, largely applied, mathematics courses. Things like numerical analysis, partial differential equations, etc.[/quote] Again we must be an uber selective group both at IMCS and where I work now. Actually at the majority of universities both in this country and abroad use the first number to designate level. First year courses are 100, second year 200 and so on. Graduate courses or dual enrolled courses are typically 500 level. I agree. All the good schools (along with traditional schools) use similar numbering systems. But if you go to a school like University of Mississippi or something random, they don't always stick to the standards of education (as preset by traditional schools). But, why would you ever go to a random school? You don't know because you don't know what you're talking about. The term advanced is not used in place of introductory. The university offers two variants of the classes. Lecture versions called Multivariable Calculus and Linear Algebra, which are available for those who opt for the AB. The Advanced variants are for engineer students and are two semesters each. Yes....of course! What was a I thinking calling a students first courses in linear algebra introductory. Actually at the majority of universities both in this country and abroad use the first number to designate level. I have no idea whether the "majority" do or not, what I do know is that there is no universal numbering system. The numbering system I've seen use the most is using 2 digit numbers for lower-division, 100's for upper-division and 200's for graduate. Regardless, like I said, I have no idea what those numbers correspond to... Quote: Originally Posted by lkb0714 These were graduate level courses (seniors at RU typically take the classes with the grad students). And I have met all of the requirements for a BA in mathematics as well as my two other BS degrees at RU. BA in mathematics? I'm sure that can make some useful toilet paper, but as far as mathematics is concerned it isn't serious.... I don't care whether or not RU lets its science, etc students get a cheap "BA in mathematics" degree as a side act, I care about the requirements for a serious mathematics degree. And if you look at the requirements for in BS degree in mathematics at any good universities you'll see that the requirements extend well beyond the mathematics courses taken by physics and engineering students. Indeed, physics and engineering students don't even learn serious mathematics...... But why would they? physicists and engineers aren't in the business of doing mathematics, they simply use mathematics. Quote: Originally Posted by lkb0714 15 years ago the Bayesian analysis was run by the math department and had a math course code number. And yet there is no "Bayesian mathematics", indeed, the mere utterance of that phrase demonstrates an almost no knowledge of the subject. To say it again, "Bayesian" refers to all sorts of things in mathematics, but what it doesn't refer to is a special sort of mathematics... But Mathematicians, and this has always been the case, aren't particularly focused on Bayesianism they usually rely on the frequency interpretation of probability. Computer scientists on the other hand are very interested in Bayesian inference, which is the foundation of machine learning. At the undergrad level the introductory sequence (Calculus, linear algebra, differential eq) is all that is required of engineering studentsMy friends who majored in engineering took the same classes as above but instead of Discrete math took Multivariable Calculus A minor in mathematics typically requires the lower-division sequence (cal, diff eq, linear algebra) and then 5~6 upper-division courses, so usually an engineering student is only going to have around 50% (give or take) of the requirements satisfied. The lower-division/upper-division separation in mathematics is pretty strict and partly based on the fact that the mathematics department has to spend a lot of its time educating engineering, science, etc students in introductory mathematics. Its a bit unfortunate pedagogically for the mathematics students since they should be introduced to "serious mathematics" much sooner. Regardless, the lower-division courses are really geared towards engineering, science, etc students and the mathematics students just go along for the ride and then get more serious material in the 3rd year. Another unfortunate side effect of the above is that most people, even those that use it a lot (e.g., engineers) , don't have a good idea about what goes on in mathematics. Its also an unpleasant experience for those that mistake the introductory courses as representative of "serious mathematics" and pick mathematics as their major based on this misunderstanding, you get a lot of drop outs and mystery in the 3rd year... In contrast computer science introduces students to rigorous material in the 2nd year (after the basic programming classes) and uses its, usually murderous, 2 semester sequence in data-structures, algorithms, etc to screen out the serious from non-serious students. But they can do this because they aren't spending much time educating students outside of computer science. BA in mathematics? I'm sure that can make some useful toilet paper, but as far as mathematics is concerned it isn't serious.... This is the summative sentence for this debate and demonstrates the breadth and depth of your ignorance. The reason Rutgers gives BA for Math is because their most selective school, Rutgers College, only gave BA degrees in everything from chemistry to math. It says literally NOTHING about their degree quality (at one point their science programs were some of the best in the country) and everything about how their 200+ year old college was originally designed. Yet again, the math program at Rutgers is one of the top 20 in the country. Hardly, worthless, unlike your staggeringly ignorant opinion. The reason Rutgers gives BA for Math is because their most selective school, Rutgers College, only gave BA degrees in everything from chemistry to math. Ugh, you are focusing on things that don't matter and ignoring the real issue. I don't care how Rutgers labels things. Here is the real issue, any "mathematics degree" that is issued as a side act to studying engineering, physics, etc is not a serious mathematics degree. Any serious program in mathematics is going to require extensive course work that goes well beyond the required mathematics courses of an engineering, physics, etc student. These students only take the introductory sequence of mathematics courses that is, in reality, created for them and not mathematics students. That is the reality of matters, engineering, physics, etc students come out of school knowing very little about real mathematics. You can continue to believe whatever you wish. Yet again, the math program at Rutgers is one of the top 20 in the country. Hardly, worthless, unlike your staggeringly ignorant opinion. Rutgers offers a very good math program. You can read about it on their website. The interdisciplinary programs administered by other departments 15 years ago have nothing to do
Find a Greenwood VillageMy General Physics Instructor at Metropolitan State University of DenverOne of the powerful attributes of probability theory, combined with statistics, is that it provides you with a mechanism you can use to determine if a given set of data supports a given hypothesis or not. This is called hypothesis testing. ACT Math covers the following subjects: Prealgebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.
Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include those that are linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on) and know the values of the trigonometric functions. Algebra I is a course of study primarily designed to prepare students for Algebra II. The 2007 Saxon Textbook Series is used and emphasizes constant review of topics that have been covered in the past. These topics include solving equations, graphing, various word problems, factoring, area and volume problems, fractions, solving systems, radicals, exponents and scientific notation. The course is structured to introduce a new topic each day. Assignments generally include 4-5 new problems and 25 review problems from past lessons. (Students who fail to maintain a "C" or higher average in Algebra I will have great difficulty passing Algebra II.) This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations, conic sections, trigonometry, logarithms, and problem solving are some of the concepts taught. The correct use of the calculator is emphasized. This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations are studied in depth and there is a heavy emphasis on problem solving. Conic sections, trigonometry, and logarithms are introduced and the correct use of the calculator is taught. Significant class time is spent in teacher assisted work on these problems; however independent homework and student responsibility are also key. This course is an advanced study of Euclidean Geometry. In addition to the topics covered in the regular geometry course, this course will emphasize proof and deductive reasoning. The class will move at a more rapid pace and will provide an in-depth study of each concept. Prerequisite: This course is offered to ninth grade students who have been recommended for Honors Mathematics classes. The students in Pre-Calculus Honors should be juniors who are on track to take AP Calculus during their senior year.The content of the curriculum will be much the same as the other Pre-Calculus courses offered at DLHS. The main difference in the honor's course is that all students will be assumed to take AP Calculus. Effectively, this class will be the first year of a two year sequence. More emphasis will be given to interpreting problems verbally, numerically, graphically, as well as analytically. The students will be expected to transfer knowledge to various situations in an effort to prepare them for AP Calculus and the AP Calculus exam. This course is designed primarily for seniors, or for juniors who plan to take Statistics or College Algebra/College Trigonometry in their senior year. Early in the year, much emphasis will be given to analytical geometry and the study of functions. The TI83+ or TI89 will be used extensively by the students and teacher via computer projection equipment to study the relationships between functions and graphs. The "reform" movement in mathematics gives much more emphasis in studying functions analytically as well as through tables and graphs. Technology improvements have dramatically changed the way Pre-Calculus is taught. Nearly a third of the year will then be given to the study of trigonometry. Circle trigonometry goes beyond the geometric concept of an angle. Circular representations of angles allow us to study many real world phenomena that are periodic in nature. Triangle trigonometry uses the geometric concepts to find distances and areas given any polygonal region. Logarithms will be studied to be able to solve problems with exponential variables as is often the case in Chemistry as well as Economics. Conics and their interesting reflective properties will be studied. As time allows, some topics of discrete mathematics including sequences will be studied. Elementary probability will give students a concept of the likelihood of an event. These ideas would be very important as a beginning point for those taking Statistics. Advanced Placement Calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is required that students who take AP Calculus will seek college credit by taking the AP Exam. Most of the year will be devoted to topics in differential and integral calculus. The course emphasizes a multi-representational approach of calculus, with concepts, results, and problems being expressed graphically, numerically, analytically and verbally. Also note that a detailed course description including philosophy, goals, prerequisites, and topical outline are given at: Prerequisite – teacher approval and summer review on teacher wiki located at dlhscalculus.wikispaces.com (College credit depends on the individual college's policies regarding acceptance of AP courses and each student's performance on the AP exam). This course is a developmental course and is a review of Algebra I and Algebra II. This course is designed for students who need to develop better math skills to prepare for college mathematics. The first semester concentrates on topics in Algebra I such as real numbers, equations, inequalities, problem solving, graphing, polynomials, factoring, systems of equations and math skills required to improve scores on the ACT. The second semester will concentrate on topics in Algebra II such as factoring, inequalities, problem solving, rational expressions, functions, exponents, radicals, and quadratic equations and functions. This course is designed for students who have below a grade of C in previous math courses. This class does not meet the requirements for NCAA Clearinghouse. Pre- requisites: 1. Teacher recommendation. 2. Regular Algebra I, Algebra II and Geometry 3. Grades below a C in previous math classes and/or an 18 or below ACT math score. 4. An Algebra I and Algebra II placement test is given at the beginning of this course. Statistics is the science of gaining information from numerical data. Although statistics can be extremely complicated in theory, this course will be concerned with the practice of statistics. There are three basic parts to the practice of statistics, which will be incorporated in this course. Data analysis concerns methods and ideas for organizing and describing data using graphs, numerical summaries, and more elaborate mathematical descriptions. Data production includes some basic concepts about how to select samples and design experiments. Finally, statistical inference moves beyond data in order to draw conclusions about a wide universe. In other words, we will attempt to put data in context. (1 High School Credit in Mathematics) Course is not for students in Honors Math The first semester is a developmental course, a review of high school Algebra that includes factoring, inequalities, problem solving, rational expressions, functions, exponents, radicals, quadratic equations and functions. The second semester will include studies of functions, graphs, polynomial functions, exponential and logarithmic functions, systems of equations and inequalities, matrices, sequences, series and probability. The second semester may be taken for 3 hours of college credit or for high school credit only. Pre-requisites: 1. The student has completed Algebra I, Geometry and Algebra II in our regular program. 2. The student has below a 22 ACT math score. 3. An Algebra II placement test will be given at the beginning of the class. (1 High School Credit in Mathematics – full year) This university level course includes the study of functions, graphs, polynomial functions, exponential and logarithmic functions, systems of equations and inequalities, matrices, sequences, series and probability in the first semester. The second semester includes the study of trigonometric and circular functions, trigonometric analysis, analytical geometry of conic sections, and rotation of axes, parametric equations and polar coordinates. There are three ways to take this year long class. The first semester may be taken for 3 hours of college credit, the entire course may be taken for 6 hours of college credit, or the course may be taken for only high school credit. Pre-requisites: 1. Teacher recommendation 2. Pre-Calculus, and a 22 ACT Math Score, or a 22 ACT math score and at least an 87% on the Algebra II placement test. 3. The Algebra II placement test will be given at the beginning of the course.
In eighth grade algebra, students focus on a study of algebra topics that are typically covered in a high school level Algebra I class. Algebra During the month of October, students will graph linear equations using a variety of techniques, including a table of values, two points, and a point and the slope of a line. They will also be able to identify equations of vertical, horizontal, and parallel lines. In addition, students will identify and evaluate functions and use graphs of linear functions to model and solve real-life problems. Announcements Extra help is available on Tuesday and Thursday mornings at 7:20 AM. Chapter 4 Sections 1-3 Test - Wednesday, 10/23/13 Algebra Textbook Link Need a little extra help? Want a problem solving challenge? Access your textbook online by clicking on Classzone to get lesson help, try an extra challenge, or explore application and career links. The site provides practice problems, practice quizzes and tests, puzzles, and games.
Calculus Demystified - 03 edition Summary: Here's an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus. With Calculus Demystified you ease into the subject one simple step at a time -- at your own speed. A user-friendly, accessible style ...show moreincorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important1393080 Used; Acceptable. A well used copy with page markings, inventory stickers, etc. \| Ships from Florida, with tracking. $9.65 +$3.99 s/h Acceptable nitax2 fl tallahassee, FL Paperback BRAND_NEW Calculus demystified a self teaching guide-best of luck! same day shipping
Introduction to Numerical Analysis Using MATLAB By Dr Rizwan Butt CHAPTER ONE Number Systems and Errors Introduction It simply provides an introduction of numerical analysis. Number Representation and Base of Numbers Here we consider methods for representing numbers on computers. 1. Normalized Floating-point Representation It describes how the numbers are stored in the computers. CHAPTER 1 NUMBER SYSTEMS AND ERRORS 1. Human Error It causes when we use inaccurate measurement of data or inaccurate representation of mathematical constants. 2. Truncation Error It causes when we are forced to use mathematical techniques which give approximate, rather than exact answer. 3. Round-off Error This type of errors are associated with the limited number of digits numbers in the computers. CHAPTER 1 NUMBER SYSTEMS AND ERRORS Effect of Round-off Errors in Arithmetic Operation Here we analysing the different ways to understand the nature of rounding errors. 1. Rounding off Errors in Addition and Subtraction It describes how addition and subtraction of numbers are performed in a computer. 2. Rounding off Errors in Multiplication It describes how multiplication of numbers are performed in a computer. CHAPTER 1 NUMBER SYSTEMS AND ERRORS 3. Rounding off Errors in Division It describes how division of numbers are performed in a computer. 4. Rounding off Errors in Powers and roots It describes how the powers and roots of numbers are performed in a computer. CHAPTER TWO Solution of Nonlinear Equations Introduction Here we discuss the ways of representing the different types of nonlinear equation f(x) = 0 and how to find approximation of its real root . Simple Root's Numerical Methods Here we discuss how to find the approximation of the simple root (non-repeating) of the nonlinear equation f(x) = 0. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS 1. Method of Bisection This is simple and slow convergence method (but convergence is guaranteed) and is based on the Intermediate Value Theorem. Its strategy is to bisect the interval from one endpoint of the interval to the other endpoint and then retain the half interval whose end still bracket the root. 2. False Position Method This is slow convergence method and may be thought of as an attempt to improve the convergence characteristic of bisection method. Its also known as the method of linear interpolation. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS 3. Fixed-Point Method This is very general method for finding the root of nonlinear equation and provides us with a theoretical framework within which the convergence properties of subsequent methods can be evaluated. The basic idea of this method is convert the equation f(x) = 0 into an equivalent form x = g(x). 4. Newtons Method This is fast convergence method (but convergence is not guaranteed) and is also known as method of tangent because after estimated the actual root, the zero of the tangent to the function at that point is determined. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS 5. Secant Method This is fast convergence method (but not like Newton's method) and is recommended as the best general-purpose method. It is very similar to false position method, but it is not necessary for the interval to contain a root and no account is taken of signs of the numbers f(x_n). Multiple Root's Numerical Methods Here we discuss how to find approximation of multiple root (repeating) of nonlinear equation f(x) = 0 and its order of multiplicity m. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS 1. First Modified Newtons Method It can be useful to find the approximation of multiple root if the order of multiplicity m is given. 2. Second Modified Newtons Method It can be useful to find the approximation of multiple root if the order of multiplicity m is not given. Convergence of Iterative Methods Here we discuss order of convergence of all the iterative methods described in the chapter. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS Acceleration of Convergence Here we discuss a method which can be applied to any linear convergence iterative method and acceleration of convergence can be achieved. Systems of Nonlinear Equations When we are given more than one nonlinear equation. Solving systems of nonlinear is a difficult task. Newtons Method We discuss this method for system of two nonlinear equations in two variables. For system of nonlinear equations that have analytical partial derivatives, this method can be used, otherwise not. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS Roots of Polynomials A very common problem in nonlinear equations is to find the roots of polynomial is discussed here. 1. Horner's Method It is one of the most efficient way to evaluate polynomials and their derivatives at a given point. It is helpful for finding the initial approximation for solution by Newton's method. It is also quit stable. CHAPTER 2 SOLUTION OF NONLINEAR EQUATIONS 2. Muller's Method It is generalization of secant method and uses quadratic interpolation among three points. It is a fast convergence method for finding the approximation of simple zero of a polynomial equation. 3. Bairstow's Method It can be used to find all the zeros of a polynomial. It is one of the most efficient method for determining real and complex roots of polynomials with real coefficients. CHAPTER THREE Systems of Linear Equations Introduction We give the brief introduction of linear equations, linear systems, and their importance. Properties of Matrices and Determinant To discuss the solution of the linear systems, it is necessary to introduce the basic properties of matrices and the determinant. Numerical Methods for Linear Systems To solve the systems of linear equations using the numerical methods, there are two types of methods available, methods of first type are called direct methods and second type are called iterative methods. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS Direct Methods for Linear Systems The method of this type refers to a procedure for computing a solution from a form that is mathematically exact. These methods are guaranteed to succeed and are recommended for general-purpose. 1. Cramers Rule This method is use for solving the linear systems by the use of determinants. It is one of the least efficient method for solving a large number of linear equations. But it is useful for explaining some problems inherent in the solution of linear equations. 2 CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 2. Gaussian Elimination Method It is most popular and widely used method for solving linear system. The basic of this method is to convert the original system into equivalent upper-triangular system and from which each unknown is determined by backward substitution. 2.1 Without Pivoting In converting original system to upper-triangular system if a diagonal element becomes zero, then we have to interchange that equation with any below equation having nonzero diagonal element. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 2.2 Partial Pivoting In using the Gauss elimination by partial pivoting (or row pivoting), the basic approach is to use the largest (in absolute value) element on or below the diagonal in the column of current interest as the pivotal element for elimination in the rest of that column. 2.3 Complete Pivoting In this case we search for the largest number (in absolute value) in the entire array instead of just in the first column, and this number is the pivot. This means we need to interchange the columns as well as rows. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 3. Gauss-Jordan Method It is a modification of Gauss elimination method and is although inefficient for practical calculation but is often useful for theoretical purposes. The basic idea of this method is to convert original system into diagonal system form. 4. LU Decomposition Method It is also a modification of Gauss elimination method and here we decompose or factorize the coefficient matrix into the product of two triangular matrices (lower and upper). CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 4.1 Dollittle's method (l_ii = 1) Here the upper-triangular matrix is obtained by forward elimination of Gauss elimination method and the lower-triangular matrix containing the multiples used in the Gauss elimination process as the elements below the diagonal with unity elements on the main diagonal. 4.2 Crout's method (u_ii = 1) The Crout's method, in which upper-triangular matrix has unity on the main diagonal, is similar to the Dollittle's method in all other aspects. The lower-triangular and upper-triangular matrices are obtained by expanding the matrix equation A = LU term by term to determine the elements of the lower-triangular and upper- triangular matrices. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 4.3 Cholesky method (l_ii = u_ii) This method is of the same form as the Dollittle's and Crout's methods except it is limited to equations involving symmetrical coefficient matrices. This method provides a convenient method for investigating the positive definiteness of symmetric matrices. Norms of Vectors and Matrices For solving linear systems, we discuss a method for quantitatively measuring the distance between vectors in R^n and a measure of how well one matrix approximates another. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS Iterative Methods for Solving Linear Systems These methods start with an arbitrary first approximation to the unknown solution of linear system and then improve this estimate in an infinite but convergent sequence of steps. This type of methods are used for large sparse systems and efficient in terms of computer storage and time requirement. 1. Jacobi Iterative Method It is a slow convergent iterative method for the linear systems. From its formula, it is seen that the new estimates for solution are computed from the old estimates. 2. Gauss-Seidel Iterative Method It is a faster convergent iterative method than the Jacobi method for the solution of the linear systems as it uses the most recent calculated values for all x_i. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS Convergence Criteria We discuss the sufficient conditions for the convergence of Jacobi and Gauss-Seidel methods by showing l_∞-norm of their corresponding iteration matrices less than one. Eigenvalues and Eigenvectors We briefly discuss the eigenvalues and eigenvectors of a matrix and show how they can be used to describe the solutions of linear systems. 3. Successive Over-Relaxation Method It is useful modification of the Gauss-Seidel method. It is the best iterative method of choice and needs to determine optimum value of the parameter. CHAPTER 3 SYSTEMS OF LINEAR EQUATIONS 4. Conjugate Gradient Method It is very useful when employed as an iterative approximation method for solving large sparse linear systems. The need for estimating parameter is removed in this method. Conditioning of Linear Systems We discuss ill-conditioning of linear systems by using the condition number of matrix. The best way to deal with ill- conditioning is to avoid it by reformulating the problem. Iterative Refinement We discuss residual corrector method which can be used to improve the approximate solution obtained by any means. CHAPTER FOUR Approximating Functions Introduction We describe several numerical methods for approximating functions other than elementary functions. The main purpose of these numerical methods is to replace a complicated function by one which is simpler and more manageable. Polynomial Interpolation for Uneven Intervals The data points we consider here in a given functional relationship are not equally spaced. CHAPTER 4 APPROXIMATING FUNCTIONS 1. Lagrange Interpolating Polynomials It is one of the popular and well known interpolation method to approximate the functions at arbitrary point and provides a direct approach for determining interpolated values regardless of data spacing. 2. Newtons General Interpolating Formula It is generally more efficient than Lagrange polynomial and it can be adjusted easily for additional data. 3. Aitkens Method It is an iterative interpolation method which is based on the repeated application of a simple interpolation method. CHAPTER 4 APPROXIMATING FUNCTIONS Polynomial Interpolation for Even Intervals The data points we consider here in a given functional relationship are equally spaced and polynomials are based on differences which are easy to use. 1. Newton's Forward-Difference Formula It can be used for interpolation near the beginning of table values. 2. Newton's Backward-Difference Formula It can be use for interpolation near the end of table values. 3. Some Central-Difference Formulas These can be used for interpolation in the middle of the table values and among them are Stirling, Bessel, and Gauss formulas. CHAPTER 4 APPROXIMATING FUNCTIONS Interpolation with Spline Functions It is an alternative approach to divide the interval into a collection of subintervals and construct a different approximating polynomial on each subinterval, called Piecewise Polynomial Approximation. 1. Linear Spline One of the simplest piecewise polynomial interpolation for approximating functions and basic of it is simply connect consecutive points with straight lines. 2. Cubic Spline The most widely cubic spline approximations are patched among ordered data that maintain continuity and smoothness and they are more powerful than polynomial interpolation. CHAPTER 4 APPROXIMATING FUNCTIONS Least Squares Approximation Least squares approximation which seeks to minimize the sum (over all data) of the squares of the differences between function values and data values, are most useful for large and rough sets of data. 1. Linear Least Squares It defines the correct straight line as the one that minimizes the sum of the squares of the distance between the data points and the line. 2. Polynomial Least Squares When data from experimental results are not linear, then we find the least squares parabola and the extension to a polynomial of higher degree is easily made. CHAPTER 4 APPROXIMATING FUNCTIONS 3. Nonlinear Least Squares In many cases, data from experimental tests are not linear, then we fit to them two popular exponential forms y = ax^b and y = ae^(bx). 4. Least Squares Plane When the dependent variable is function of two variables, then the least squares plane can be used to find the approximation of the function. 5. Overdetermined Linear Systems The least squares solution of overdetermined linear system can be obtained by minimizing the l_2-norm of the residual. CHAPTER 4 APPROXIMATING FUNCTIONS 6. Least Squares with QR Decomposition The least squares solution of the overdetermined linear system can be obtained by using QR (the orthogonal matrix Q and upper-triangular matrix R) decomposition of a given matrix. 7. Least Squares with Singular Value Decomposition The least squares solution of the overdetermined linear system can be obtained by using singular value (UDV^T, the two orthogonal matrices U, V and a generalized diagonal matrix D) decomposition of a given matrix. CHAPTER FIVE Differentiation and Integration Introduction Here, we deal with techniques for approximating numerically the two fundamental operations of the calculus, differentiation and integration. Numerical Differentiation A polynomial p(x) is differentiated to obtain p′(x), which is taken as an approximation to f′(x) for any numerical value x. Numerical Differentiation Formulas Here we gave many numerical formulas for approximating the first derivative and second derivative of a function. CHAPTER 5 DIFFERENTIATION AND INTEGRATION 1. First Derivatives Formulas For finding the approximation of the first derivative of a function, we used two-point, three-point, and five-point formulas. 2. Second Derivatives Formulas For finding the approximation of the second derivative of a function, we used three-point and five-point formulas. 3. Formulas for Computing Derivatives Here we gave many forward-difference, backward-difference, and central-difference formulas for approximating the first and second derivative of the function. CHAPTER 5 DIFFERENTIATION AND INTEGRATION Numerical Integration Here, we pass a polynomial through points of a function and then integrate this polynomial approximation to a function. For approximating the integral of f(x) between a and b we used Newton-Cotes techniques. 1. Closed Newton-Cotes Formulas For these formulas, the end-points a and b of the given interval [a, b] are in the set of interpolating points and the formulas can be obtained by integrating polynomials fitted to equispaced data points. 1.1 Trapezoidal Rule This rule is based on integration of the linear interpolation. CHAPTER 5 DIFFERENTIATION AND INTEGRATION 1.2 Simpson's Rule This rule approximates the function f(x) with a quadratic interpolating polynomial. 2. Open Newton-Cotes Formulas These formulas contain all the points used for approximating within the open interval (a, b) and can be obtained by integrating polynomials fitted to equispaced data points. 3. Repeated use of the Trapezoidal Rule The repeated Trapezoidal rule is derived by repeating the Trapezoidal rule and for a given domain of integration, error of the repeated Trapezoidal rule is proportional to h_2. CHAPTER 5 DIFFERENTIATION AND INTEGRATION 4. Romberg Integration The Romberg integration is based on the repeated Trapezoidal rule and using the results of repeated Trapezoidal rule with two different data spacings, a more accurate integral is evaluated. 5. Gaussian Quadratures The Gauss(-Legendre) quadratures are based on integrating a polynomial fitted to the data points at the roots of a Legendre polynomial and the order of accuracy of a Gauss quadrature is approximately twice as high as that of the Newton-Cotes closed formula using the same number of data points. CHAPTER SIX Ordinary Differential Equations Introduction We discussed many numerical methods for solving first-order ordinary differential equations and systems of first-order ordinary differential equations. Numerical Methods for Solving IVP Here we discuss many single-step numerical methods and multi- step numerical methods for solving the initial-value problem (IVP) and some numerical methods for solving boundary-value problem (BVP). 1. Single-Step Methods for IVP These types of methods are self-starting, refer to estimate y′(x) from the initial condition and proceed step-wise. All the information used by these methods is consequently obtained within the interval over which the solution is being approximated. CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS 1.1 Euler's Method One of the simplest and straight forward but not an efficient numerical method for solving initial-value problem (IVP). 1.2 Higher-Order Taylor's Methods For getting higher accuracy, the Taylor's methods are excellent when the higher-order derivative can be found. 1.3 Runge-Kutta Methods An important group of methods which allow us to obtain great accuracy at each step and at the same time avoid the need of higher derivatives by evaluating the function at selected points on each subintervals. CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS 2. Multi-Steps Methods for IVP This type of methods make use of information about the solution at more than one point. 2.1 Adams Methods These methods use the information at multiple steps of the solution to obtain the solution at the next x-value. 2.2 Predictor-Corrector Methods These methods are combination of an explicit method and implicit method and they are consist of predictor step and corrector step in each interval. CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS Systems of Simultaneous ODE Here, we require the solution of a system of simultaneous first- order differential equations rather than a single equation. Higher-Order Differential Equations Here, we deal the higher-order differential equation (nth-order) and solve it by converting to an equivalent system of (n) first- order equations. Boundary-Value Problems Here, we solve ordinary differential equation with known conditions at more than one value of the independent variable. CHAPTER 6 ORDINARY DIFFERENTIAL EQUATIONS 1. The Shooting Method It is based on by forming a linear combination of the solution to two initial-value problems (linear shooting method) and by converting a boundary-value problem to a sequence of initial-value problems (nonlinear shooting method) which can be solved using the single steps method. 2. The Finite Difference Method It is based on finite differences and it reduces a boundary-value problem to a system a system of linear equations which can be solved by using the methods discussed in the linear system chapter. CHAPTER SEVEN Eigenvalues and Eigenvectors Introduction Here we discussed many numerical methods for solving eigenvalue problems which seem to be a very fundamental part of the structure of universe. Linear Algebra and Eigenvalues Problems The solution of many physical problems require the calculations of the eigenvalues and corresponding eigenvectors of a matrix associated with linear system of equations. Basic Properties of Eigenvalue Problems We discussed many properties concerning with eigenvalue problems which help us a lot in solving different problems. CHAPTER 7 EIGENVALUES AND EIGENVECTORS Numerical Methods for Eigenvalue Problems Here we discussed many numerical methods for finding approximation of the eigenvalues and corresponding eigenvectors of the matrices. Vector Iterative Methods for Eigenvalues This type of numerical methods are most useful when matrix involved be comes large and also they are easy means to compute eigenvalues and eigenvectors of a matrix. 1. Power Method It can be used to compute the eigenvalue of largest modules (dominant eigenvalue) and the corresponding eigenvector of a general matrix. CHAPTER 7 EIGENVALUES AND EIGENVECTORS 2. Inverse Power Method This modification of the power method can be used to compute the smallest (least) eigenvalue and the corresponding eigenvector of a general matrix. 3. Shifted Inverse Power Method This modification of the power method consists of by replacing the given matrix A by (A−μI) and the eigenvalues of (A−μI) are the same as those of A except that they have all been shifted by an amount μ. CHAPTER 7 EIGENVALUES AND EIGENVECTORS Location of Eigenvalues We deal here with the location of eigenvalues of both symmetric and non- symmetric matrices, that is, the location of zeros of the characteristic poly nomial by using the Gerschgorin Circles Theorem and Rayleigh Quotient Theorem. Intermediate Eigenvalues Here we discussed the Deflation method to obtain other eigenvalues of a matrix once the dominant eigenvalue is known. Eigenvalues of Symmetric Matrices Here, we developed some methods to find all eigenvalues of a symmetric matrix by using a sequence of similarity transformation that transformed the original matrix into a diagonal or tridiagonal matrix. CHAPTER 7 EIGENVALUES AND EIGENVECTORS 1. Jacobi Method It can be used to find all eigenvalues and corresponding eigenvectors of a symmetric matrix and it permits the transformation of a matrix into a diagonal. 2. Sturm Sequence Iteration It can be used in the calculation of eigenvalues of any symmetric tridiagonal matrix. 3. Given's Method It can be used to find all eigenvalues of a symmetric matrix (corresponding eigenvectors can be obtained by using shifted inverse power method) and it permits the transformation of a matrix into a tridiagonal. 4. Householder's Method This method is a variation of the Given's method and enable us to reduce a symmetric matrix to a symmetric tridiagonal matrix form. CHAPTER 7 EIGENVALUES AND EIGENVECTORS Matrix Decomposition Methods Here we used three matrix decomposition methods and find all the eigenvalues of a general matrix. 1. QR Method In this method we decomposed the given matrix into a product orthogonal matrix and a upper-triangular matrix which find all the eigenvalues of a general matrix. 2. LR Method This method is based upon the decomposition of the given matrix into a product lower-triangular matrix (with unit diagonal elements) and a upper- triangular matrix. 3. Singular Value Decomposition Here we decomposed rectangular real matrix into a product of two orthogonal matrices and generalized diagonal matrix. Appendices 1. Appendix A includes some mathematical preliminaries. 2. Appendix B includes the basic commands for software package MATLAB. 3. Appendix C includes the index of MATLAB programs and MATLAB built-in- functions. 4. Appendix D includes symbolic computation and Symbolic Math Toolbox functions. 5. Appendix E includes answers to selected odd-number exercises for all

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