Algebra Books

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Book SynopsisDiscover the relevance of mathematics in your own life as you master important concepts and skills in Waner/Costenoble's APPLIED CALCULUS, 8th Edition. Updated, numerous examples and applications use real data from well-known businesses, current economic and life events -- from cryptocurrency to COVID -- to demonstrate how the principles you are learning impact you. Readable, streamlined content clearly presents concepts while numerous learning features and tools help you review and practice. Spreadsheet and TI graphing calculator instructions appear where needed. In addition, WebAssign online tools and an interactive eTextbook include teaching videos by an award-winning instructor. You can refine your skills in the necessary math prerequisites with additional examples and powerful adaptive practice sessions. A helpful website from the authors also offers online tutorials and videos on every topic to support your learning, no matter what your learning style.Table of Contents0. PRECALCULUS REVIEW. Real Numbers. Exponents and Radicals. Using Exponent Identities Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. The Coordinate Plane. Logarithms. 1. FUNCTIONS AND APPLICATIONS. Functions from the Numerical, Algebraic, and Graphical Viewpoints. Functions and Models. Linear Functions and Models. Linear Regression. 2. NONLINEAR FUNCTIONS AND MODELS. Quadratic Functions and Models. Exponential Functions and Models. The Number e and Exponential Growth and Decay. Logistic and Logarithmic Functions and Models.. 3. INTRODUCTION TO THE DERIVATIVE. Limits: Numerical and GraphicalViewpoints. Limits and Continuity. Limits: Algebraic Viewpoint. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint. 4. TECHNIQUES OF DIFFERENTIATION. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. 5. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. Higher Order Derivatives: Acceleration and Concavity. Analyzing Graphs. Related Rates. Elasticity. 6. THE INTEGRAL. The Indefinite Integral. Substitution. The Definite Integral. The Fundamental Theorem of Calculus. 7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. 8. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications. 9. TRIGONOMETRIC MODELS. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications.

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Book SynopsisNow available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added.The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.From the reviews of previous editions:Altogether, the text is a didactic masterpiece. — zbMATHThe determinant-free proofs are elegant and intuitive. — American Mathematical MonthlyThe most original linear algebra book to appear in years, it certainly belongs in every undergraduate library — CHOICETable of ContentsPreface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces.- 2. Finite-Dimensional Vector Spaces.- 3. Linear Maps.- 4. Polynomials.- 5. Eigenvalues, Eigenvectors, and Invariant Subspaces.- 6. Inner Product Spaces.- 7. Operators on Inner Product Spaces.- 8. Operators on Complex Vector Spaces.- 9. Operators on Real Vector Spaces.- 10. Trace and Determinant-Photo Credits-Symbol Index-Index.

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Book SynopsisTable of Contents 1. Vector Spaces. Introduction. Vector Spaces. Subspaces. Linear Combinations and Systems of Linear Equations. Linear Dependence and Linear Independence. Bases and Dimension. Maximal Linearly Independent Subsets. 2. Linear Transformations and Matrices. Linear Transformations, Null Spaces, and Ranges. The Matrix Representation of a Linear Transformation. Composition of Linear Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations with Constant Coefficients. 3. Elementary Matrix Operations and Systems of Linear Equations. Elementary Matrix Operations and Elementary Matrices. The Rank of a Matrix and Matrix Inverses. Systems of Linear Equations—Theoretical Aspects. Systems of Linear Equations—Computational Aspects. 4. Determinants. Determinants of Order 2. Determinants of Order n. Properties of Determinants. Summary—Important Facts about Determinants. A Characterization of the Determinant. 5. Diagonalization. Eigenvalues and Eigenvectors. Diagonalizability. Matrix Limits and Markov Chains. Invariant Subspaces and the Cayley-Hamilton Theorem. 6. Inner Product Spaces. Inner Products and Norms. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear Operator. Normal and Self-Adjoint Operators. Unitary and Orthogonal Operators and Their Matrices. Orthogonal Projections and the Spectral Theorem. The Singular Value Decomposition and the Pseudoinverse. Bilinear and Quadratic Forms. Einstein's Special Theory of Relativity. Conditioning and the Rayleigh Quotient. The Geometry of Orthogonal Operators. Appendices. Sets. Functions. Fields. Complex Numbers. Polynomials. Answers to Selected Exercises. Index.

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Book SynopsisAl-Khwarizmi was a mathematician, astronomer and geographer. He worked most of his life as a scholar in the House of Wisdom in Baghdad during the first half of the 9th century and is considered by many to be the father of algebra. This book deals with algebraic theory, and focuses on the calculation of inheritances and legacies.

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Book SynopsisEmphasizes a vectors approach and prepares students to make the transition from computational to theoretical mathematics. This book includes applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.Table of Contents1. VECTORS. Introduction: The Racetrack Game. The Geometry and Algebra of Vectors. Length and Angle: The Dot Product. Exploration: Vectors and Geometry. Lines and Planes. Exploration: The Cross Product. Writing Project: Origins of the Dot Product and the Cross Product. Applications. 2. SYSTEMS OF LINEAR EQUATIONS. Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems. Writing Project: A History of Gaussian Elimination. Explorations: Lies My Computer Told Me; Partial Pivoting; Counting Operations: An Introduction to the Analysis of Algorithms. Spanning Sets and Linear Independence. Applications. Vignette: The Global Positioning System. Iterative Methods for Solving Linear Systems. 3. MATRICES. Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and Rank. Introduction to Linear Transformations. Vignette: Robotics. Applications. 4. EIGENVALUES AND EIGENVECTORS. Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and Eigenvectors. Determinants. Writing Project: Which Came First-the Matrix or the Determinant? Vignette: Lewis Carroll's Condensation Method. Exploration: Geometric Applications of Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Writing Project: The History of Eigenvalues. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications and the Perron-Frobenius Theorem. Vignette: Ranking Sports Teams and Searching the Internet. 5. ORTHOGONALITY. Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Explorations: The Modified QR Factorization; Approximating Eigenvalues with the QR Algorithm. Orthogonal Diagonalization of Symmetric Matrices. Applications. 6. VECTOR SPACES. Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Writing Project: The Rise of Vector Spaces. Exploration: Magic Squares. Change of Basis. Linear Transformations. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Exploration: Tilings, Lattices and the Crystallographic Restriction. Applications. 7. DISTANCE AND APPROXIMATION. Introduction: Taxicab Geometry. Inner Product Spaces. Explorations: Vectors and Matrices with Complex Entries; Geometric Inequalities and Optimization Problems. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Vignette: Digital Image Compression. Applications. 8. CODES. (Online) Code Vectors. Vignette: The Codabar System. Error-Correcting Codes. Dual Codes. Linear Codes. The Minimum Distance of a Code. Appendix A: Mathematical Notation and Methods of Proof. Appendix B: Mathematical Induction. Appendix C: Complex Numbers. Appendix D: Polynomials.

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Book SynopsisAn engaging, accessible introduction into how numbers work and why we shouldn't be afraid of them, frommaths expertRachel Riley.Do you know your fractions from your percentages? Your adjacent to your hypotenuse? And who really knows how to do long division, anyway?Puzzled already? Don't blame youBut fret not! You won't be At Sixes and Sevens for long. In this brilliant, well-rounded guide, Countdown''s Rachel Riley will take you back to the very basics, allow you to revisit what you learnt at school (and may have promptly forgotten, *ahem*), build your understanding of maths from the get-go and provide you with the essential toolkit to gain confidence in your numerical abilities.Discover how to divide and conquer, make your decimal debut, become a pythagoras professional and so much more with these easy-to-learn tips and tricks. Packed full of working examples, fool-proof methods, quirky trivia and brainteasers to try from puzzle-pro Dr Gareth Moore, this book is an absolute must-read for anyone and everyone who ever thought maths was above' them. Because the truth is: you can do it. What's more, it can be pretty fun too!

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Book SynopsisTable of ContentsBasic Math and Pre-Algebra For Dummies, 2nd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: Playing the Numbers Game 7 CHAPTER 2: It’s All in the Fingers: Numbers and Digits 23 CHAPTER 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Part 2: Getting a Handle on Whole Numbers 47 CHAPTER 4: Putting the Big Four Operations to Work 49 CHAPTER 5: A Question of Values: Evaluating Arithmetic Expressions 63 CHAPTER 6: Say What? Turning Words into Numbers 75 CHAPTER 7: Divisibility 87 CHAPTER 8: Fabulous Factors and Marvelous Multiples 95 Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109 CHAPTER 9: Fooling with Fractions 111 CHAPTER 10: Parting Ways: Fractions and the Big Four Operations 125 CHAPTER 11: Dallying with Decimals 149 CHAPTER 12: Playing with Percents 171 CHAPTER 13: Word Problems with Fractions, Decimals, and Percents 183 Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195 CHAPTER 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 CHAPTER 15: How Much Have You Got? Weights and Measures 205 CHAPTER 16: Picture This: Basic Geometry 217 CHAPTER 17: Seeing Is Believing: Graphing as a Visual Tool 239 CHAPTER 18: Solving Geometry and Measurement Word Problems 247 CHAPTER 19: Figuring Your Chances: Statistics and Probability 259 CHAPTER 20: Setting Things Up with Basic Set Theory 271 Part 5: The X-Files: Introduction to Algebra 279 CHAPTER 21: Enter Mr X: Algebra and Algebraic Expressions 281 CHAPTER 22: Unmasking Mr X: Algebraic Equations 299 CHAPTER 23: Putting Mr X to Work: Algebra Word Problems 311 Part 6: The Part of Tens 321 CHAPTER 24: Ten Little Math Demons That Trip People Up 323 CHAPTER 25: Ten Important Number Sets to Know 329 Index 337 Basic Math and Pre-Algebra Workbook For Dummies, 3rd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: We've Got Your Numbers 7 CHAPTER 2: Smooth Operators: Working with the Big Four Operations 23 CHAPTER 3: Getting Down with Negative Numbers 37 CHAPTER 4: It's Just an Expression 49 CHAPTER 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 CHAPTER 6: Fractions Are a Piece of Cake 91 CHAPTER 7: Fractions and the Big Four 109 CHAPTER 8: Getting to the Point with Decimals 143 CHAPTER 9: Playing the Percentages 165 Part 3: A Giant Step Forward: Intermediate Topics 177 CHAPTER 10: Seeking a Higher Power through Scientific Notation 179 CHAPTER 11: Weighty Questions on Weights and Measures 189 CHAPTER 12: Shaping Up with Geometry 203 CHAPTER 13: Getting Graphic: Xy-Graphs 223 Part 4: The X Factor: Introducing Algebra 235 CHAPTER 14: Expressing Yourself with Algebraic Expressions 237 CHAPTER 15: Finding the Right Balance: Solving Algebraic Equations 259 Part 5: The Part of Tens 277 CHAPTER 16: Ten Alternative Numeral and Number Systems 279 CHAPTER 17: Ten Curious Types of Numbers 287 Index 293

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Book SynopsisLinear Algebra For Dummies serves as an easy-to-follow guide that introduces (or re-introduces) readers to key concepts such as matrices, vector spaces, and eigenvalues and eigenvectors. It presents the information in a way that allows readers to fully digest not just the "how" of solving linear algebraic problems, but also the "why.Table of ContentsIntroduction. Part I: Lining Up the Basics of Linear Algebra. Chapter 1: Putting a Name to Linear Algebra. Chapter 2: The Value of Involving Vectors. Chapter 3: Mastering Matrices and Matrix Algebra. Chapter 4: Getting Systematic with Systems of Equations. Part II: Relating Vectors and Linear Transformations. Chapter 5: Lining Up Linear Combinations. Chapter 6: Investigating the Matrix Equation Ax = b. Chapter 7: Homing In on Homogeneous Systems and Linear Independence. Chapter 8: Making Changes with Linear Transformations. Part III: Evaluating Determinants. Chapter 9: Keeping Things in Order with Permutations. Chapter 10: Evaluating Determinants. Chapter 11: Personalizing the Properties of Determinants. Chapter 12: Taking Advantage of Cramer’s Rule. Part IV: Involving Vector Spaces. Chapter 13: Involving Vector Spaces. Chapter 14: Seeking Out Subspaces of Vector Spaces. Chapter 15: Scoring Big with Vector Space Bases. Chapter 16: Eyeing Eigenvalues and Eigenvectors. Part V: The Part of Tens. Chapter 17: Ten Real-World Applications Using Matrices. Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator. Chapter 19: Ten Mathematical Meanings of Greek Letters. Glossary. Index.

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Book SynopsisCovers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

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Book SynopsisAlgebra is like a foreign language for many students. They have difficulty translating the words, their definitions and how it applies to problem-solving. Tussy/Gustafson''s ELEMENTARY AND INTERMEDIATE ALGEBRA, 6th Edition, addresses these concerns, giving you the tools needed to understand the language of algebra. Strategy and Why explanations in the worked examples show the how and the why behind problem-solving. Algebra is not just about the x -- it''s also about the WHY. The text contains many opportunities to apply the algebraic skills you have learned to solve a wide variety of interesting real-life applications using a six-step problem-solving strategy. In combination, the text and WebAssign will guide you through an integrated learning process that will expand your reasoning abilities as it teaches you how to read, write and think mathematically using the language of Algebra.

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Book SynopsisElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjectureTrade Review"The authors present their discussion in an informal, sometimes playful manner and with detail that will appeal to an audience with a basic understanding of calculus. This book will captivate math enthusiasts as well as readers curious about an intriguing and still unanswered question."--Margaret Dominy, Library Journal "Minimal prerequisites and its clear writing make this book (which even has a few exercises) a great choice for a seminar for mathematics majors, who at some point should have such an excursion to one of the frontiers of mathematics."--Mathematics Magazine "The authors of Elliptic Tales do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves."--Sungkon Chang, Times Higher Education "One cannot help being impressed, in reading the book and pursuing a few of the references, by the magnitude of the enterprise it chronicles."--James Case, SIAM News "Ash and Gross thoroughly explain the statement and significance of the linchpin Birch and Swinnerton-Dyer conjection... [A]sh and Gross deliver ample and current intellectual and technical substance."--Choice "I would envision this book as an excellent text for an undergraduate 'capstone' course in mathematics; the book lends itself to independent reading, but topics may be explored in much greater depth and rigor in the classroom. Additionally, the book indeed brings together ideas from calculus, complex variables and algebra, showing how a single mathematical research question may require an integrated understanding of the various branches of mathematics. Thus, it encourages students to reinforce their understanding of these various fields, while simultaneously introducing them to an open question in mathematics and a vibrant field of study."--Lisa A. Berger, Mathematical Reviews Clippings "The book is very pleasantly written, and in my opinion, the authors have done an admirable job in giving an idea to non-experts what the Birch-Swinnerton Dyer conjecture is about."--Jan-Hendrik Evertse, Zentralblatt MATH "The book's most important contributions ... are the sense of discovery, invention, and insight into the habits of mind used by mathematicians on this journey. I would recommend this book to anyone who wants to be challenged mathematically or who wants to experience mathematics as creative and exciting."--Jacqueline Coomes, Mathematics Teacher "[T]his book is a wonderful introduction to what is arguably one of the most important mathematical problems of our time and for that reason alone it deserves to be widely read. Another reason to recommend this book is the opportunity to share in the readily apparent joy the authors have for their subject and the beauty they see in it, not least because ... joy and beauty are the most important reasons for doing mathematics, irrespective of its dollar value."--Rob Ashmore, Mathematics Today "This book has many nice aspects. Ash and Gross give a truly stimulating introduction to elliptic curves and the BSD conjecture for undergraduate students. The main achievement is to make a relative easy exposition of these so technical topics."--Jonathan Sanchez-Hernandez, Mathematical SocietyTable of ContentsPreface xiii Acknowledgments xix Prologue 1 PART I. DEGREE Chapter 1. Degree of a Curve 13 1.Greek Mathematics 13 2.Degree 14 3.Parametric Equations 20 4.Our Two Definitions of Degree Clash 23 Chapter 2. Algebraic Closures 26 1.Square Roots of Minus One 26 2.Complex Arithmetic 28 3.Rings and Fields 30 4.Complex Numbers and Solving Equations 32 5.Congruences 34 6.Arithmetic Modulo a Prime 38 7.Algebraic Closure 38 Chapter 3. The Projective Plane 42 1.Points at Infinity 42 2.Projective Coordinates on a Line 46 3.Projective Coordinates on a Plane 50 4.Algebraic Curves and Points at Infinity 54 5.Homogenization of Projective Curves 56 6.Coordinate Patches 61 Chapter 4. Multiplicities and Degree 67 1.Curves as Varieties 67 2.Multiplicities 69 3.Intersection Multiplicities 72 4.Calculus for Dummies 76 Chapter 5. B'ezout's Theorem 82 1.A Sketch of the Proof 82 2.An Illuminating Example 88 PART II. ELLIPTIC CURVES AND ALGEBRA Chapter 6. Transition to Elliptic Curves 95 Chapter 7. Abelian Groups 100 1.How Big Is Infinity? 100 2.What Is an Abelian Group? 101 3.Generations 103 4.Torsion 106 5.Pulling Rank 108 Appendix: An Interesting Example of Rank and Torsion 110 Chapter 8. Nonsingular Cubic Equations 116 1.The Group Law 116 2.Transformations 119 3.The Discriminant 121 4.Algebraic Details of the Group Law 122 5.Numerical Examples 125 6.Topology 127 7.Other Important Facts about Elliptic Curves 131 5.Two Numerical Examples 133 Chapter 9. Singular Cubics 135 1.The Singular Point and the Group Law 135 2.The Coordinates of the Singular Point 136 3.Additive Reduction 137 4.Split Multiplicative Reduction 139 5.Nonsplit Multiplicative Reduction 141 6.Counting Points 145 7.Conclusion 146 Appendix A: Changing the Coordinates of the Singular Point 146 Appendix B: Additive Reduction in Detail 147 Appendix C: Split Multiplicative Reduction in Detail 149 Appendix D: Nonsplit Multiplicative Reduction in Detail 150 Chapter 10. Elliptic Curves over Q 152 1.The Basic Structure of the Group 152 2.Torsion Points 153 3.Points of Infinite Order 155 4.Examples 156 PART III. ELLIPTIC CURVES AND ANALYSIS Chapter 11. Building Functions 161 1.Generating Functions 161 2.Dirichlet Series 167 3.The Riemann Zeta-Function 169 4.Functional Equations 171 5.Euler Products 174 6.Build Your Own Zeta-Function 176 Chapter 12. Analytic Continuation 181 1.A Difference that Makes a Difference 181 2.Taylor Made 185 3.Analytic Functions 187 4.Analytic Continuation 192 5.Zeroes, Poles, and the Leading Coefficient 196 Chapter 13. L-functions 199 1.A Fertile Idea 199 2.The Hasse-Weil Zeta-Function 200 3.The L-Function of a Curve 205 4.The L-Function of an Elliptic Curve 207 5.Other L-Functions 212 Chapter 14. Surprising Properties of L-functions 215 1.Compare and Contrast 215 2.Analytic Continuation 220 3.Functional Equation 221 Chapter 15. The Conjecture of Birch and Swinnerton-Dyer 225 1.How Big Is Big? 225 2.Influences of the Rank on the Np's 228 3.How Small Is Zero? 232 4.The BSD Conjecture 236 5.Computational Evidence for BSD 238 6.The Congruent Number Problem 240 Epilogue 245 Retrospect 245 Where DoWe Go from Here? 247 Bibliography 249 Index 251

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Book SynopsisOver 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

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Book SynopsisMatrix Differential Calculus With Applications in Statistics and Econometrics Revised Edition Jan R. Magnus, CentER, Tilburg University, The Netherlands and Heinz Neudecker, Cesaro, Schagen, The Netherlands .deals rigorously with many of the problems that have bedevilled the subject up to the present time. - Stephen Pollock, Econometric Theory I continued to be pleasantly surprised by the variety and usefulness of its contents - Isabella Verdinelli, Journal of the American Statistical Association Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises. * CoTrade Review"...the best book to learn matrix and related ideas...statisticians, econometricians, computer scientists, engineers, and psychometricians will find this extremely useful." (Journal of Statistical Computation and Simulation, March 2006) "a most welcome revision" (Computational Statistics & Data Analysis, 28 August 2001)Table of ContentsPreface xv Preface to the first revised printing xvii Preface to the second revised printing xviii Part One- Matrices Part Two- Differentials: the theory Part Three- Differentials: the practice Part Four- Inequalities Part Five- The linear model Part Six- Applications to maximum likelihood estimation Bibliography 379 Index of Symbols 387 Subject Index 390

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Book SynopsisWidely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics.Table of ContentsPreface. Preliminaries. PART I: GROUP THEORY. Chapter 1. Introduction to Groups. Chapter 2. Subgroups. Chapter 3. Quotient Group and Homomorphisms. Chapter 4. Group Actions. Chapter 5. Direct and Semidirect Products and Abelian Groups. Chapter 6. Further Topics in Group Theory. PART II: RING THEORY. Chapter 7. Introduction to Rings. Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains. Chapter 9. Polynomial Rings. PART III: MODULES AND VECTOR SPACES. Chapter 10. Introduction to Module Theory. Chapter 11. Vector Spaces. Chapter 12. Modules over Principal Ideal Domains. PART IV: FIELD THEORY AND GALOIS THEORY. Chapter 13. Field Theory. Chapter 14. Galois Theory. PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA. Chapter 15. Commutative Rings and Algebraic Geometry. Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains. Chapter 17. Introduction to Homological Algebra and Group Cohomology. PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS. Chapter 18. Representation Theory and Character Theory. Chapter 19. Examples and Applications of Character Theory. Appendix I: Cartesian Products and Zorn's Lemma. Appendix II: Category Theory. Index.

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Book SynopsisAccessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

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Book SynopsisLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading pTrade ReviewThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *Table of Contents1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors

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Book SynopsisAn introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines.Written in an engaging and straightforward style, and assuming little background in mathematics, the book is

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Book SynopsisThis book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quadratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.Table of ContentsPreface to the Second Edition.- Preface to the First Edition.- A Study Guide.- 1. Methods of Proof.- 2. Algebra.- 3. Real Analysis.- 4. Geometry and Trigonometry.- 5. Number Theory.- 6. Combinatorics and Probability.- Solutions.- Index of Notation.- Index.

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Book SynopsisThis volume is a collection of articles on themes related to the book Laws of Form by George Spencer-Brown. Laws of Form was first published in 1969 and brings forth a new articulation of the foundations of thought. In Laws of Form we have a mathematical formalism based on one symbol and an approach to the question how the world would appear if a distinction could be drawn. Laws of Form does not answer the question how, given nothing as a beginning, a distinction can, indeed must, inevitably take place. This second question must, in its own structure, be left to each individual thinker. Nevertheless, Laws of Form, beautifully written and content free (form is emptiness, emptiness is form) is the most powerful mathematical text on the edge of nothing that has been produced since Euclid''s Elements. These papers are a tribute to Spencer-Brown and his singular achievement.

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Table of ContentsAxiomatic homotopy theory.- Examples of simplicial homotopy theories.

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Book Synopsis"Revised and expanded edition of Matrix mathematics, retitled Scalar, vector, and matrix mathematics"--Preface.Trade ReviewPraise for the previous editions: "When a matrix question is thrown my way, I will now refer my correspondents ... to Bernstein's handbook."--Philip J. Davis, SIAM News Praise for the previous editions: "The amount of material that is covered is quite impressive and well structured... I highly recommend the book as a source for retrieving or verifying matrix results that one would otherwise have to search for in the extensive literature on matrix theory."--Paul Van Dooren, IEEE Control Systems Magazine Praise for the previous editions: "The author was very successful in collecting the enormous amount of results in matrix theory in a single source... A beautiful work and an admirable performance!"--Monatshefte fur Mathematik Praise for the previous editions: "A remarkable source of matrix results. I will put it on the shelf near to my desk so that I have quick access to it. The book is an impressive accomplishment."--Helmut Lutkepohl, Image Praise for the previous editions: "A well-organized treasure trove of information for anyone interested in matrices and their applications."--Henry Ricardo, MAA Reviews

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Book SynopsisReveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. The book aims to convince the reader that the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous.Trade ReviewThis book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar." —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition)Table of Contents Differential equations Developing PDE intuition The story of solitons Elliptic curves and KdV traveling waves KdV $n$-solitons and $\tau$-functions Multiplying and factoring differential operators Eigenfunctions and isospectrality Lax form for KdV and other soliton equations The KP equation and bilinear KP equation $\Gamma_{2,4}$ and the bilinear KP equation Pseudo-differential operators and the KP hierarchy $\Gamma{k,n}$ and the bilinear KP hierarchy Concluding remarks Mathematica guide Complex numbers Ideas for independent projects References Glossary of symbols Index

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Book SynopsisA unique and effective way to learn Algebraâupdated with the latest instruction and reviewMust Know High School Algebra provides a fresh approach to learning. As part of our Must Know series, this new edition makes sure what you really need to know is clear up-front. Rather than starting with goals to be met, chapters begin by telling you the most important concepts about the topic at handâand then show you exactly how these concepts help you accomplish your goals.Written by excerpt algebra educators, Must Know High School Algebra, Second Edition provides updated lesson content and useful examples to help clarify each topic. Every chapter closes with reinforcing exercises to get you the practice you need to gain confidence. New features to this edition focus on extra support and helping you avoid common mistakes. In the end, you get everything you need to build your algebra skills quickly and painlessly.Features:Mo

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Book SynopsisRich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.Trade Review“The aim of this book is to survey the basic notions and results of general algebra; also, it is a detailed and self-contained introduction to general algebra from the point of view of categories and functors. … The author takes care in writing full proofs throughout the book and he shows also ways of possible applications. The text contains a wealth material and should serve as a textbook for readers interested in this field.” (Danica Jakubíková-Studenovská, zbMATH 1317.08001, 2015)Table of Contents1 About the course, and these notes.- Part I: Motivation and Examples.- 2 Making Some Things Precise.- 3 Free Groups.- 4 A Cook's Tour.- Part II: Basic Tools and Concepts.- 5 Ordered Sets, Induction, and the Axiom of Choice.- 6 Lattices, Closure Operators, and Galois Connections.- 7 Categories and Functors.- 8 Universal Constructions.- 9 Varieties of Algebras.- Part III: More on Adjunctions.- 10 Algebras, Coalgebras, and Adjunctions.- References.- List of Exercises.- Symbol Index.- Word and Phrase Index.

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Book SynopsisSuitable for computational scientists and engineers in addition to researchers in numerical linear algebra community, this title includes an introduction to tensor computations and fresh sections on: discrete Poisson solvers; pseudospectra; structured linear equation problems; structured eigenvalue problems; and, polynomial eigenvalue problems.Trade ReviewProblems, solutions, and discussions of the formulas, methods and literature surrounding matrix computations make for a reference that is specific and well detailed: perfect for any college-level math collection appealing to engineers. Midwest Book Review Written for scientists and engineers, Matrix Computations, fourth edition provides comprehensive coverage of numerical linear algebra. Anyone whose work requires the solution to a matrix problem and an appreciation of mathematical properties will find this book to be an indispensable tool. MathWorksTable of ContentsPrefaceGlobal ReferencesOther BooksUseful URLsCommon NotationChapter 1. Matrix Multiplication1.1. Basic Algorithms and Notation1.2. Structure and Efficiency1.3. Block Matrices and Algorithms1.4. Fast Matrix-Vector Products1.5. Vectorization and Locality1.6. Parallel Matrix MultiplicationChapter 2. Matrix Analysis2.1. Basic Ideas from Linear Algebra2.2. Vector Norms2.3. Matrix Norms2.4. The Singular Value Decomposition2.5. Subspace Metrics2.6. The Sensitivity of Square Systems2.7. Finite Precision Matrix ComputationsChapter 3. General Linear Systems3.1. Triangular Systems3.2. The LU Factorization3.3. Roundoff Error in Gaussian Elimination3.4. Pivoting3.5. Improving and Estimating Accuracy3.6. Parallel LUChapter 4. Special Linear Systems4.1. Diagonal Dominance and Symmetry4.2. Positive Definite Systems4.3. Banded Systems4.4. Symmetric Indefinite Systems4.5. Block Tridiagonal Systems4.6. Vandermonde Systems4.7. Classical Methods for Toeplitz Systems4.8. Circulant and Discrete Poisson SystemsChapter 5. Orthogonalization and Least Squares5.1. Householder and Givens Transformations5.2. The QR Factorization5.3. The Full-Rank Least Squares Problem5.4. Other Orthogonal Factorizations5.5. The Rank-Deficient Least Squares Problem5.6. Square and Underdetermined SystemsChapter 6. Modified Least Squares Problems and Methods6.1. Weighting and Regularization6.2. Constrained Least Squares6.3. Total Least Squares6.4. Subspace Computations with the SVD6.5. Updating Matrix FactorizationsChapter 7. Unsymmetric Eigenvalue Problems7.1. Properties and Decompositions7.2. Perturbation Theory7.3. Power Iterations7.4. The Hessenberg and Real Schur Forms7.5. The Practical QR Algorithm7.6. Invariant Subspace Computations7.7. The Generalized Eigenvalue Problem7.8. Hamiltonian and Product Eigenvalue Problems7.9. PseudospectraChapter 8. Symmetric Eigenvalue Problems8.1. Properties and Decompositions8.2. Power Iterations8.3. The Symmetric QR Algorithm8.4. More Methods for Tridiagonal Problems8.5. Jacobi Methods8.6. Computing the SVD8.7. Generalized Eigenvalue Problems with SymmetryChapter 9. Functions of Matrices9.1. Eigenvalue Methods9.2. Approximation Methods9.3. The Matrix Exponential9.4. The Sign, Square Root, and Log of a MatrixChapter 10. Large Sparse Eigenvalue Problems10.1. The Symmetric Lanczos Process10.2. Lanczos, Quadrature, and Approximation10.3. Practical Lanczos Procedures10.4. Large Sparse SVD Frameworks10.5. Krylov Methods for Unsymmetric Problems10.6. Jacobi-Davidson and Related MethodsChapter 11. Large Sparse Linear System Problems11.1. Direct Methods11.2. The Classical Iterations11.3. The Conjugate Gradient Method11.4. Other Krylov Methods11.5. Preconditioning11.6. The Multigrid FrameworkChapter 12. Special Topics12.1. Linear Systems with Displacement Structure12.2. Structured-Rank Problems12.3. Kronecker Product Computations12.4. Tensor Unfoldings and Contractions12.5. Tensor Decompositions and IterationsIndex

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Book Synopsis

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Book SynopsisTodayâs Developmental Math students enter college needing more than just the math, and this has directly impacted the instructorâs role in the classroom. Instructors have to teach to different learning styles, within multiple teaching environments, and to a student population that is mostly unfamiliar with how to be a successful college student. Authors Andrea Hendricks and Pauline Chow have noticed this growing trend in their combined 30+ years of teaching at their respective community colleges, both in their face-to-face and online courses. As a result, they set out to create course materials that help todayâs students not only learn the mathematical concepts but also build life skills for future success. Understanding the time constraints for instructors, these authors have worked to integrate success strategies into both the print and digital materials, so that there is no sacrifice of time spent on the math. Furthermore, Andrea and Pauline have taken the time to write purpoTable of ContentsChapter S: Success StrategiesS.1: Time Management and Goal SettingS.2: Learning StylesS.3: Study SkillsS.4: Test TakingS.5: Blended and Online ClassesChapter 1: Real Numbers and Algebraic Expressions1.1: The Set of Real Numbers1.2: Fractions Review1.3: The Order of Operations, Algebraic Expressions and Equations1.4: Addition of Real Numbers1.5: Subtraction of Real Numbers1.6: Multiplication and Division of Real Numbers1.7: Properties of Real Numbers1.8: Algebraic ExpressionsChapter 2: Linear Equations & Inequalities in One Variable2.1: Equations and Their Solutions2.2: The Addition Property of Equality2.3: The Multiplication Property of Equality2.4: More on Solving Linear Equations2.5: Formulas and Applications from Geometry2.6: Percent, Rate, and Mixture Problems2.7: Linear Inequalities in One VariableChapter 3: Linear Equations in Two Variables3.1: Equations and the Rectangular Coordinate System3.2: Graphing Linear Equations3.3: The Slope of a Line3.4: More about Slope3.5: Writing Equations of Lines3.6: FunctionsChapter 4: Systems of Linear Equations in Two and Three Variables4.1: Solving Systems of Linear Equations Graphically4.2: Solving Systems of Linear Equations by Substitution4.3: Solving Systems of Linear Equations by Elimination4.4: Applications of Systems of Linear Equations in Two Variables 4.5: Solving Systems of Linear Equations in Three Variables and Their Applications Chapter 5: Exponents, Polynomials, and Polynomial Functions5.1: Rules of Exponents and Zero and Negative Exponents5.2: More Rules of Exponents and Scientific Notation5.3: Polynomial Functions, Addition and Subtraction of Polynomials5.4: Multiplication of Polynomials and Polynomial Functions5.5: Special Products5.6: Division of Polynomials5.7: Synthetic Division and the Remainder TheoremChapter 6: Factoring Polynomials and Polynomial Equations6.1: Greatest Common Factor and Grouping6.2: Factoring Trinomials6.3: More on Factoring Trinomials6.4: Factoring Binomials6.5: Solving Quadratic Equations and Other Polynomial Equations by Factoring6.6: Applications of Quadratic EquationsChapter 7: Rational Functions and Equations7.1: Rational Functions and Simplifying Rational Expressions7.2: Multiplication and Division of Rational Expressions7.3: Least Common Denominator and Equivalent Fractions7.4: Addition and Subtraction of Rational Expressions7.5: Complex Fractions7.6: Solving Rational Equations7.7: Proportions and Other Applications of Rational EquationsChapter 8: More on Functions and Graphs; Variation8.1: The Domain and Range of Functions8.2: Graphing and Writing Linear Functions8.3: Graphing Nonlinear Functions and Piecewise Defined Functions8.4: Variation and ApplicationsChapter 9: Inequalities and Absolute Value9.1: Compound Inequalities9.2: Absolute Value Equations9.3: Absolute Value Inequalities9.4: Linear Inequalities in Two Variables and Systems of Linear InequalitiesChapter 10: Rational Exponents, Radicals, and Complex Numbers10.1: Radicals and Radical Functions10.2: Rational Exponents10.3: Simplifying Radical Expressions10.4: Adding, Subtracting, and Multiplying Radical Expressions10.5: Dividing Radicals and Rationalizing10.6: Radical Equations and their Applications10.7: Complex NumbersChapter 11: Quadratic Equations and Functions11.1: Quadratic Functions and their Graphs11.2: Solving Quadratic Equations by the Square Root Property and Completing the Square11.3: Solving Quadratic Equations by the Quadratic Formula11.4: Solving Equations by Using Quadratic Methods11.5: More on Graphing Quadratic Functions11.6: Solving Quadratic and Rational Inequalities in One VariableChapter 12: Exponential and Logarithmic Functions12.1: Operations and Composition of Functions12.2: Inverse Functions12.3: Exponential Functions12.4: Logarithmic Functions12.5: Properties of Logarithms12.6: The Common Log, Natural Log, and Change of Base Formula12.7: Exponential and Logarithmic Equations and ApplicationsChapter 13: Conic Sections and Nonlinear Systems13.1: The Parabola and the Circle13.2: The Ellipse and the Hyperbola13.3: Solving Nonlinear Systems of Equations13.4: Solving Nonlinear Inequalities and Systems of InequalitiesChapter 14: Sequences, Series, and the Binomial Theorem14.1: Sequences14.2: Arithmetic Sequences and Series14.3: Geometric Sequences and Series14.4: The Binomial Theorem

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Book SynopsisTable of ContentsCollege Algebra: Graphs & Models Chapter R: A Review of Basic Concepts and Skills R.1: Algebraic Expressions and the Properties of Real Numbers R.2: Exponents, Scientific Notation, and a Review of Polynomials R.3: Solving Linear Equations and Inequalities R.4: Factoring Polynomials and Solving Polynomial Equations by Factoring R.5: Rational Expressions and Equations R.6: Radicals, Rational Exponents, and Radical Equations Chapter 1: Functions and Graphs 1.1: Rectangular Coordinates, Graphing Circles and Other Relations1.2: Functions, Function Notation, and the Graph of a Function 1.3: Linear Equations and Rates of Change1.4: Linear Functions, Special Forms, and More on Rates of Change1.5: Solving Equations and Inequalities Graphically; Formulas and Problem Solving1.6: Linear Models and Real Data Chapter 2: Relations, More on Functions 2.1: Analyzing the Graph of a Function 2.2: The Toolbox Functions and Transformations 2.3: Absolute Value Functions, Equations, and Inequalities 2.4: Rational and Radical Functions; More on the Domain 2.5: Piecewise-Defined Functions 2.6: Variation: The Toolbox Functions in Action Chapter 3: Quadratic Functions and Operations on Functions 3.1: Complex Numbers 3.2: Solving Quadratic Equations and Inequalities 3.3: Quadratic Functions and Applications 3.4: Quadratic Models; More on Rates of Change 3.5: The Algebra of Functions 3.6: Composition of Functions and the Difference Quotient Chapter 4: Polynomial and Rational Functions 4.1: Synthetic Division; the Remainder and Factor Theorems 4.2: The Zeros of Polynomial Functions 4.3: Graphing Polynomial Functions 4.4: Graphing Rational Functions 4.5: Additional Insights into Rational Functions Chapter 5: Exponential and Logarithmic Functions 5.1: One-to-One and Inverse Functions 5.2: Exponential Functions 5.3: Logarithms and Logarithmic Functions 5.4: Properties of Logarithms 5.5: Solving Exponential/Logarithmic Equations 5.6: Applications from Business, Finance, and Science 5.7: Exponential, Logarithmic, and Logistic Equation Models Chapter 6: Systems of Equations and Inequalities 6.1: Linear Systems in Two Variables with Applications 6.2: Linear Systems in Three Variables with Applications 6.3: Nonlinear Systems of Equations and Inequalities 6.4: Systems of Inequalities and Linear Programming Chapter 7: Matrices and Matrix Applications 7.1: Solving Linear Systems Using Matrices and Row Operations 7.2: The Algebra of Matrices 7.3: Solving Linear Systems Using Matrix Equations 7.4: Applications of Matrices and Determinants: Cramer’s rule, Partial Fractions, and More 7.5: Matrix Applications and Technology Use Chapter 8: Analytic Geometry and the Conic Sections 8.1: A Brief Introduction to Analytic Geometry 8.2: The Circle and the Ellipse 8.3: The Hyperbola 8.4: The Analytic Parabola: More on Nonlinear Systems Chapter 9: Additional Topics in Algebra 9.1: Sequences and Series 9.2: Arithmetic Sequences 9.3: Geometric Sequences 9.4: Mathematical Induction 9.5: Counting Techniques 9.6: Introduction to Probability 9.7: The Binomial Theorem Appendices The Language, Notation, and Numbers of Mathematics Geometry Review with Unit Conversions More on Synthetic Division More on Matrices Deriving the Equation of a Conic Proof Positive - A Selection of Proofs from College Algebra

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Book Synopsis- The only program that supports the Common Core State Standards throughout four-years of high school mathematics with an unmatched depth of resources and adaptive technology that helps you differentiate instruction for every student. * Connects students to math content with print, digital and interactive resources. * Prepares students to meet the rigorous Common Core Standards with aligned content and focus on Standards of Mathematical Practice. * Meets the needs of every student with resources that enable you to tailor your instruction at the classroom and individual level. * Assesses student mastery and achievement with dynamic, digital assessment and reporting. Includes Print Student Edition

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