Algebra Books

Book SynopsisDomina Álgebra II con explicaciones claras y práctica guiada. Álgebra II Paso a Paso para...

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Book Synopsis Estás listo para explorar los fundamentos del álgebra y sus aplicaciones?"Álgebra: Fundamentos y Estructuras Matemáticas", escrito por Helbert Justo Luque Zevallos, es un texto diseñado para llevarte de la mano en un viaje a través del fascinante mundo del álgebra. Con un enfoque accesible y riguroso, este libro aborda desde los conceptos básicos de conjuntos hasta las complejidades de los números complejos y sus extensiones, convirtiéndose en una herramienta imprescindible para estudiantes, autodidactas y apasionados de las matemáticas. Qué encontrarás en este libro? Teoría de Conjuntos y Números Naturales: Aprende las operaciones fundamentales entre conjuntos, las leyes de Morgan y el principio de inducción matemática. Números Enteros: Explora la construcción de los números enteros, el conjunto cociente. Números Racionales y Reales: Descubre cómo se construyen los números racionales y reales, y entiende conceptos como sucesiones de Cauchy, cortes de Dedekind y completitud. Características destacadas: Explicaciones claras: Una teoría detallada presentada con un lenguaje accesible para facilitar su comprensión. Ejemplos ilustrativos: Cada tema incluye ejemplos resueltos paso a paso que conectan la teoría con la práctica. Ejercicios propuestos: Diseñados para fortalecer tu aprendizaje y desarrollar tus habilidades matemáticas. Conexión con aplicaciones prácticas: Vincula los conceptos algebraicos con problemas del mundo real y otras disciplinas. Este libro es ideal para: Estudiantes de matemáticas, ingeniería y ciencias aplicadas. Profesores que buscan un recurso claro y completo para sus cursos. Autodidactas interesados en profundizar en el álgebra como base para otros campos matemáticos. Ya sea que estés iniciando tu aprendizaje en álgebra o necesites un texto confiable como referencia, "Álgebra: Fundamentos y Estructuras Matemáticas" será tu guía ideal en esta travesía hacia el conocimiento. Descubre la belleza y la utilidad del álgebra con este libro único y accesible!

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Book SynopsisTrade Review"The authors give a clear and logically correct exposition of the foundations of linear algebra and rightly determinate the balance between the computational parts and the more theoretical parts." --K.Burian, zbMATH Open "A 35-page appendix gives brief descriptions of commands needed when using computational tools such as Derive, Maple, MATLAB, Mathematica and various graphing calculators." --J.D.Dixon, zbMATH OpenTable of Contents1. Vectors and Matrices 2. Systems of Linear Equations 3. Determinants and Eigenvalues 4. Finite Dimensional Vector Spaces 5. Linear Transformations 6. Orthogonality 7. Complex Vector Spaces and General Inner Products 8. Additional Applications 9. Numerical Methods Appendices A: Miscellaneous Proofs B: Functions C: Complex Numbers D: Elementary Matrices E: Answers to Selected Exercies

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Book SynopsisTable of Contents1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1 - 1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3 - 1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5 - 1.6) Summary Review Exercises Test 2. Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1 - 2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4 - 2.6) Summary Review Exercises Test 3. Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1 - 3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3 - 3.4) Summary Review Exercises Test 4. Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1 - 4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3 - 4.4) Unifying Polynomial Functions Summary Review Exercises Test 5. Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1 - 5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4 - 5.5) Unifying Root Functions Summary Review Exercises Test 6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1 - 6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4 - 6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test 7. Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1 - 7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer's Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4 - 7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7 - 7.8) Summary Review Exercises Test 8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1 - 8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3 - 8.4) Summary Review Exercises Test 9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures 9.2 Trigonometric Functions and Fundamental Identities 9.3 Right Triangles and Evaluating Trigonometric Functions 9.4 Applications of Right Triangles 9.5 The Circular Functions 9.6 Graphs of the Sine and Cosine Functions 9.7 Graphs of the Other Circular Functions 9.8 Harmonic Motion Summary Review Exercises Test 10. Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test 11. Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test 12. Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 12.1 - 12.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 12.4 -12.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 12.6 - 12.7) Summary Review Exercises Test R. Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendices A: Geometry Formulas B: Vectors in Space C: Polar Form of Conic Sections D: Rotation of Axes Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index

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Book SynopsisTable of ContentsTable of Contents Review R.1 Real Numbers R.2 Algebra Essentials R.3 Geometry Essentials R.4 Polynomials R.5 Factoring Polynomials R.6 Synthetic Division R.7 Rational Expressions R.8 nth Roots; Rational Exponents Equations and Inequalities 1.1 Linear Equations 1.2 Quadratic Equations 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations 1.5 Solving Inequalities 1.6 Equations and Inequalities Involving Absolute Value 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Chapter 1 Review, Test, and Projects Graphs 2.1 The Distance and Midpoint Formulas 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 2.3 Lines 2.4 Circles 2.5 Variation Chapter 2 Review, Test, and Projects Functions and Their Graphs 3.1 Functions 3.2 The Graph of a Function 3.3 Properties of Functions 3.4 Library of Functions; Piecewise-defined Functions 3.5 Graphing Techniques: Transformations 3.6 Mathematical Models: Building Functions Chapter 3 Review, Test, and Projects Linear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models 4.2 Building Linear Models from Data 4.3 Quadratic Functions and Their Properties 4.4 Build Quadratic Models from Verbal Descriptions and from Data 4.5 Inequalities Involving Quadratic Functions Chapter 4 Review, Test, and Projects Polynomial and Rational Functions 5.1 Polynomial Functions 5.2 Graphing Polynomials Functions; Models 5.3 Properties of Rational Functions 5.4 The Graph of a Rational Function 5.5 Polynomial and Rational Inequalities 5.6 The Real Zeros of a Polynomial Function Chapter 5 Review, Test, and Projects Exponential and Logarithmic Functions 6.1 Composite Functions 6.2 One-to-One Functions; Inverse Functions 6.3 Exponential Functions 6.4 Logarithmic Functions 6.5 Properties of Logarithms 6.6 Logarithmic and Exponential Equations 6.7 Financial Models 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 6.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter 6 Review, Test, and Projects Trigonometric Functions 7.1 Angles, Arc, Length, and Circular Motion 7.2 Right Triangle Trigonometry 7.3 Computing the Values of Trigonometric Functions of Acute Angles 7.4 Trigonometric Functions of Any Angle 7.5 Unit Circle Approach; Properties of the Trigonometric Functions 7.6 Graphs of the Sine and Cosine Functions 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 7.8 Phase Shift; Sinusoidal Curve Fitting Chapter 7 Review, Test, and Projects Analytic Trigonometry 8.1 The Inverse Sine, Cosine, and Tangent Functions 8.2 The Inverse Trigonometric Functions (Continued) 8.3 Trigonometric Equations 8.4 Trigonometric Identities 8.5 Sum and Difference Formulas 8.6 Double-angle and Half-angle Formulas 8.7 Product-to-Sum and Sum-to-Product Formulas Chapter 8 Review, Test, and Projects Applications of Trigonometric Functions 9.1 Applications Involving Right Triangles 9.2 The Law of Sines 9.3 The Law of Cosines 9.4 Area of a Triangle 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter 9 Review, Test, and Projects Polar Coordinates; Vectors 10.1 Polar Coordinates 10.2 Polar Equations and Graphs 10.3 The Complex Plane; De Moivre’s Theorem 10.4 Vectors 10.5 The Dot Product Chapter 10 Review, Test, and Projects Analytic Geometry 11.1 Conics 11.2 The Parabola 11.3 The Ellipse 11.4 The Hyperbola 11.5 Rotation of Axes; General Form of a Conic 11.6 Polar Equations of Conics 11.7 Plane Curves and Parametric Equations Chapter 11 Review, Test, and Projects Systems of Equations and Inequalities 12.1 Systems of Linear Equations: Substitution and Elimination 12.2 Systems of Linear Equations: Matrices 12.3 Systems of Linear Equations: Determinants 12.4 Matrix Algebra 12.5 Partial Fraction Decomposition 12.6 Systems of Nonlinear Equations 12.7 Systems of Inequalities 12.8 Linear Programming Chapter 12 Review, Test, and Projects Sequences; Induction; the Binomial Theorem 13.1 Sequences 13.2 Arithmetic Sequences 13.3 Geometric Sequences; Geometric Series 13.4 Mathematical Induction 13.5 The Binomial Theorem Chapter 13 Review, Test, and Projects Counting and Probability 14.1 Counting 14.2 Permutations and Combinations 14.3 Probability Chapter 14 Review, Test, and Projects Appendix: Graphing Utilities A.1 The Viewing Rectangle A.2 Using a Graphing Utility to Graph Equations A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry A.4 Using a Graphing Utility to Solve Equations A.5 Square Screens A.6 Using a Graphing Utility to Graph Inequalities A.7 Using a Graphing Utility to Solve Systems of Linear Equations A.8 Using a Graphing Utility to Graph a Polar Equation A.9 Using a Graphing Utility to Graph Parametric Equations Answers Credits Index

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Book SynopsisThe theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative rings. Students, mathematicians working in g-inverses of matrices, along with algebraists, and control theorists will find new and indispensable data, presented with clarity and insight. This book is also well suited to graduate courses on g-inverses in algebra.Table of ContentsElementary Results on Rings. Matrix Algebra Over Rings. Regular Elements in a Ring. Regularity - Principal Ideal Rings. Regularity - Basics. Regularity - Integral Domains. Regularity - Commutative Rings. Special Topics.

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Book SynopsisThe description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.Table of ContentsPreface Introduction I. General Ramification Theory 1. Elementary lemmas from ideal theory 2. Primary decomposition in non-noetherian rings 3. Integral dependence 4. Linear algebra 5. Discriminant of an algebra 6. The discriminant ideal 7. Galois theory of local rings II. Valuation Theory 8. Ordered abelian groups 9. Valuations 10. Specialization and composition of valuations 11. Ramification theory of valuations 12. Valuations of algebraic function fields III. Noetherian Local Rings 13. The dimension of a noetherian local ring 14. Quadratic transforms IV. Two-Dimensional Local Domains 15. Limits of quadratic sequences 16. Uniformization in a two-dimensional regular local domain 17. Uniformization for a two-dimensional algebraic function field V. Varieties and Transformations 18. Projective varieties 19. Resolution of singularities of algebraic surfaces Bibliography

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisA collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.Table of ContentsPreface -- Contributors -- New approach to octonions and Cayley algebras /Helena Albuquerque and Shahn Majid -- Identities of graded alternative algebras /Y. Bahturin and M. Zaicev -- Invariant connections on symmetric spaces /Pilar Benito, Cristina Draper, and Alberto Elduque -- £-ideals in Bernstein algebras /A. Catalan -- Octonions and affine connections on spheres /Alberto Elduque and Hyo Chul Myung -- Immediate applications of a new classification of finite dimensional simple Lie algebras /Mohammed El Houari -- An approach to integrable theories in any dimension: the role of non-semi simple Lie algebras /Luiz A. Ferreira -- Versal deformations of Lie algebras /Alice Fialowski -- Derivations in second order Bernstein algebras /M. A. Garcia-Muniz and C. Martinez -- Algebraic structure of the non-abelian Toda models /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Alternative rings of small order and the hunt for Moufang circle loops /Edgar G. Goodaire -- A note on linearization of some identities /H. Guzzo, Jr., and P. Vicente -- The commuting nucleus of right alternative rings /Irvin Roy Hentzel -- A construction of Jordan superalgebras from Jordan-Lie triple systems /Noriaki Kamiya and Susumu Okubo -- Rings with (x,y,z) = (x,z,y) /Erwin Kleinfeld and Margaret Kleinfeld -- On the semi simplicity of special Jordan superalgebras /Carlos Gomez-Ambrosi and Jesus Laliena -- Bernstein superalgebras of dimension four /S. Gonzalez, C. Lopez-Diaz, and C. Martinez -- Banach-Bemstein algebras and their applications /Yu. Lyubich -- Jordan superalgebras /C. Martinez -- Derivations of structurable / /*-algebras /J. Martinez Moreno -- Lie mappings of C* -algebras /Martin Mathieu -- Sur des anneaux commutatifs a puissances associatives de caracteristique premiere p> 0 /Joao Carlos da Motta Ferreira and Artibano Micali -- Principal ^-bundles /Alexander I. Nesterov -- Z x Z-graded Lie algebras containing a Heisenberg algebra /J. Marshall Osborn and Kaiming Zhao -- A„(l) Toda solitons: a relation between dressing transformations and vertex operators /H. Belich and R. Paunov -- Generalized quadratic rings /Luiz Antonio Peresi -- The derivation algebra of a division composition algebra /J. M. Perez-Izquierdo -- On the structure of the simple Moufang loop GLL (F2) /M. L. Merlini Giuliani and Cesar Polcino Milies -- Lie groups, differential geometry, and nonlinear integrable systems /A V. Razumov and M. V. Saveliev -- Smooth quasigroups and loops. Recent achievements and open problems /L. V. Sabinin -- On smooth left square distributive quasigroup /Liudmila Sabinina -- Algebraic structure of trans symmetric spaces /L. V. Sbitneva -- Bernstein algebras whose lattice of ideals is distributive /C. Martinez and J. Setd -- Specialty problem for Malcev algebras and Poisson Malcev algebras /Ivan P. Shestakov -- Applications of Lie ring methods to group theory /Pavel Shumyatsky -- Computable rings, groups and their isomorphisms /Bakhadyr Khoussainov and Arkadii Slinko -- Quantum F-algebras /J. F. Gomes, F. E. Mendonga da Silveira, G. M. Sotkov, and A. H. Zimerman -- Conditions d’existence d’une loi de Hardy-Weinberg periodique dans des populations selectivement neutres /C. Mallol and R. Varro -- Finite semi fields three-dimensional over the left nuclei /G. P. Wene -- Supplementing radicals of nonassociative rings /Richard Wiegandt.

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Book SynopsisAn Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand''s representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann''s double commutant theorem, Kaplansky''s density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

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Book SynopsisTo find more information about Rowman and Littlefield titles, please visit www.rowmanlittlefield.com.

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Book SynopsisThe theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules. Table of ContentsRings related to finite posets. Distributive and semidistributive rings. The group of extensions. Modules over semiperfect rings. Representations of primitive posets. Representations of quivers, species and finite dimensional algebras. Artinian rings of finite representation type. O-species and SPSD-rings of bounded representation type.

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Book SynopsisTable of ContentsR. Review of Basic Concepts. R.1 Sets R.2 Real Numbers and Their Properties R.3 Polynomials R.4 Factoring Polynomials R.5 Rational Expressions R.6 Rational Exponents R.7 Radical Expressions 1. Equations and Inequalities 1.1 Linear Equations 1.2 Applications and Modeling with Linear Equations 1.3 Complex Numbers 1.4 Quadratic Equations 1.5 Applications and Modeling with Quadratic Equations 1.6 Other Types of Equations and Applications 1.7 Inequalities 1.8 Absolute Value Equations and Inequalities 2. Graphs and Functions 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions 2.5 Equations of Lines and Linear Models 2.6 Graphs of Basic Functions 2.7 Graphing Techniques 2.8 Function Operations and Composition 3. Polynomial and Rational Functions. 3.1 Quadratic Functions and Models 3.2 Synthetic Division 3.3 Zeros of Polynomial Functions 3.4 Polynomial Functions: Graphs, Applications, and Models 3.5 Rational Functions: Graphs, Applications, and Models 3.6 Variation 4. Inverse, Exponential, and Logarithmic Functions. 4.1 Inverse Functions 4.2 Exponential Functions 4.3 Logarithmic Functions 4.4 Evaluating Logarithms and the Change-of-Base Theorem 4.5 Exponential and Logarithmic Equations 4.6 Applications and Models of Exponential Growth and Decay 5. Systems and Matrices 5.1 Systems of Linear Equations 5.2 Matrix Solution of Linear Systems 5.3 Determinant Solution of Linear Systems 5.4 Partial Fractions 5.5 Nonlinear Systems of Equations 5.6 Systems of Inequalities and Linear Programming 5.7 Properties of Matrices 5.8 Matrix Inverses Glossary Solutions to Selected Exercises Answers to Selected Exercises Index of Applications Index

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Book SynopsisBob Blitzer is a native of Manhattan and received aBachelor of Arts degree with dual majors in mathematics and psychology (minor:English literature) from the City College of New York. His unusual combinationof academic interests led him toward a Master of Arts in mathematics from theUniversity of Miami and a doctorate in behavioral sciences from NovaUniversity. Bob's love for teaching mathematics was nourished for nearly 30years at Miami Dade College, where he received numerous teaching awards,including Innovator of the Year from the League for Innovations in theCommunity College and an endowed chair based on excellence in the classroom. Inaddition to Algebra and Trigonometry, Bob has written textbookscovering developmental mathematics, introductory algebra, intermediate algebra,trigonometry, precalculus, and liberal arts mathematics, all published byPearson. When not secluded in his Northern California writer's cabin, Bob canbe found hikinTable of Contents P. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials P.5 Factoring Polynomials P.6 Rational Expressions 1. Equations and Inequalities 1.1 Graphs and Graphing Utilities 1.2 Linear Equations and Rational Equations 1.3 Models and Applications 1.4 Complex Numbers 1.5 Quadratic Equations 1.6 Other Types of Equations 1.7 Linear Inequalities and Absolute Value Inequalities 2. Functions and Graphs 2.1 Basics of Functions and Their Graphs 2.2 More on Functions and Their Graphs 2.3 Linear Functions and Slope 2.4 More on Slope 2.5Transformations of Functions 2.6 Combinations of Functions; Composite Functions 2.7 Inverse Functions 2.8 Distance and Midpoint Formulas; Circles 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions and Their Graphs 3.3 Dividing Polynomials; Remainder and Factor Theorems 3.4 Zeros of Polynomial Functions 3.5 Rational Functions and Their Graphs 3.6 Polynomial and Rational Inequalities 3.7 Modeling Using Variation 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms 4.4 Exponential and Logarithmic Equations 4.5 Exponential Growth and Decay; Modeling Data 5. Trigonometric Functions 5.1 Angles and Radian Measure 5.2 Right Triangle Trigonometry 5.3 Trigonometric Functions of Any Angle 5.4 Trigonometric Functions of Real Numbers; Periodic Functions 5.5 Graphs of Sine and Cosine Functions 5.6 Graphs of Other Trigonometric Functions 5.7 Inverse Trigonometric Functions 5.8 Applications of Trigonometric Functions 6. Analytic Trigonometry 6.1 Verifying Trigonometric Identities 6.2 Sum and Difference Formulas 6.3Double-Angle, Power-Reducing, and Half-Angle Formulas 6.4 Product-to-Sumand Sum-to-Product Formulas 6.5 Trigonometric Equations 7. Additional Topics in Trigonometry 7.1 The Law of Sines 7.2 The Law of Cosines 7.3 Polar Coordinates 7.4 Graphs of Polar Equations 7.5 Complex Numbers in Polar Form; De Moivre's Theorem 7.6 Vectors 7.7 The Dot Product 8. Systems of Equations and Inequalities 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations in Three Variables 8.3 Partial Fractions 8.4 Systems of Nonlinear Equations in Two Variables 8.5 Systems of Inequalities 8.6 Linear Programming 9. Matrices and Determinants 9.1 Matrix Solutions to Linear Systems 9.2 Inconsistent and Dependent Systems and Their Applications 9.3 Matrix Operations and Their Applications 9.4 Multiplicative Inverses of Matrices and Matrix Equations 9.5 Determinants and Cramer's Rule 10. Conic Sections and Analytic Geometry 10.1 The Ellipse 10.2 The Hyperbola 10.3 The Parabola 10.4 Rotation of Axes 10.5 Parametric Equations 10.6 Conic Sections in Polar Coordinates 11. Sequences, Induction, and Probability 11.1 Sequences and Summation Notation 11.2 Arithmetic Sequences 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 The Binomial Theorem 11.6 Counting Principles, Permutations, and Combinations 11.7 Probability

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Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but afTable of ContentsR. Review of Basic Concepts R.1. Fractions, Decimals, and Percents R.2. Sets and Real Numbers R.3. Real Number Operations and Properties R.4. Integer and Rational Exponents R.5. Polynomials R.6. Factoring Polynomials R.7. Rational Expressions R.8. Radical Expressions 1. Equations and Inequalities 1.1. Linear Equations 1.2. Applications and Modeling with Linear Equations 1.3. Complex Numbers 1.4. Quadratic Equations 1.5. Applications and Modeling with Quadratic Equations 1.6. Other Types of Equations and Applications 1.7. Inequalities 1.8. Absolute Value Equations and Inequalities 2. Graphs and Functions 2.1. Rectangular Coordinates and Graphs 2.2. Circles 2.3. Functions 2.4. Linear Functions 2.5. Equations of Lines and Linear Models 2.6. Graphs of Basic Functions 2.7. Graphing Techniques 2.8. Function Operations and Composition 3. Polynomial and Rational Functions 3.1. Quadratic Functions and Models 3.2. Synthetic Division 3.3. Zeros of Polynomial Functions 3.4. Polynomial Functions: Graphs, Applications, and Models 3.5. Rational Functions: Graphs, Applications, and Models 3.6. Polynomial and Rational Inequalities 3.7. Variation 4. Inverse, Exponential, and Logarithmic Functions 4.1. Inverse Functions 4.2. Exponential Functions 4.3. Logarithmic Functions 4.4. Evaluating Logarithms and the Change-of-Base Theorem 4.5. Exponential and Logarithmic Equations 4.6. Applications of Models of Exponential Growth and Decay 5. Trigonometric Functions 5.1. Angles 5.2. Trigonometric Functions 5.3. Trigonometric Function Values and Angle Measures 5.4. Solutions and Applications of Right Triangles 6. The Circular Functions and Their Graphs 6.1. Radian Measure 6.2. The Unit Circle and Circular Functions 6.3. Graphs of the Sine and Cosine Functions 6.4. Translations of the Graphs of the Sine and Cosine Functions 6.5. Graphs of the Tangent and Cotangent Functions 6.6. Graphs of the Secant and Cosecant Functions 6.7. Harmonic Motion 7. Trigonometric Identities and Equations 7.1. Fundamental Identities 7.2. Verifying Trigonometric Identities 7.3. Sum and Difference Identities 7.4. Double-Angle and Half-Angle Identities 7.5. Inverse Circular Functions 7.6. Trigonometric Equations 7.7. Equations Involving Inverse Trigonometric Functions 8. Applications of Trigonometry 8.1. The Law of Sines 8.2. The Law of Cosines 8.3. Geometrically Defined Vectors and Applications 8.4. Algebraically Defined Vectors and the Dot Product 8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 8.6. De Moivre's Theorem; Powers and Roots of Complex Numbers 8.7. Polar Equations and Graphs 8.8. Parametric Equations, Graphs, and Applications 9. Systems and Matrices 9.1. Systems of Linear Equations 9.2. Matrix Solution of Linear Systems 9.3. Determinant Solution of Linear Systems 9.4. Partial Fractions 9.5. Nonlinear Systems of Equations 9.6. Systems of Inequalities and Linear Programming 9.7. Properties of Matrices 9.8. Matrix Inverses 10. Analytic Geometry 10.1. Parabolas 10.2. Ellipses 10.3. Hyperbolas 10.4. Summary of the Conic Sections 11. Further Topics in Algebra 11.1. Sequences and Series 11.2. Arithmetic Sequences and Series 11.3. Geometric Sequences and Series 11.4. The Binomial Theorem 11.5. Mathematical Induction 11.6. Basics of Probability Appendix A Polar Form of Conic Sections Appendix B Rotation of Axes Appendix C Geometry Formulas

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Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but af

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