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1. Abstract algebra [2003]
 Solomon, Ronald.
 Providence, R.I. : American Mathematical Society, [2009?]
 Description
 Book — xii, 227 p. : ill. ; 24 cm.
 Summary

This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semihistorical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.
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QA162 .S63 2009  Unknown 
2. Abstract algebra [2008]
 Garrett, Paul B.
 Boca Raton, FL : Chapman & Hall/CRC, c2008.
 Description
 Book — 451 p. : ill. ; 26 cm.
 Summary

 PREFACE INTRODUCTION THE INTEGERS Unique factorization Irrationalities Z/m, the integers mod m Fermat's little theorem SunZe's theorem Worked examples GROUPS I Groups Subgroups Homomorphisms, kernels, normal subgroups Cyclic groups Quotient groups Groups acting on sets The Sylow theorem Trying to classify finite groups, part I Worked examples THE PLAYERS: RINGS, FIELDS Rings, fields Ring homomorphisms Vector spaces, modules, algebras Polynomial rings I COMMUTATIVE RINGS I Divisibility and ideals Polynomials in one variable over a field Ideals and quotients Ideals and quotient rings Maximal ideals and fields Prime ideals and integral domains FermatEuler on sums of two squares Worked examples LINEAR ALGEBRA I: DIMENSION Some simple results Bases and dimension Homomorphisms and dimension FIELDS I Adjoining things Fields of fractions, fields of rational functions Characteristics, finite fields Algebraic field extensions Algebraic closures SOME IRREDUCIBLE POLYNOMIALS Irreducibles over a finite field Worked examples CYCLOTOMIC POLYNOMIALS Multiple factors in polynomials Cyclotomic polynomials Examples Finite subgroups of fields Infinitude of primes p =
 1 mod n Worked examples FINITE FIELDS Uniqueness Frobenius automorphisms Counting irreducibles MODULES OVER PIDS The structure theorem Variations Finitely generated abelian groups Jordan canonical form Conjugacy versus k[x]module isomorphism Worked examples FINITELY GENERATED MODULES Free modules Finitely generated modules over a domain PIDs are UFDs Structure theorem, again Recovering the earlier structure theorem Submodules of free modules POLYNOMIALS OVER UFDS Gauss's lemma Fields of fractions Worked examples SYMMETRIC GROUPS Cycles, disjoint cycle decompositions Transpositions Worked examples NAIVE SET THEORY Sets Posets, ordinals Transfinite induction Finiteness, infiniteness Comparison of infinities Example: transfinite Lagrange replacement Equivalents of the axiom of choice SYMMETRIC POLYNOMIALS The theorem First examples A variant: discriminants EISENSTEIN'S CRITERION Eisenstein's irreducibility criterion Examples VANDERMONDE DETERMINANTS Vandermonde determinants Worked examples CYCLOTOMIC POLYNOMIALS II Cyclotomic polynomials over Z Worked examples ROOTS OF UNITY Another proof of cyclicness Roots of unity Q with roots of unity adjoined Solution in radicals, Lagrange resolvents Quadratic fields, quadratic reciprocity Worked examples CYCLOTOMIC III Primepower cyclotomic polynomials over Q Irreducibility of cyclotomic polynomials over Q Factoring Fn(x) in Fp[x] with p
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QA162 .G375 2008  Unknown 
3. Abstract algebra [2007]
 Grillet, Pierre A. (Pierre Antoine), 1941
 2nd ed.  New York : Springer, c2007.
 Description
 Book — xii, 669 p. ; 25 cm.
 Summary

 Preface. Groups. Structure of Groups. Rings. Field Extensions. Galois Theory. Fields with Orders or Valuations. Commutative Rings. Modules. Semisimple Rings and Modules. Projectives and Injectives. Constructions. Ext and Tor. Algebras. Lattices. Universal Algebra.Categories. Appendix. References. Further Readings. Index.
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QA162 .G75 2007  Unknown 
 Hodge, Jonathan K., 1980 author.
 Boca Raton : CRC Press, Taylor & Francis Group, [2014]
 Description
 Book — xxii, 573 pages : illustrations ; 26 cm.
 Summary

 The Integers The Integers: An Introduction Introduction Integer Arithmetic Ordering Axioms What's Next Concluding Activities Exercises Divisibility of Integers Introduction Quotients and Remainders TheWellOrdering Principle Proving the Division Algorithm Putting It All Together Congruence Concluding Activities Exercises Greatest Common Divisors Introduction Calculating Greatest Common Divisors The Euclidean Algorithm GCDs and Linear Combinations WellOrdering, GCDs, and Linear Combinations Concluding Activities Exercises Prime Factorization Introduction Defining Prime The Fundamental Theorem of Arithmetic Proving Existence Proving Uniqueness Putting It All Together Primes and Irreducibles in Other Number Systems Concluding Activities Exercises Other Number Systems Equivalence Relations and Zn Congruence Classes Equivalence Relations Equivalence Classes The Number System Zn Binary Operations Zero Divisors and Units in Zn Concluding Activities Exercises Algebra Introduction Subsets of the Real Numbers The Complex Numbers Matrices Collections of Sets Putting It All Together Concluding Activities Exercises Rings An Introduction to Rings Introduction Basic Properties of Rings Commutative Rings and Rings with Identity Uniqueness of Identities and Inverses Zero Divisors and Multiplicative Cancellation Fields and Integral Domains Concluding Activities Exercises Connections Integer Multiples and Exponents Introduction Integer Multiplication and Exponentiation Nonpositive Multiples and Exponents Properties of Integer Multiplication and Exponentiation The Characteristic of a Ring Concluding Activities Exercises Connections Subrings, Extensions, and Direct Sums Introduction The Subring Test Subfields and Field Extensions Direct Sums Concluding Activities Exercises Connections Isomorphism and Invariants Introduction Isomorphisms of Rings Proving Isomorphism Disproving Isomorphism Invariants Concluding Activities Exercises Connections Polynomial Rings Polynomial Rings Polynomial Rings Polynomials over an Integral Domain Polynomial Functions Concluding Activities Exercises Connections Appendix  Proof that R[x] Is a Commutative Ring Divisibility in Polynomial Rings Introduction The Division Algorithm in F[x] Greatest Common Divisors of Polynomials Relatively Prime Polynomials The Euclidean Algorithm for Polynomials Concluding Activities Exercises Connections Roots, Factors, and Irreducible Polynomials Polynomial Functions and Remainders Roots of Polynomials and the Factor Theorem Irreducible Polynomials Unique Factorization in F[x] Concluding Activities Exercises Connections Irreducible Polynomials Introduction Factorization in C[x] Factorization in R[x] Factorization in Q[x] Polynomials with No Linear Factors in Q[x] Reducing Polynomials in Z[x] Modulo Primes Eisenstein's Criterion Factorization in F[x] for Other Fields F Summary The Cubic Formula Concluding Activities Exercises Appendix  Proof of the Fundamental Theorem of Algebra Quotients of Polynomial Rings Introduction CongruenceModulo a Polynomial Congruence Classes of Polynomials The Set F[x]/hf(x)i Special Quotients of Polynomial Rings Algebraic Numbers Concluding Activities Exercises Connections More Ring Theory Ideals and Homomorphisms Introduction Ideals CongruenceModulo an Ideal Maximal and Prime Ideals Homomorphisms The Kernel and Image of a Homomorphism The First Isomorphism Theorem for Rings Concluding Activities Exercises Connections Divisibility and Factorization in Integral Domains Introduction Divisibility and Euclidean Domains Primes and Irreducibles Unique Factorization Domains Proof
 1: Generalizing Greatest Common Divisors Proof
 2: Principal Ideal Domains Concluding Activities Exercises Connections From Z to C Introduction FromW to Z Ordered Rings From Z to Q Ordering on Q From Q to R From R to C A Characterization of the Integers Concluding Activities Exercises Connections VI Groups
 269 Symmetry Introduction Symmetries Symmetries of Regular Polygons Concluding Activities Exercises An Introduction to Groups Groups Examples of Groups Basic Properties of Groups Identities and Inverses in a Group The Order of a Group Groups of Units Concluding Activities Exercises Connections Integer Powers of Elements in a Group Introduction Powers of Elements in a Group Concluding Activities Exercises Connections Subgroups Introduction The Subgroup Test The Center of a Group The Subgroup Generated by an Element Concluding Activities Exercises Connections Subgroups of Cyclic Groups Introduction Subgroups of Cyclic Groups Properties of the Order of an Element Finite Cyclic Groups Infinite Cyclic Groups Concluding Activities Exercises The Dihedral Groups Introduction Relationships between Elements in Dn Generators and Group Presentations Concluding Activities Exercises Connections The Symmetric Groups Introduction The Symmetric Group of a Set Permutation Notation and Cycles The Cycle Decomposition of a Permutation Transpositions Even and Odd Permutations and the Alternating Group Concluding Activities Exercises Connections Cosets and Lagrange's Theorem Introduction A Relation in Groups Cosets Lagrange's Theorem Concluding Activities Exercises Connections Normal Subgroups and Quotient Groups Introduction An Operation on Cosets Normal Subgroups Quotient Groups Cauchy's Theorem for Finite Abelian Groups Simple Groups and the Simplicity of An Concluding Activities Exercises Connections Products of Groups External Direct Products of Groups Orders of Elements in Direct Products Internal Direct Products in Groups Concluding Activities Exercises Connections Group Isomorphisms and Invariants Introduction Isomorphisms of Groups Proving Isomorphism Some Basic Properties of Isomorphisms WellDefined Functions Disproving Isomorphism Invariants Isomorphism Classes Isomorphisms and Cyclic Groups Cayley's Theorem Concluding Activities Exercises Connections Homomorphisms and Isomorphism Theorems Homomorphisms The Kernel of a Homomorphism The Image of a Homomorphism The Isomorphism Theorems for Groups Concluding Activities Exercises Connections The Fundamental Theorem of Finite Abelian Groups Introduction The Components: pGroups The Fundamental Theorem Concluding Activities Exercises The First Sylow Theorem Introduction Conjugacy and the Class Equation Cauchy's Theorem The First Sylow Theorem The Second and Third Sylow Theorems Concluding Activities Exercises Connections The Second and Third Sylow Theorems Introduction Conjugate Subgroups and Normalizers The Second Sylow Theorem The Third Sylow Theorem Concluding Activities Exercises Special Topics RSA Encryption Introduction Congruence and Modular Arithmetic The Basics of RSA Encryption An Example Why RSA Works Concluding Thoughts and Notes Exercises Check Digits Introduction Check Digits Credit Card Check Digits ISBN Check Digits Verhoeff's Dihedral Group D5 Check Concluding Activities Exercises Connections Games: NIM and the
 15 Puzzle The Game of NIM The
 15 Puzzle Concluding Activities Exercises Connections Finite Fields, the Group of Units in Zn, and Splitting Fields Introduction Finite Fields The Group of Units of a Finite Field The Group of Units of Zn Splitting Fields Concluding Activities Exercises Connections Groups of Order
 8 and
 12: Semidirect Products of Groups Introduction Groups of Order
 8 Semidirect Products of Groups Groups of Order
 12 and p3 Concluding Activities Exercises Connections Appendices Functions Special Types of Functions: Injections and Surjections Composition of Functions Inverse Functions Theorems about Inverse Functions Concluding Activities Exercises Mathematical Induction and the WellOrdering Principle Introduction The Principle of Mathematical Induction The Extended Principle of Mathematical Induction The Strong Form of Mathematical Induction TheWellOrdering Principle The Equivalence of the WellOrdering Principle and the Principles of Mathematical Induction. Concluding Activities Exercises.
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QA162 .H63 2014  Unknown 
 Introduction to abstract algebra
 Robinson, Derek John Scott, author.
 2nd edition.  Berlin : De Gruyter, [2015]
 Description
 Book — x, 337 pages : illustrations ; 24 cm
 Summary

This is the second edition of the introduction to abstract algebra. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. There is ample material here for a two semester course in abstract algebra.
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This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe, and should ease the transition to (post)graduate studies.
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QA162 .R63 2015  Unknown 
 Lovett, Stephen (Stephen T.), author.
 Boca Raton, FL : CRC Press, Taylor & Francis Group, [2016]
 Description
 Book — xii, 708 pages : illustrations ; 29 cm
 Summary

 SET THEORY Sets and Functions The Cartesian Product Operations Relations Equivalence Relations Partial Orders
 NUMBER THEORY Basic Properties of Integers Modular Arithmetic Mathematical Induction
 GROUPS Symmetries of the Regular ngon Introduction to Groups Properties of Group Elements Symmetric Groups Subgroups Lattice of Subgroups Group Homomorphisms Group Presentations Groups in Geometry DiffieHellman Public Key Semigroups and Monoids
 QUOTIENT GROUPS Cosets and Lagrange's Theorem Conjugacy and Normal Subgroups Quotient Groups Isomorphism Theorems Fundamental Theorem of Finitely Generated Abelian Groups
 RINGS Introduction to Rings Rings Generated by Elements Matrix Rings Ring Homomorphisms Ideals Quotient Rings Maximal and Prime Ideals
 DIVISIBILITY IN COMMUTATIVE RINGS Divisibility in Commutative Rings Rings of Fractions Euclidean Domains Unique Factorization Domains Factorization of Polynomials RSA Cryptography Algebraic Integers
 FIELD EXTENSIONS Introduction to Field Extensions Algebraic Extensions Solving Cubic and Quartic Equations Constructible Numbers Cyclotomic Extensions Splitting Fields and Algebraic Closures Finite Fields
 GROUP ACTIONS Introduction to Group Actions Orbits and Stabilizers Transitive Group Actions Groups Acting on Themselves Sylow's Theorem A Brief Introduction to Representations of Groups
 CLASSIFICATION OF GROUPS Composition Series and Solvable Groups Finite Simple Groups Semidirect Product. Classification Theorems Nilpotent Groups
 MODULES AND ALGEBRAS Boolean Algebras Vector Spaces Introduction to Modules Homomorphisms and Quotient Modules Free Modules and Module Decomposition Finitely Generated Modules over PIDs, I Finitely Generated Modules over PIDs, II Applications to Linear Transformations Jordan Canonical Form Applications of the Jordan Canonical Form A Brief Introduction to Path Algebras
 GALOIS THEORY Automorphisms of Field Extensions Fundamental Theorem of Galois Theory First Applications of Galois Theory Galois Groups of Cyclotomic Extensions Symmetries among Roots The Discriminant Computing Galois Groups of Polynomials Fields of Finite Characteristic Solvability by Radicals
 MULTIVARIABLE POLYNOMIAL RINGS Introduction to Noetherian Rings Multivariable Polynomial Rings and Affine Space The Nullstellensatz Polynomial Division Monomial Orders Grobner Bases Buchberger's Algorithm Applications of Grobner Bases A Brief Introduction to Algebraic Geometry
 CATEGORIES Introduction to Categories Functors
 APPENDICES LIST OF NOTATIONS BIBLIOGRAPHY INDEX
 Projects appear at the end of each chapter.
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QA162 .L68 2016  Unknown 
7. Advanced calculus [2006]
 Fitzpatrick, Patrick, 1946
 2nd ed.  Providence, R.I. : American Mathematical Society, [2009?]
 Description
 Book — xviii, 590 p. : ill. ; 24 cm.
 Summary

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is selfcontained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, ""Advanced Calculus"" is a perfect book for undergraduate students of analysis.
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QA303.2 .F58 2009  Unknown 
8. Advanced calculus : theory and practice [2014]
 Petrovic, John Srdjan, author.
 Boca Raton, FL : CRC Press, Taylor & Francis Group, [2014]
 Description
 Book — xii, 560 pages : illustrations ; 26 cm.
 Summary

 Sequences and Their Limits Computing the Limits Definition of the Limit Properties of Limits Monotone Sequences The Number e Cauchy Sequences Limit Superior and Limit Inferior Computing the LimitsPart II
 Real Numbers The Axioms of the Set R Consequences of the Completeness Axiom BolzanoWeierstrass Theorem Some Thoughts about R
 Continuity Computing Limits of Functions A Review of Functions Continuous Functions: A Geometric Viewpoint Limits of Functions Other Limits Properties of Continuous Functions The Continuity of Elementary Functions Uniform Continuity Two Properties of Continuous Functions
 The Derivative Computing the Derivatives The Derivative Rules of Differentiation Monotonicity. Local Extrema Taylor's Formula L'Hopital's Rule
 The Indefinite Integral Computing Indefinite Integrals The Antiderivative
 The Definite Integral Computing Definite Integrals The Definite Integral Integrable Functions Riemann Sums Properties of Definite Integrals The Fundamental Theorem of Calculus Infinite and Improper Integrals
 Infinite Series A Review of Infinite Series Definition of a Series Series with Positive Terms The Root and Ratio Tests Series with Arbitrary Terms
 Sequences and Series of Functions Convergence of a Sequence of Functions Uniformly Convergent Sequences of Functions Function Series Power Series Power Series Expansions of Elementary Functions
 Fourier Series Introduction Pointwise Convergence of Fourier Series The Uniform Convergence of Fourier Series Cesaro Summability Mean Square Convergence of Fourier Series The Influence of Fourier Series
 Functions of Several Variables Subsets of Rn Functions and Their Limits Continuous Functions Boundedness of Continuous Functions Open Sets in Rn The Intermediate Value Theorem Compact Sets
 Derivatives Computing Derivatives Derivatives and Differentiability Properties of the Derivative Functions from Rn to Rm Taylor's Formula Extreme Values
 Implicit Functions and Optimization Implicit Functions Derivative as a Linear Map Open Mapping Theorem Implicit Function Theorem Constrained Optimization The Second Derivative Test
 Integrals Depending on a Parameter Uniform Convergence The Integral as a Function Uniform Convergence of Improper Integrals Integral as a Function Some Important Integrals
 Integration in Rn Double Integrals over Rectangles Double Integrals over Jordan Sets Double Integrals as Iterated Integrals Transformations of Jordan Sets in R2 Change of Variables in Double Integrals Improper Integrals Multiple Integrals
 Fundamental Theorems Curves in Rn Line Integrals Green's Theorem Surface Integrals The Divergence Theorem Stokes' Theorem Differential Forms on Rn Exact Differential Forms on Rn
 Solutions and Answers to Selected Problems
 Bibliography
 Subject Index Author Index.
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QA303.2 .P47 2014  Unknown 
 Hayek, Sabih I., 1938
 2nd ed.  Boca Raton, FL : CRC Press, c2011.
 Description
 Book — xxi, 844 p. : ill. ; 27 cm.
 Summary

 Ordinary Differential Equations DEFINITIONS LINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER LINEAR INDEPENDENCE AND THE WRONSKIAN LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION OF ORDER N WITH CONSTANT COEFFICIENTS EULER'S EQUATION PARTICULAR SOLUTIONS BY METHOD OF UNDETERMINED COEFFICIENTS PARTICULAR SOLUTIONS BY THE METHOD OF VARIATIONS OF PARAMETERS ABEL'S FORMULA FOR THE WRONSKIAN INITIAL VALUE PROBLEMS Series Solutions of Ordinary Differential Equations INTRODUCTION POWER SERIES SOLUTIONS CLASSIFICATION OF SINGULARITIES FROBENIUS SOLUTION Special Functions BESSEL FUNCTIONS BESSEL FUNCTION OF ORDER ZERO BESSEL FUNCTION OF AN INTEGER ORDER N RECURRENCE RELATIONS FOR BESSEL FUNCTIONS BESSEL FUNCTIONS OF HALF ORDERS SPHERICAL BESSEL FUNCTIONS HANKEL FUNCTIONS MODIFIED BESSEL FUNCTIONS GENERALIZED EQUATIONS LEADING TO SOLUTIONS IN TERMS OF BESSEL FUNCTIONS BESSEL COEFFICIENTS INTEGRAL REPRESENTATION OF BESSEL FUNCTIONS ASYMPTOTIC APPROXIMATIONS OF BESSEL FUNCTIONS FOR SMALL ARGUMENTS ASYMPTOTIC APPROXIMATIONS OF BESSEL FUNCTIONS FOR LARGE ARGUMENTS INTEGRALS OF BESSEL FUNCTIONS ZEROES OF BESSEL FUNCTIONS LEGENDRE FUNCTIONS LEGENDRE COEFFICIENTS RECURRENCE FORMULAE FOR LEGENDRE POLYNOMIALS INTEGRAL REPRESENTATION FOR LEGENDRE POLYNOMIALS INTEGRALS OF LEGENDRE POLYNOMIALS EXPANSIONS OF FUNCTIONS IN TERMS OF LEGENDRE POLYNOMIALS LEGENDRE FUNCTION OF THE SECOND KIND QN(X) ASSOCIATED LEGENDRE FUNCTIONS GENERATING FUNCTION FOR ASSOCIATED LEGENDRE FUNCTIONS RECURRENCE FORMULAE FOR Pnm INTEGRALS OF ASSOCIATED LEGENDRE FUNCTIONS ASSOCIATED LEGENDRE FUNCTION OF THE SECOND KIND Qnm Boundary Value Problems and Eigenvalue Problems INTRODUCTION VIBRATION, WAVE PROPAGATION OR WHIRLING OF STRETCHED STRINGS LONGITUDINAL VIBRATION AND WAVE PROPAGATION IN ELASTIC BARS VIBRATION, WAVE PROPAGATION AND WHIRLING OF BEAMS WAVES IN ACOUSTIC HORNS STABILITY OF COMPRESSED COLUMNS IDEAL TRANSMISSION LINES (TELEGRAPH EQUATION) TORSIONAL VIBRATION OF CIRCULAR BARS ORTHOGONALITY AND ORTHOGONAL SETS OF FUNCTIONS GENERALIZED FOURIER SERIES ADJOINT SYSTEMS BOUNDARY VALUE PROBLEMS EIGENVALUE PROBLEMS PROPERTIES OF EIGENFUNCTIONS OF SELFADJOINT SYSTEMS STURMLIOUVILLE SYSTEM STURMLIOUVILLE SYSTEM FOR FOURTHORDER EQUATIONS SOLUTION OF NONHOMOGENEOUS EIGENVALUE PROBLEMS FOURIER SINE SERIES FOURIER COSINE SERIES COMPLETE FOURIER SERIES FOURIERBESSEL SERIES FOURIERLEGENDRE SERIES Functions of a Complex Variable COMPLEX NUMBERS ANALYTIC FUNCTIONS ELEMENTARY FUNCTIONS INTEGRATION IN THE COMPLEX PLANE CAUCHY'S INTEGRAL THEOREM CAUCHY'S INTEGRAL FORMULA INFINITE SERIES TAYLOR'S EXPANSION THEOREM LAURENT'S SERIES CLASSIFICATION OF SINGULARITIES RESIDUES AND RESIDUE THEOREM INTEGRALS OF PERIODIC FUNCTIONS IMPROPER REAL INTEGRALS IMPROPER REAL INTEGRAL INVOLVING CIRCULAR FUNCTIONS IMPROPER REAL INTEGRALS OF FUNCTIONS HAVING SINGULARITIES ON THE REAL AXIS THEOREMS ON LIMITING CONTOURS INTEGRALS OF EVEN FUNCTIONS INVOLVING LOG X INTEGRALS OF FUNCTIONS INVOLVING Xa INTEGRALS OF ODD OR ASYMMETRIC FUNCTIONS INTEGRALS OF ODD OR ASYMMETRIC FUNCTIONS INVOLVING LOG X INVERSE LAPLACE TRANSFORMS Partial Differential Equations of Mathematical Physics INTRODUCTION THE DIFFUSION EQUATION THE VIBRATION EQUATION THE WAVE EQUATION HELMHOLTZ EQUATION POISSON AND LAPLACE EQUATIONS CLASSIFICATION OF PARTIAL DIFFERENTIAL EQUATIONS UNIQUENESS OF SOLUTIONS THE LAPLACE EQUATION THE POISSON EQUATION THE HELMHOLTZ EQUATION THE DIFFUSION EQUATION THE VIBRATION EQUATION THE WAVE EQUATION Integral Transforms FOURIER INTEGRAL THEOREM FOURIER COSINE TRANSFORM FOURIER SINE TRANSFORM COMPLEX FOURIER TRANSFORM MULTIPLE FOURIER TRANSFORM HANKEL TRANSFORM OF ORDER ZERO HANKEL TRANSFORM OF ORDER nu GENERAL REMARKS ABOUT TRANSFORMS DERIVED FROM THE FOURIER INTEGRAL THEOREM GENERALIZED FOURIER TRANSFORM TWOSIDED LAPLACE TRANSFORM ONESIDED GENERALIZED FOURIER TRANSFORM LAPLACE TRANSFORM MELLIN TRANSFORM OPERATIONAL CALCULUS WITH LAPLACE TRANSFORMS SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS BY LAPLACE TRANSFORMS OPERATIONAL CALCULUS WITH FOURIER COSINE TRANSFORM OPERATIONAL CALCULUS WITH FOURIER SINE TRANSFORM OPERATIONAL CALCULUS WITH COMPLEX FOURIER TRANSFORM OPERATIONAL CALCULUS WITH MULTIPLE FOURIER TRANSFORM OPERATIONAL CALCULUS WITH HANKEL TRANSFORM Green's Functions INTRODUCTION GREEN'S FUNCTION FOR ORDINARY DIFFERENTIAL BOUNDARY VALUE PROBLEM GREEN'S FUNCTION FOR AN ADJOINT SYSTEM SYMMETRY OF THE GREEN'S FUNCTIONS AND RECIPROCITY GREEN'S FUNCTION FOR EQUATIONS WITH CONSTANT COEFFICIENTS GREEN'S FUNCTIONS FOR HIGHER ORDERED SOURCES GREEN'S FUNCTION FOR EIGENVALUE PROBLEMS GREEN'S FUNCTION FOR SEMIINFINITE ONE DIMENSIONAL MEDIA GREEN'S FUNCTION FOR INFINITE ONEDIMENSIONAL MEDIA GREEN'S FUNCTION FOR PARTIAL DIFFERENTIAL EQUATIONS GREEN'S IDENTITIES FOR THE LAPLACIAN OPERATOR GREEN'S IDENTITY FOR THE HELMHOLTZ OPERATOR GREEN'S IDENTITY FOR BILAPLACIAN OPERATOR GREEN'S IDENTITY FOR THE DIFFUSION OPERATOR GREEN'S IDENTITY FOR THE WAVE OPERATOR GREEN'S FUNCTION FOR UNBOUNDED MEDIAFUNDAMENTAL SOLUTION FUNDAMENTAL SOLUTION FOR THE LAPLACIAN FUNDAMENTAL SOLUTION FOR THE BILAPLACIAN FUNDAMENTAL SOLUTION FOR THE HELMHOLTZ OPERATOR FUNDAMENTAL SOLUTION FOR THE OPERATOR, 
 2 + mu2 CAUSAL FUNDAMENTAL SOLUTION FOR THE DIFFUSION OPERATOR CAUSAL FUNDAMENTAL SOLUTION FOR THE WAVE OPERATOR FUNDAMENTAL SOLUTIONS FOR THE BILAPLACIAN HELMHOLTZ OPERATOR GREEN'S FUNCTION FOR THE LAPLACIAN OPERATOR FOR BOUNDED MEDIA CONSTRUCTION OF THE AUXILIARY FUNCTIONMETHOD OF IMAGES GREEN'S FUNCTION FOR THE LAPLACIAN FOR HALFSPACE GREEN'S FUNCTION FOR THE LAPLACIAN BY EIGENFUNCTION EXPANSION FOR BOUNDED MEDIA GREEN'S FUNCTION FOR A CIRCULAR AREA FOR THE LAPLACIAN GREEN'S FUNCTION FOR SPHERICAL GEOMETRY FOR THE LAPLACIAN GREEN'S FUNCTION FOR THE HELMHOLTZ OPERATOR FOR BOUNDED MEDIA GREEN'S FUNCTION FOR THE HELMHOLTZ OPERATOR FOR HALFSPACE GREEN'S FUNCTION FOR A HELMHOLTZ OPERATOR IN QUARTERSPACE CAUSAL GREEN'S FUNCTION FOR THE WAVE OPERATOR IN BOUNDED MEDIA CAUSAL GREEN'S FUNCTION FOR THE DIFFUSION OPERATOR FOR BOUNDED MEDIA METHOD OF SUMMATION OF SERIES SOLUTIONS IN TWO DIMENSIONAL MEDIA Asymptotic Methods INTRODUCTION METHOD OF INTEGRATION BY PARTS LAPLACE'S INTEGRAL STEEPEST DESCENT METHOD DEBYE'S FIRST ORDER APPROXIMATION ASYMPTOTIC SERIES APPROXIMATION METHOD OF STATIONARY PHASE STEEPEST DESCENT METHOD IN TWO DIMENSIONS MODIFIED SADDLE POINT METHOD: SUBTRACTION OF A SIMPLE POLE MODIFIED SADDLE POINT METHOD: SUBTRACTION OF POLE OF ORDER N SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS FOR LARGE ARGUMENTS CLASSIFICATION OF POINTS AT INFINITY SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH REGULAR SINGULAR POINTS ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULAR POINTS OF RANK ONE THE PHASE INTEGRAL AND WKBJ METHOD FOR AN IRREGULAR SINGULAR POINT OF RANK ONE ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULAR POINTS OF RANK HIGHER THAN ONE ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH LARGE PARAMETERS Numerical Methods INTRODUCTION ROOTS OF NONLINEAR EQUATIONS ROOTS OF A SYSTEM OF NONLINEAR EQUATION FINITE DIFFERENCES NUMERICAL DIFFERENTIATION NUMERICAL INTEGRATION ORDINARY DIFFERENTIAL EQUATIONS: INITIAL VALUE PROBLEMS ORDINARY DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS ORDINARY DIFFERENTIAL EQUATIONS: EIGENVALUE PROBLEMS PARTIAL DIFFERENTIAL EQUATIONS Appendix A: Infinite Series Appendix B: Special Functions Appendix C: Orthogonal Coordinate Systems Appendix D: Dirac Delta Functions Appendix E: Plots of Special Functions Appendix F: Vector Analysis Appendix G: Matrix Algebra References Answers Index Problems appear at the end of each chapter.
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QA37.3 .H39 2011  Unknown 
 Ramachandran, P. A., author.
 Cambridge : Cambridge University Press, 2014.
 Description
 Book — xxx, 774 pages : illustrations ; 26 cm
 Summary

 1. Introduction
 2. Examples of transport and system models
 3. Flow kinematics
 4. Forces and their representation
 5. Equations of motion and NavierStokes equation
 6. Illustration flow problems
 7. Energy balance equation
 8. Illustrative heat transport problems
 9. Equations of mass transfer
 10. Illustrative mass transfer problems
 11. Analysis and solution of transient transport processes
 12. Convective heat and mass transfer
 13. Coupled transport problems
 14. Scaling and perturbation analysis
 15. More flow analysis
 16. Bifurcation and stability analysis
 17. Turbulent flow analysis
 18. More convective heat transfer
 19. Radiation heat transfer
 20. More convective mass transfer
 21. Mass transfer: multicomponent systems
 22. Mass transport in charged systems.
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TP156 .T7 R36 2014  Unknown 
 Leal, L. Gary.
 Cambridge ; New York : Cambridge University Press, 2007.
 Description
 Book — xix, 912 p. : ill. ; 27 cm.
 Summary

 1. A preview
 2. Basic principles
 3. Unidirectional and onedimensional flow and heat transfer processes
 4. An introduction to asymptotic approximations
 5. The thin gap approximation  lubrication problems
 6. The thin gap approximation  films with a free surface
 7. Creeping flow  general properties and solutions for 2D and axisymmetric problems
 8. Creeping flow  3D problems
 9. Convection effects and heat transfer for viscous flows
 10. Boundary layer theory for laminar flows
 11. Heat and mass transfer at large Reynolds number
 12. Hydrodynamic stability Appendix A. Governing equations and vector operations in cartesian, cylindrical and spherical coordinate systems Appendix B. Cartesian component notation.
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QC145.2 .L43 2007  Unknown 
 Railsback, Steven F.
 Princeton : Princeton University Press, c2012.
 Description
 Book — xviii, 329 p. : ill ; 26 cm.
 Summary

 Preface xi Acknowledgments xvii
 Part I: AgentBased Modeling and NetLogo Basics
 1
 Chapter 1: Models, AgentBased Models, and the Modeling Cycle
 3 1.1 Introduction, Motivation, and Objectives
 3 1.2 What Is a Model?
 4 1.3 The Modeling Cycle
 7 1.4 What Is AgentBased Modeling? How Is It Different?
 9 1.5 Summary and Conclusions
 11 1.6 Exercises
 12
 Chapter 2: Getting Started with NetLogo
 15 2.1 Introduction and Objectives
 15 2.2 A Quick Tour of NetLogo
 16 2.3 A Demonstration Program: Mushroom Hunt
 18 2.4 Summary and Conclusions
 29 2.5 Exercises
 32
 Chapter 3: Describing and Formulating ABMs: The ODD Protocol
 35 3.1 Introduction and Objectives
 35 3.2 What Is ODD and Why Use It?
 36 3.3 T he ODD Protocol
 37 3.4 Our First Example: Virtual Corridors of Butterflies
 42 3.5 Summary and Conclusions
 44 3.6 Exercises
 45
 Chapter 4: Implementing a First AgentBased Model
 47 4.1 Introduction and Objectives
 47 4.2 ODD and NetLogo
 47 4.3 Butterfly Hilltopping: From ODD to NetLogo
 48 4.4 Comments and the Full Program
 55 4.5 Summary and Conclusions
 58 4.6 Exercises
 59
 Chapter 5: From Animations to Science
 61 5.1 Introduction and Objectives
 61 5.2 Observation of Corridors
 62 5.3 Analyzing the Model
 67 5.4 TimeSeries Results: Adding Plots and File Output
 67 5.5 A Real Landscape
 69 5.6 Summary and Conclusions
 72 5.7 Exercises
 72
 Chapter 6: Testing Your Program
 75 6.1 Introduction and Objectives
 75 6.2 Common Kinds of Errors
 76 6.3 Techniques for Debugging and Testing NetLogo Programs
 79 6.4 Documentation of Tests
 89 6.5 An Example and Exercise: The Marriage Model
 90 6.6 Summary and Conclusions
 92 6.7 Exercises
 94
 Part II: Model Design Concepts
 95
 Chapter 7: Introduction to Part II
 97 7.1 Objectives of Part II?
 97 7.2 Overview
 98
 Chapter 8: Emergence
 101 8.1 Introduction and Objectives
 101 8.2 A Model with LessEmergent Dynamics
 102 8.3 Simulation Experiments and BehaviorSpace
 103 8.4 A Model with Complex Emergent Dynamics
 108 8.5 Summary and Conclusions
 113 8.6 Exercises
 114
 Chapter 9: Observation
 115 9.1 Introduction and Objectives
 115 9.2 Observing the Model via NetLogo's View
 116 9.3 Other Interface Displays
 119 9.4 File Output
 120 9.5 Behavior Space as an Output Writer
 123 9.6 Export Primitives and Menu Commands
 124 9.7 Summary and Conclusions
 124 9.8 Exercises
 125
 Chapter 10: Sensing
 127 10.1 Introduction and Objectives
 127 10.2 Who Knows What: The Scope of Variables
 128 10.3 Using Variables of Other Objects
 131 10.4 Putting Sensing to Work: The Business Investor Model
 132 10.5 Summary and Conclusions
 140 10.6 Exercises
 141
 Chapter 11: Adaptive Behavior and Objectives
 143 11.1 Introduction and Objectives
 143 11.2 Identifying and Optimizing Alternatives in NetLogo
 144 11.3 Adaptive Behavior in the Business Investor Model
 148 11.4 Nonoptimizing Adaptive Traits: A Satisficing Example
 149 11.5 The Objective Function
 152 11.6 Summary and Conclusions
 153 11.7 Exercises
 154
 Chapter 12: Prediction
 157 12.1 Introduction and Objectives
 157 12.2 Example Effects of Prediction: The Business Investor Model's Time Horizon
 158 12.3 Implementing and Analyzing Submodels
 159 12.4 Analyzing the Investor Utility Function
 163 12.5 Modeling Prediction Explicitly
 165 12.6 Summary and Conclusions
 166 12.7 Exercises
 167
 Chapter 13: Interaction
 169 13.1 Introduction and Objectives
 169 13.2 Programming Interaction in NetLogo
 170 13.3 The Telemarketer Model
 171 13.4 The March of Progress: Global Interaction
 175 13.5 Direct Interaction: Mergers in the Telemarketer Model
 176 13.6 The Customers Fight Back: Remembering Who Called
 179 13.7 Summary and Conclusions
 181 13.8 Exercises
 181
 Chapter 14: Scheduling
 183 14.1 Introduction and Objectives
 183 14.2 Modeling Time in NetLogo
 184 14.3 Summary and Conclusions
 192 14.4 Exercises
 193
 Chapter 15: Stochasticity
 195 15.1 Introduction and Objectives
 195 15.2 Stochasticity in ABMs
 196 15.3 Pseudorandom Number Generation in NetLogo
 198 15.4 An Example Stochastic Process: Empirical Model of Behavior
 203 15.5 Summary and Conclusions
 205 15.6 Exercises
 206
 Chapter 16: Collectives
 209 16.1 Introduction and Objectives
 209 16.2 What Are Collectives?
 209 16.3 Modeling Collectives in NetLogo
 210 16.4 Example: A Wild Dog Model with Packs
 212 16.5 Summary and Conclusions
 221 16.6 Exercises
 222
 Part III: PatternOriented Modeling
 225
 Chapter 17: Introduction to Part III
 227 17.1 Toward Structurally Realistic Models
 227 17.2 Single and Multiple, Strong and Weak Patterns
 228 17.3 Overview of Part III?230
 Chapter 18: Patterns for Model Structure
 233 18.1 Introduction
 233 18.2 Steps in POM to Design Model Structure
 234 18.3 Example: Modeling European Beech Forests
 235 18.4 Example: Management Accounting and Collusion
 239 18.5 Summary and Conclusions
 240 18.6 Exercises
 241
 Chapter 19: Theory Development
 243 19.1 Introduction
 243 19.2 Theory Development and Strong Inference in the Virtual Laboratory
 244 19.3 Examples of Theory Development for ABMs
 246 19.4 Exercise Example: Stay or Leave?
 249 19.5 Summary and Conclusions
 253 19.6 Exercises
 254
 Chapter 20: Parameterization and Calibration
 255 20.1 Introduction and Objectives
 255 20.2 Parameterization of ABMs Is Different
 256 20.3 Parameterizing Submodels
 257 20.4 Calibration Concepts and Strategies
 258 20.5 Example: Calibration of the Woodhoopoe Model
 264 20.6 Summary and Conclusions
 267 20.7 Exercises
 268
 Part IV: Model Analysis
 271
 Chapter 21: Introduction to Part IV
 273 21.1 Objectives of Part IV?273 21.2 Overview of Part IV?274
 Chapter 22: Analyzing and Understanding ABMs
 277 22.1 Introduction
 277 22.2 Example Analysis: The Segregation Model
 278 22.3 Additional Heuristics for Understanding ABMs
 283 22.4 Statistics for Understanding
 287 22.5 Summary and Conclusions
 288 22.6 Exercises
 288
 Chapter 23: Sensitivity, Uncertainty, and Robustness Analysis
 291 23.1 Introduction and Objectives
 291 23.2 Sensitivity Analysis
 293 23.3 Uncertainty Analysis
 297 23.4 Robustness Analysis
 302 23.5 Summary and Conclusions
 306 23.6 Exercises
 307
 Chapter 24: Where to Go from Here
 309 24.1 Introduction
 309 24.2 Keeping Your Momentum: Reimplementation
 310 24.3 Your First Model from Scratch
 310 24.4 Modeling Agent Behavior
 311 24.5 ABM Gadgets
 312 24.6 Coping with NetLogo's Limitations
 313 24.7 Beyond NetLogo
 315 24.8 An Odd Farewell
 316
 References
 317 Index
 323 Index of Programming Notes 329.
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QA76.76 .I58 R35 2012  Unknown 
13. Algebra [2010]
 Sepanski, Mark R. (Mark Roger)
 Providence, R.I. : American Mathematical Society, c2010.
 Description
 Book — xiv, 256 p. : ill. ; 27 cm.
 Summary

Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarises the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems and come equipped with hints when needed. Appropriate for both selfstudy and the classroom, the material is efficiently arranged so that milestones such as the Sylow theorems and Galois theory can be reached in one semester.
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QA152.3 .S46 2010  Unknown 
14. Algebra [2006  ]
 Lorenz, Falko.
 New York : Springer, 2006
 Description
 Book — 2 v. : ill. ; 24 cm.
 Summary

 v. 1. Fields and Galois theory /
 with the collaboration of the translator, Silvio Levy  v. 2. Fields with structure, algebras and advanced topics.
(source: Nielsen Book Data)
From Math Reviews: "This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. Thus, for instance, the transformation of the classical geometrical problems on constructions with ruler and compass in their algebraic setting in the first chapter introduces the reader spontaneously to such fundamental algebraic notions as field extension, the degree of an extension, etc. The book ends with an appendix containing exercises and notes on the previous parts of the book. However, brief historical comments and suggestions for further reading are also scattered through the text.".
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QA154.3 .L67 2006 V.1  Unknown 
QA154.3 .L67 2006 V.2  Unknown 
15. Algebra : a combined approach [2016]
 MartinGay, K. Elayn, 1955 author.
 Fifth edition.  Boston : Pearson, [2016]
 Description
 Book — 1 volume (various pagings) : illustrations (chiefly color) ; 28 cm
 Summary

 R. Prealgebra Review R.1 Factors and the Least Common Multiple R.2 Fractions R.3 Decimals and Percents Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test
 1. Real Numbers and Introduction to Algebra 1.1 Study Skills Tips for Sucess in Mathematics 1.2 Symbols and Sets of Numbers 1.3 Expnents, Order of Operations, and Variable Expressions 1.4 Adding Real Numbers 1.5 Subtracting Real Numbers 1.6 Multiplying and Dividing Real Numbers 1.7 Properties of Real Numbers 1.8 Simplifying Expressions Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test
 2. Equations, Inequalities, and Problem Solving 2.1 The Addition Property of Equality 2.2 The Multiplication Property of Equality 2.3 Further Solving Linear Equations 2.4 An Introduction to Problem Solving 2.5 Formulas and Problem Solving 2.6 Percent and Mixture Problem Solving 2.7 Linear Inequalities and Problem Solving Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 3. Graphing Equations and Inequalities 3.1 Reading Graphs and the Rectangular Coordinate System 3.2 Graphing Linear Equations 3.3 Intercepts 3.4 Slope and Rate of Change 3.5 Equations of Lines 3.6 Graphing Linear Inequalities in Two Variables Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 4. Systems of Equations 4.1 Solving Systems of Linear Equations by Graphing 4.2 Solving Systems of Linear Equations by Substitution 4.3 Solving Systems of Linear Equations by Addtion 4.4 Systems of Linear Equations and Problem Solving Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 5. Exponents and Polynomials 5.1 Exponents 5.2 Negative Exponents and Scientific Notation 5.3 Introduction to Polynomials 5.5 Multiplying Polynomials 5.6 Special Products 5.7 Dividing Polynomials Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 6. Factoring Polynomials 6.1 The Greatest Common Factor and Factoring by Grouping 6.2 Factoring Trinomials of the Form x2 + bx + c 6.3 Factoring Trinomials of the Form ax2 + bx + c 6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping 6.5 Factoring by Special Products 6.6 Solving Quadratic Equations and Problem Solving Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 7. Rational Expressions 7.1 Simplifying Rational Expressions 7.2 Multiplying and Dividing Rational Expressions 7.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator 7.4 Adding and Subtracting Rational Expressions with Different Denominators 7.5 Solving Equations Containing Rational Expressions 7.6 Proportions and Problem Solving with Rational Equations 7.7 Simplifying Complex Fractions Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 8. Graphs and Functions 8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines 8.2 Introduction to Functions 8.3 Polynomial and Rational Functions 8.4 Interval Notation, Finding Domains and Ranges from Graphs, and Graphing PiecewiseDefined Functions 8.5 Shifting and Reflecting Graphs of Functions Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 9. Systems of Equations and Inequalities and Variation 9.1 Solving Systems of Linear Equations in Three Variables and Problem Solving 9.2 Solving Systems of Equations Using Matrices 9.3 Systems of Linear Inequalities 9.4 Variation and Problem Solving Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 10. Rational Exponents, Radicals, and Complex Numbers 10.1 Radical Expressions and Radical Functions 10.2 Rational Exponents 10.3 Simplifying Radical Expressions 10.4 Adding, Subtracting, and Multiplying Radical Expressions 10.5 Rationalizing Numerators and Denominators of Radical Expressions 10.6 Radical Equations and Problem Solving 10.7 Complex Numbers Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 11. Quadratic Equations and Functions 11.1 Solving Quadratic Equations by Completing the Square 11.2 Solving Quadratic Equations by Using the Quadratic Formula 11.3 Solving Equations by Using Quadratic Methods 11.4 Nonlinear Inequalities in One Variable 11.5 Quadratic Functions and Their Graphs 11.6 Further Graphing of Quadratic Functions Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 12. Exponential and Logarithmic Functions 12.1 The Algebra of Functions 12.2 Inverse Functions 12.3 Exponential Functions 12.4 Exponential Functions 12.5 Logarithmic Functions 12.6 Properties of Logarithms 12.7 Common Logarithms, Natural Logarithms, and Change of Base 12.8 Exponential and Logarithmic Equations and Problem Solving Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review
 13. Conic Sections 13.1 The Parabola and the Circle 13.2 The Ellipse and the Hyperbola 13.3 Solving Nonlinear Systems of Equations 13.4 Nonlinear Inequalities and Systems of Inequalities Group Activity Vocabulary Check Chapter Highlights Chapter Review Chapter Test Cumulative Review Appendices Appendix A: Transition Review: Exponents, Polynomials, and Factoring Strategies Appendix B: Transition Review: Solving Linear and Quadratic Equations Appendix C: Sets and Compound Inequalities Appendix D: Absolute Value Equations and Inequalities Appendix E: Determinants and Cramer's Rule Appendix F: Review of Angles, Lines, and Special Triangles Appendix G: Stretching and Compressing Graphs of Absolute Value Functions Appendix H: An Introduction to Using a Graphing Utility.
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QA152.3 .M35 2016  Unknown 
 Larson, Ron, 1941 author.
 Seventh Edition.  Boston, MA, USA : Cengage Learning, [2016]
 Description
 Book — 1 volume (various pagings) : illustrations (chiefly color) ; 29 cm
 Summary

 CHAPTER P PREREQUISITES. P.1. Real Numbers. P.2. Exponents and Radicals. P.3. Polynomials and Factoring. P.4. Rational Expressions. P.5. The Cartesian Plane. P.6. Representing Data Graphically. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 1. FUNCTIONS AND THEIR GRAPHS. Introduction to Library of Functions.1.1 Graphs of Equations. 1.2 Lines in the Plane. 1.3 Functions. 1.4 Graphs of Functions.1.5 Shifting, Reflecting, and Stretching Graphs. 1.6 Combinations of Functions. 1.7 Inverse Functions. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 2. SOLVING EQUATIONS AND INEQUALITIES. 2.1 Linear Equations and Problem Solving. 2.2 Solving Equations Graphically. 2.3 Complex Numbers. 2.4 Solving Quadratic Equations Algebraically. 2.5 Solving Other Types of Equations Algebraically. 2.6 Solving Inequalities Algebraically and Graphically. 2.7 Linear Models and Scatter Plots. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters P2. Proofs in Mathematics. Progressive Summary (Ch P2).
 3. POLYNOMIAL AND RATIONAL FUNCTIONS. 3.1 Quadratic Functions. 3.2 Polynomial Functions of Higher Degree. 3.3 Real Zeros of Polynomial Functions. 3.4 The Fundamental Theorem of Algebra. 3.5 Rational Functions and Asymptotes. 3.6 Graphs of Rational Functions. 3.7 Quadratic Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. 4.1 Exponential Functions and Their Graphs . 4.2 Logarithmic Functions and Their Graphs. 4.3 Properties of Logarithms. 4.4 Solving Exponential and Logarithmic Equations. 4.5 Exponential and Logarithmic Models. 4.6 Nonlinear Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 34. Proofs in Mathematics. Progressive Summary (Ch P4).
 5. TRIGONOMETRIC FUNCTIONS. 5.1 Angles and Their Measure. 5.2 Right Triangle Trigonometry. 5.3 Trigonometric Functions of Any Angle. 5.4 Graphs of Sine and Cosine Functions. 5.5 Graphs of Other Trigonometric Functions. 5.6 Inverse Trigonometric Functions. 5.7 Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Library of Parent Functions Review. Proofs in Mathematics.
 6. ANALYTIC TRIGONOMETRY. 6.1 Using Fundamental Identities. 6.2 Verifying Trigonometric Identities. 6.3 Solving Trigonometric Equations. 6.4 Sum and Difference Formulas. 6.5 MultipleAngle and ProducttoSum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 7. ADDITIONAL TOPICS IN TRIGONOMETRY. 7.1 Law of Sines. 7.2 Law of Cosines. 7.3 Vectors in the Plane. 7.4 Vectors and Dot Products. 7.5 Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 57. Proofs in Mathematics. Progressive Summary (Ch P7).
 8. LINEAR SYSTEMS AND MATRICES. 8.1 Solving Systems of Equations. 8.2 Systems of Linear Equations in Two Variables. 8.3 Multivariable Linear Systems. 8.4 Matrices and Systems of Equations. 8.5 Operations with Matrices. 8.6 The Inverse of a Square Matrix. 8.7 The Determinant of a Square Matrix. 8.8 Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 9. SEQUENCES, SERIES, AND PROBABILITY. 9.1 Sequences and Series. 9.2 Arithmetic Sequences and Partial Sums. 9.3 Geometric Sequences and Series. 9.4 The Binomial Theorem. 9.5 Counting Principles. 9.6 Probability. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
 10. TOPICS IN ANALYTIC GEOMETRY. 10.1 Circles and Parabolas. 10.2 Ellipses. 10.3 Hyperbolas. 10.4 Parametric Equations. 10.5 Polar Coordinates. 10.6 Graphs of Polar Equations. 10.7 Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 810. Proofs in Mathematics. Progressive Summary (Ch P10). Appendix A: Technology Support Guide. Appendix B: Concepts in Statistics (WEB only). B.1 Measures of Central Tendency and Dispersion. B.2 Least Squares Regression. Appendix C: Variation (WEB only). Appendix D: Solving Linear Equations and Inequalities (WEB only). Appendix E: Systems of Inequalities (WEB only). E.1 Solving Systems of Inequalities. E.2 Linear Programming. Appendix F Mathematical Induction (WEB only).
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QA154.3 .L3455 2016  Unavailable In transit Request 
17. Algebra : chapter 0 [2009]
 Aluffi, Paolo, 1960
 Providence, R.I. : American Mathematical Society, c2009.
 Description
 Book — xix, 713 p. : ill. ; 26 cm.
 Summary

"Algebra: Chapter 0" is a selfcontained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a followup introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of crossreferences.
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QA154.3 .A527 2009  Unknown 
18. Algebra : Einführung in die Galoistheorie [1998]
 Stroth, Gernot, 1949
 Berlin ; New York : Walter de Gruyter, 1998.
 Description
 Book — xi, 287 p. : ill. ; 23 cm.
 Online
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QA247 .S83 1998  Unknown 
19. Algebra for college students [2016]
 Lial, Margaret L. author.
 8th edition  Boston : Pearson, [2016]
 Description
 Book — 1 volume (various pagings) : illustrations (chiefly color) ; 29 cm
 Summary

 Preface Study Skills: Using Your Math Textbook
 R. Review of the Real Number System R.1 Basic Concepts R.2 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Chapter R Summary Chapter R Test Study Skills: Reading Your Math Textbook
 1. Linear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable Study Skills: Completing Your Homework 1.2 Formulas and Percent Study Skills: Taking Lecture Notes 1.3 Applications of Linear Equations 1.4 Further Applications of Linear Equations Summary Exercises: Applying ProblemSolving Techniques 1.5 Linear Inequalities in One Variable Study Skills: Using Study Cards 1.6 Set Operations and Compound Inequalities Study Skills: Using Study Cards Revisited 1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities Study Skills: Reviewing a Chapter
 Chapter 1 Summary
 Chapter 1 Review Exercises
 Chapter 1 Mixed Review Exercises
 Chapter 1 Test
 2. Linear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables Study Skills: Managing Your Time 2.2 The Slope of a Line 2.3 Writing Equations of Lines Study Skills: Taking Math Tests Summary Exercises: Finding Slopes and Equations of Lines 2.4 Linear Inequalities in Two Variables 2.5 Introduction to Relations and Functions Study Skills: Analyzing Your Test Results 2.6 Function Notation and Linear Functions
 Chapter 2 Summary
 Chapter 2 Review Exercises
 Chapter 2 Mixed Review Exercises
 Chapter 2 Test
 3. Systems of Linear Equations 3.1 Systems of Linear Equations in Two Variables Study Skills: Preparing for Your Math Final Exam 3.2 Systems of Linear Equations in Three Variables 3.3 Applications of Systems of Linear Equations
 Chapter 3 Summary
 Chapter 3 Review Exercises
 Chapter 3 Mixed Review Exercises
 Chapter 3 Test Chapters R3 Cumulative Review Exercises
 4. Exponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents and Scientific Notation 4.2 Adding and Subtracting Polynomials 4.3 Polynomial Functions, Graphs, and Composition 4.4 Multiplying Polynomials 4.5 Dividing Polynomials
 Chapter 4 Summary
 Chapter 4 Review Exercises
 Chapter 4 Mixed Review Exercises
 Chapter 4 Test Chapters R4 Cumulative Review Exercises
 5. Factoring 5.1 Greatest Common Factors and Factoring by Grouping 5.2 Factoring Trinomials 5.3 Special Factoring 5.4 A General Approach to Factoring 5.5 Solving Equations by the ZeroFactor Property
 Chapter 5 Summary
 Chapter 5 Review Exercises
 Chapter 5 Mixed Review Exercises
 Chapter 5 Test Chapters R5 Cumulative Review Exercises
 6. Rational Expressions and Functions 6.1 Rational Expressions and Functions Multiplying and Dividing 6.2 Adding and Subtracting Rational Expressions 6.3 Complex Fractions 6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.5 Applications of Rational Expressions 6.6 Variation
 Chapter 6 Summary
 Chapter 6 Review Exercises
 Chapter 6 Mixed Review Exercises
 Chapter 6 Test Chapters R6 Cumulative Review Exercises
 7. Roots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs 7.2 Rational Exponents 7.3 Simplifying Radicals, the Distance Formula, and Circles 7.4 Adding and Subtracting Radical Expressions 7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 7.6 Solving Equations with Radicals 7.7 Complex Numbers
 Chapter 7 Summary
 Chapter 7 Review Exercises
 Chapter 7 Mixed Review Exercises
 Chapter 7 Test Chapters R7 Cumulative Review Exercises
 8. Quadratic Equations and Inequalities 8.1 The Square Root Property and Completing the Square 8.2 The Quadratic Formula 8.3 Equations Quadratic in Form Summary Exercises: Applying Methods for Solving Quadratic Equations 8.4 Formulas and Further Applications 8.5 Polynomial and Rational Inequalities
 Chapter 8 Summary
 Chapter 8 Review Exercises
 Chapter 8 Mixed Review Exercises
 Chapter 8 Test Chapters R8 Cumulative Review Exercises
 9. Additional Graphs of Functions and Relations 9.1 Review of Operations and Composition 9.2 Graphs of Quadratic Functions 9.3 More About Parabolas and Their Applications 9.4 Symmetry Increasing and Decreasing Functions 9.5 Piecewise Linear Functions
 Chapter 9 Summary
 Chapter 9 Review Exercises
 Chapter 9 Mixed Review Exercises
 Chapter 9 Test Chapters R9 Cumulative Review Exercises
 10. Inverse, Exponential, and Logarithmic Functions 10.1 Inverse Functions 10.2 Exponential Functions 10.3 Logarithmic Functions 10.4 Properties of Logarithms 10.5 Common and Natural Logarithms 10.6 Exponential and Logarithmic Equations Further Applications
 Chapter 10 Summary
 Chapter 10 Review Exercises
 Chapter 10 Mixed Review Exercises
 Chapter 10 Test Chapters R10 Cumulative Review Exercises
 11. Polynomial and Rational Functions 11.1 Zeros of Polynomial Functions (I) 11.2 Zeros of Polynomial Functions (II) 11.3 Graphs and Applications of Polynomial Functions Summary Exercises: Examining Polynomial Functions and Graphs 11.4 Graphs and Applications of Rational Functions
 Chapter 11 Summary
 Chapter 11 Review Exercises
 Chapter 11 Mixed Review Exercises
 Chapter 11 Test Chapters R11 Cumulative Review Exercises
 12. Conic Sections and Nonlinear Systems 12.1 Circles Revisited and Ellipses 12.2 Hyperbolas and Functions Defined by Radicals 12.3 Nonlinear Systems of Equations 12.4 SecondDegree Inequalities, Systems of Inequalities, and Linear Programming
 Chapter 12 Summary
 Chapter 12 Review Exercises
 Chapter 12 Mixed Review Exercises
 Chapter 12 Test Chapters R12 Cumulative Review Exercises
 13. Further Topics in Algebra 13.1 Sequences and Series 13.2 Arithmetic Sequences 13.3 Geometric Sequences 13.4 The Binomial Theorem 13.5 Mathematical Induction 13.6 Counting Theory 13.7 Basics of Probability
 Chapter 13 Summary
 Chapter 13 Review Exercises
 Chapter 13 Mixed Review Exercises
 Chapter 13 Test Chapters R13 Cumulative Review Exercises
 Appendix A: Solving Systems of Linear Equations by Matrix Methods Appendix B: Determinants and Cramer's Rule Appendix C: Properties of Matrices Appendix D: Matrix Inverses
 Photo Credits Answers to Selected Exercises Index.
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QA154.3 .L53 2016  Unknown 
 Shahriari, Shahriar, author.
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — xvii, 675 pages : illustrations ; 27 cm.
 Summary

 (Mostly finite) group theory: Four basic examples Groups: The basics The alternating groups Group actions A subgroup acts on the group: Cosets and Lagrange's theorem A group acts on itself: Counting and the conjugation of action Acting on subsets, cosets, and subgroups: The Sylow theorems Counting the number of orbits The lattice of subgroups Acting on its subgroups: Normal subgroups and quotient groups Group homomorphisms Using Sylow theorems to analyze finite groups Direct and semidirect products Solvable and nilpotent groups (Mostly commutative) ring theory: Rings Homomorphisms, ideals, and quotient rings Field of fractions and localization Factorization, EDs, PIDs, and UFDs Polynomial rings Gaussian integers and (a little) number theory Field and Galois theory: Introducing field theory and Galois theory Field extensions Straightedge and compass constructions Splitting fields and Galois groups Galois, normal, and separable extensions Fundamental theorem of Galois theory Finite fields and cyclotomic extensions Radical extensions, solvable groups, and the quintic Hints for selected problems Short answers for selected problems Complete solutions for selected (oddnumbered) problems Bibliography Index.
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QA162 .S465 2017  Unknown 