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1. The induction book [2017]
 Weintraub, Steven H., author.
 Mineola : Dover Publications, [2017]
 Description
 Book — 1 online resource ( 129 p.) :.
 Summary

 Pages:1 to 25; Pages:26 to 50; Pages:51 to 75; Pages:76 to 100; Pages:101 to 125; Pages:126 to 129
 Online

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2. The induction book [2017]
 Weintraub, Steven H., author.
 Mineola, New York : Dover Publications, Inc., 2017.
 Description
 Book — 1 online resource (117 pages).
3. Differential forms : theory and practice [2014]
 Weintraub, Steven H., author.
 Second edition.  Oxford, UK : Elsevier, 2014.
 Description
 Book — 1 online resource
 Summary

 Half Title; Title Page; Copyright; Dedication; Contents; Preface;
 1 Differential Forms in Rn, I; 1.0 Euclidean spaces, tangent spaces, and tangent vector fields; 1.1 The algebra of differential forms; 1.2 Exterior differentiation; 1.3 The fundamental correspondence; 1.4 The Converse of Poincaré's Lemma, I; 1.5 Exercises;
 2 Differential Forms in Rn, II; 2.1 1Forms; 2.2 kForms; 2.3 Orientation and signed volume; 2.4 The converse of Poincaré's Lemma, II; 2.5 Exercises;
 3 Pushforwards and Pullbacks in Rn; 3.1 Tangent vectors; 3.2 Points, tangent vectors, and pushforwards.
 3.3 Differential forms and pullbacks3.4 Pullbacks, products, and exterior derivatives; 3.5 Smooth homotopies and the Converse of Poincaré's Lemma, III; 3.6 Exercises;
 4 Smooth Manifolds; 4.1 The notion of a smooth manifold; 4.2 Tangent vectors and differential forms; 4.3 Further constructions; 4.4 Orientations of manifolds'227intuitive discussion; 4.5 Orientations of manifolds'227careful development; 4.6 Partitions of unity; 4.7 Smooth homotopies and the Converse of Poincaré's Lemma in general; 4.8 Exercises;
 5 Vector Bundles and the Global Point of View.
 5.1 The definition of a vector bundle5.2 The dual bundle, and related bundles; 5.3 The tangent bundle of a smooth manifold, and related bundles; 5.4 Exercises;
 6 Integration of Differential Forms; 6.1 Definite integrals in textmathbbRn; 6.2 Definition of the integral in general; 6.3 The integral of a 0form over a point; 6.4 The integral of a 1form over a curve; 6.5 The integral of a 2form over a surface; 6.6 The integral of a 3form over a solid body; 6.7 Chains and integration on chains; 6.8 Exercises;
 7 The Generalized Stokes's Theorem; 7.1 Statement of the theorem.
 7.2 The fundamental theorem of calculus and its analog for line integrals7.3 Cap independence; 7.4 Green's and Stokes's theorems; 7.5 Gauss's theorem; 7.6 Proof of the GST; 7.7 The converse of the GST; 7.8 Exercises;
 8 de Rham Cohomology; 8.1 Linear and homological algebra constructions; 8.2 Definition and basic properties; 8.3 Computations of cohomology groups; 8.4 Cohomology with compact supports; 8.5 Exercises; Index; A; B; C; D; E; F; G; H; I; L; M; N; O; P; R; S; T; V; W.
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4. Fundamentals of algebraic topology [2014]
 Weintraub, Steven H., author.
 New York, NY : Springer, [2014]
 Description
 Book — 163 pages : illustrations ; 24 cm.
 Summary

 Preface.
 1. The Basics.
 2. The Fundamental Group.
 3. Generalized Homology Theory.
 4. Ordinary Homology Theory.
 5. Singular Homology Theory.
 6. Manifolds.
 7. Homotopy Theory.
 8. Homotopy Theory. A. Elementary Homological Algebra. B. Bilinear Forms. C. Categories and Functors. Bibliography. Index.
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QA612 .W45 2014  Unknown 
5. A Guide to Advanced Linear Algebra [2012]
 Weintraub, Steven H.
 Cambridge : Cambridge University Press, 2012.
 Description
 Book — 1 online resource.
 Summary

 Preface
 1. Vector spaces and linear transformations
 2. Coordinates
 3. Determinants
 4. The structure of a linear transformation I
 5. The structure of a linear transformation II
 6. Bilinear, sesquilinear, and quadratic forms
 7. Real and complex inner product spaces
 8. Matrix groups as Lie groups A. Polynomials: A.1 Basic properties A.2 Unique factorization A.3 Polynomials as expressions and polynomials as functions B. Modules over principal ideal domains: B.1 Definitions and structure theorems B.2 Derivation of canonical forms Bibliography Index.
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6. A guide to advanced linear algebra [2011]
 Weintraub, Steven H.
 Washington, DC : Mathematical Association of America, 2011.
 Description
 Book — xii, 251 p. : ill. ; 23 cm.
 Summary

 Preface
 1. Vector spaces and linear transformations
 2. Coordinates
 3. Determinants
 4. The structure of a linear transformation I
 5. The structure of a linear transformation II
 6. Bilinear, sesquilinear, and quadratic forms
 7. Real and complex inner product spaces
 8. Matrix groups as Lie groups A. Polynomials: A.1 Basic properties A.2 Unique factorization A.3 Polynomials as expressions and polynomials as functions B. Modules over principal ideal domains: B.1 Definitions and structure theorems B.2 Derivation of canonical forms Bibliography Index.
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QA184.2 .W45 2011  Unknown 
7. Galois theory [2009]
 Weintraub, Steven H.
 2nd ed.  New York : Springer, c2009.
 Description
 Book — xi, 211 p. ; 24 cm.
 Summary

 Introduction to Galois Theory. Field Theory and Galois Theory. Development and Applications of Galois Theory. Extensions of the Field of Rational Numbers. Further Topics in Field Theory. Transcendental Extensions. A. Some Results from Group Theory. B. A Lemma on Constructing Fields. C. A Lemma from Elementary Number Theory. References. Index.
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QA214 .W45 2009  Unknown 
 Weintraub, Steven H.
 San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2009.
 Description
 Book — 1 electronic text (x, 96 p.) : ill.
 Summary

 1. Fundamentals on vector spaces and linear transformations
 Bases and coordinates
 Linear transformations and matrices
 Some special matrices
 Polynomials in T and A
 Subspaces, complements, and invariant subspaces
 2. The structure of a linear transformation
 Eigenvalues, eigenvectors, and generalized eigenvectors
 The minimum polynomial
 Reduction to BDBUTCD form
 The diagonalizable case
 Reduction to Jordan Canonical Form
 Exercises
 3. An algorithm for Jordan Canonical Form and Jordan Basis
 The ESP of a linear transformation
 The algorithm for Jordan Canonical Form
 The algorithm for a Jordan Basis
 Examples
 Exercises
 A. Answers to oddnumbered exercises
 Notation
 Index.
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 Weintraub, Steven H.
 San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008.
 Description
 Book — 1 electronic text (viii, 85 p.) : ill.
 Summary

 Jordan canonical form
 The diagonalizable case
 The general case
 Solving systems of linear differential equations
 Homogeneous systems with constant coefficients
 Homogeneous systems with constant coefficients
 Inhomogeneous systems with constant coefficients
 The matrix exponential
 Background results
 A.1. Bases, coordinates, and matrices
 A.2. Properties of the complex exponential
 B. Answers to oddnumbered exercises.
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10. Galois theory [2006]
 Weintraub, Steven H.
 New York ; London : Springer, c 2006.
 Description
 Book — xi, 185 p. : 23 cm.
 Summary

 Introduction to Galois Theory. Field Theory and Galois Theory. Development and Applications of Galois Theory. Extensions of the Field of Rational Numbers. Further Topics in Field Theory. A. Some Results from Group Theory. B. A Lemma on Constructing Fields. C. A Lemma from Elementary Number Theory. References. Index.
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SAL3 (offcampus storage)
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QA214 .W45 2006  Available 
11. Galois theory [electronic resource] [2006]
 Weintraub, Steven H.
 New York ; London : Springer, c2006.
 Description
 Book — xi, 185 p.
 Weintraub, Steven H.
 Providence, R.I. : American Mathematical Society, c2003.
 Description
 Book — ix, 212 p. ; 27 cm.
 Summary

 Dedication page Introduction Semisimple rings and modules Semisimple group representations Induced representations and applications Introduction to modular representations General rings and modules Modular group representations Some useful results Bibliography Index.
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QA176 .W45 2003  Unknown 
 Weintraub, Steven H.
 San Diego : Academic Press, c1997.
 Description
 Book — xii, 256 p. : ill. ; 23 cm.
 Summary

 Differential Forms The Algrebra of Differential Forms Exterior Differentiation The Fundamental Correspondence Oriented Manifolds The Notion Of A Manifold (With Boundary) Orientation Differential Forms Revisited lForms KForms PushForwards And PullBacks Integration Of Differential Forms Over Oriented Manifolds The Integral Of A 0Form Over A Point (Evaluation) The Integral Of A 1Form Over A Curve (Line Integrals) The Integral Of A2Form Over A Surface (Flux Integrals) The Integral Of A 3Form Over A Solid Body (Volume Integrals) Integration Via PullBacks The Generalized Stokes' Theorem Statement Of The Theorem The Fundamental Theorem Of Calculus And Its Analog For Line Integrals Green's And Stokes' Theorems Gauss's Theorem Proof of the GST For The Advanced Reader Differential Forms In IRN And Poincare's Lemma Manifolds, Tangent Vectors, And Orientations The Basics of De Rham Cohomology Appendix Answers To Exercises Subject Index.
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QA381 .W45 1997  Unknown 
14. Algebra : an approach via module theory [1992]
 Adkins, William A.
 New York : SpringerVerlag, c1992.
 Description
 Book — x, 526 p. : ill. ; 25 cm.
 Summary

 1: Groups.
 2: Rings.
 3: Modules and Vector Spaces.
 4: Linear Algebra.
 5: Matrices over PIDs.
 6: Bilinear and Quadratic Forms.
 7: Topics in Module Theory.
 8: Group Representations.
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 Groups. Rings. Modules and Vector Spaces. Linear Algebra. Matrices over PIDs. Bilinear and Quadratic Forms. Topics in Module Theory. Group Representations. Appendix. Bibliography. Index of Notation. Index of Terminology.
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This book is designed as a text for a firstyear graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely generated modules over a principal ideal domain. They then treat canonical form theory in linear algebra as an application of this fundamental theorem. Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and modules and apply these results in the final chapter to study group representations by viewing a representation of a group G over a field F as an F(G)module. The book emphasizes proofs with a maximum of insight and a minimum of computation in order to promote understanding. However, extensive material on computation (for example, computation of canonical forms) is provided.
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SAL3 (offcampus storage)
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QA154 .A33 1992  Available 
15. Algebra : an Approach via Module Theory [1992]
 Adkins, William A.
 New York, NY : Springer New York, 1992.
 Description
 Book — 1 online resource (x, 526 pages).
 Summary

 1 Groups. 1.1 Definitions and Examples. 1.2 Subgroups and Cosets. 1.3 Normal Subgroups, Isomorphism Theorems, and Automorphism Groups. 1.4 Permutation Representations and the Sylow Theorems. 1.5 The Symmetric Group and Symmetry Groups. 1.6 Direct and Semidirect Products. 1.7 Groups of Low Order. 1.8 Exercises.
 2 Rings. 2.1 Definitions and Examples. 2.2 Ideals, Quotient Rings, and Isomorphism Theorems. 2.3 Quotient Fields and Localization. 2.4 Polynomial Rings. 2.5 Principal Ideal Domains and Euclidean Domains. 2.6 Unique Factorization Domains. 2.7 Exercises.
 3 Modules and Vector Spaces. 3.1 Definitions and Examples. 3.2 Submodules and Quotient Modules. 3.3 Direct Sums, Exact Sequences, and Horn. 3.4 Free Modules. 3.5 Projective Modules. 3.6 Free Modules over a PID. 3.7 Finitely Generated Modules over PIDs. 3.8 Complemented Submodules. 3.9 Exercises.
 4 Linear Algebra. 4.1 Matrix Algebra. 4.2 Determinants and Linear Equations. 4.3 Matrix Representation of Homomorphisms. 4.4 Canonical Form Theory. 4.5 Computational Examples. 4.6 Inner Product Spaces and Normal Linear Transformations. 4.7 Exercises.
 5 Matrices over PIDs. 5.1 Equivalence and Similarity. 5.2 Hermite Normal Form. 5.3 Smith Normal Form. 5.4 Computational Examples. 5.5 A Rank Criterion for Similarity. 5.6 Exercises.
 6 Bilinear and Quadratic Forms. 6.1 Duality. 6.2 Bilinear and Sesquilinear Forms. 6.3 Quadratic Forms. 6.4 Exercises.
 7 Topics in Module Theory. 7.1 Simple and Semisimple Rings and Modules. 7.2 Multilinear Algebra. 7.3 Exercises.
 8 Group Representations. 8.1 Examples and General Results. 8.2 Representations of Abelian Groups. 8.3 Decomposition of the Regular Representation. 8.4 Characters. 8.5 Induced Representations. 8.6 Permutation Representations. 8.7 Concluding Remarks. 8.8 Exercises. Index of Notation. Index of Terminology.
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 Lee, Ronnie, 1942
 Providence, R.I. : American Mathematical Society, 1998.
 Description
 Book — ix, 75 p. ; 26 cm.
 Summary

 The Siegel Modular Variety of Degree Two and Level Four: Introduction Algebraic background Geometric background Taking stock Type III A Type II A Type II B Type IV C Summing up Appendix. An exact sequence in homology References Cohomology of the Siegel Modular Group of Degree Two and Level Four: Introduction The building Cycles The main theorems References.
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SAL1&2 (oncampus shelving)
SAL1&2 (oncampus shelving)  Status 

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Shelved by Series title NO.631  Unknown 
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