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  1. Title

    Abstract algebra: theory and applications

    Description
    This book contains integers, groups, cyclic groups, permutation groups, cosets and Lagrange's Theorem, introduction to cryptography, algebraic coding theory, isomorphisms, normal subgroups and factor groups, homomorphisms, matrix groups and symmetry, structure of groups, group actions, the Sylow Theorems, rings, polynomials, integral domains, lattices and Boolean algebras, vector spaces, fields, finite fields and Galois theory
    Author
    Thomas W. Judson
    http://abstract.ups.edu/
  2. Title

    Analysis of functions of a single variable

    Description
    This book contains real and complex numbers, the limit of a sequence of numbers, functions and continuity, differentiation and local behaviour, integration and average behaviour, integration over smooth curves in the plane, the fundamental theorem of algebra and the fundamental theorem of analysis.
    Author
    Lawrence W. Baggett
    http://spot.colorado.edu/~baggett/analysis.html
  3. Title

    Elementary linear algebra

    Description
    This book includes linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations and three-dimensional geometry. Solutions to the exercises are available in a separate document.
    Author
    K. R. Matthews
    http://www.numbertheory.org/book/
  4. Title

    Elementary linear algebra: solutions to problems

    Description
    This document includes solutions to the exercises found in the book Elementary Linear Algebra by Keith Matthews (which includes linear equations, matrices, subspaces, determinants, complex numbers, eigenvalues and eigenvectors, identifying second degree equations and three-dimensional geometry).
    Author
    K. R. Matthews
    http://www.numbertheory.org/book/
  5. Title

    Elements of abstract and linear algebra

    Description
    This book contains chapters on the background and fundamentals of mathematics, groups, rings, matrices and matrix rings and linear algebra.
    Author
    E. H. Connell
    http://www.math.miami.edu/~ec/book/
  6. Title

    Inquiry-based introduction to proofs

    Description
    This book includes number theory, sets, functions and relations, infinity and Peano axioms. Answers to the exercises are available in a separate document.
    Author
    Jim Hefferon
    http://joshua.smcvt.edu/proofs/
  7. Title

    Inquiry-based introduction to proofs: answers to exercises

    Description
    This document includes answers to the exercises that can by found in the book Inquiry-Based Introduction to Proofs by Jim Hefferon (which includes number theory, sets, functions and relations, infinity and Peano axioms).
    Author
    Jim Hefferon
    http://joshua.smcvt.edu/proofs/
  8. Title

    Introduction to vectors and tensors: linear and multilinear algebra, Volume 1

    Description
    This book (in two volumes) contains chapters on elementary matrix theory; sets, relations and functions; groups, rings and fields; vector spaces; linear transformations; determinants and matrices; spectral decompositions; tensor algebra and exterior alge...
    Author
    Ray M. Bowen; C.-C. Wang
    http://rbowen.tamu.edu/
  9. Title

    Introduction to vectors and tensors: vectors and tensor analysis, Volume 2

    Description
    This book (in two volumes) contains chapters on Euclidean manifolds, vector fields and differential forms, hypersurfaces in a Euclidean manifold, elements of classical continuous groups and integration of fields on Euclidean manifolds, hypersurfaces and continuous groups.
    Author
    Ray M. Bowen; C.-C. Wang
    http://rbowen.tamu.edu/
  10. Title

    Lie algebras

    Description
    This book on Lie algebras covers: the Campbell Baker Hausdorff Formula; sl(2) and its representations; the classical simple algebras; Engel-Lie-Cartan-Weyl; the conjugacy of Cartan sub-algebras; simple finite dimensional algebras; cyclic highest weight modules; Serre's theorem; Clifford algebras and spin representations; the Kostant Dirac operator; and the centre of U(g). The book was written by Shlomo Sternberg from the Department of Mathematics, Harvard University, USA.
    Author
    Shlomo Sternberg
    Publisher
    Department of Mathematics, Harvard University
    http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf
  11. Title

    Linear algebra

    Description
    This book includes linear systems, vector spaces, maps between spaces, determinants and similarity. Answers to the exercise are available in a separate document.
    Author
    Jim Hefferon
    http://joshua.smcvt.edu/linalg.html/
  12. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 11: Applications to differential equations and Chapter 12: The simple paradigm from E to E

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover applications to differential equations and the simple paradigm from E to E.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  13. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 13: Adjoint operators and Chapter 14: Compact sets

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover adjoint operators and compact sets.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  14. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 15: Compact operators and Chapter 16: The space of bounded linear operators

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover compact operators and the space of bounded linear operators.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  15. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 17: The Eigenvalue problem and Chapter 18: Normal operators and the more general paradigm

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover the Eigenvalue problem and normal operators and the more general paradigm.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  16. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 19: Compact operators & orthonormal families and Chapter 20: A characterisation of compact operators

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover compact operators & orthonormal families and a characterisation of compact operators.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  17. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 1: Decomposition for matrices and Chapter 2: Exp(tA)

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. This chapter is about decomposition for matrices and Exp(tA).
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  18. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 21: The Fredholm alternative theorems and Chapter 22: Closed operators

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover the Fredholm alternative theorems and closed operators.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  19. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 23: The deficiency of A

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. This chapter covers the deficiency of A.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  20. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 24: A problem in control

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. This chapter covers problems in control.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  21. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 25: Approximation in a Hilbert Space with a reproducing kernel

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. This chapter covers approximation in a Hilbert Space with a reproducing kernel.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  22. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 3: Self adjoint transformations in inner-product spaces and Chapter 4: The Gerschgorin Circle Theorem

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These two chapters cover self adjoint transformations in inner-product spaces and the Gerschgorin Circle Theorem.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  23. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 5: Convergence and Chapter 6: Orthogonality and closest point projection

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover convergence and orthogonality and closest point projection.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  24. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 7: Orthogonal, nonexpansive & self-adjoint projections and Chapter 8: Orthonormal vectors

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover orthogonal, nonexpansive & self-adjoint projections and orthonormal vectors.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html
  25. Title

    Linear algebra, infinite dimensions, and Maple, Chapter 9: The finite dimensional paradigm and chapter 10: Bounded linear maps from E to C

    Description
    This book on linear algebra and infinite dimensional spaces includes chapters about decomposition for matrices, transformations in inner-product spaces, the Gerschgorin Circle Theorem, convergence, orthogonality, projections, orthonormal vectors, the finite dimensional paradigm, bounded linear maps, differential equations, adjoint operators, compact sets, compact operators, the Eigenvalue problem, normal operators, the Fredholm alternative theorems, closed operators and approximation in a Hilbert space. These chapters cover the finite dimensional paradigm and bounded linear maps from E to C.
    Author
    James Herod
    http://people.math.gatech.edu/~herod/Hspace/Hspace.html

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