Basics of Algebra, Topology, and Differential Calculus

Basics of Algebra, Topology, and Differential Calculus

Basics of Algebra, Topology, and Di erential Calculus, by Jean Gallier, is a book in progress which is available as a free pdf download.


In the first chapter, the basic algebraic structures (groups, rings, elds, vector spaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear algebra such as vector spaces, subspaces, linear combinations, linear independence, bases, quotient spaces, linear maps, matrices, change of bases, direct sums, linear forms, dual spaces, hyperplanes, transpose of a linear maps, are reviewed.

Table of Contents

  • Linear Algebra
  • Determinants
  • Gaussian Elimination, LU, Cholesky, Echelon Form
  • Vector Norms and Matrix Norms
  • Iterative Methods for Solving Linear Systems
  • Euclidean Spaces
  • QR-Decomposition for Arbitrary Matrices
  • Hermitian Spaces
  • Eigenvectors and Eigenvalues
  • Spectral Theorems
  • Bilinear Forms and Their Geometries
  • Introduction to The Finite Elements Method
  • Singular Value Decomposition and Polar Form
  • Applications of SVD and Pseudo-inverses
  • Quadratic Optimization Problems
  • Basics of Affine Geometry
  • Polynomials, Ideals and PID’s
  • UFD’s, Noetherian Rings, Hilbert’s Basis Theorem
  • Annihilating Polynomials; Primary Decomposition
  • Tensor Algebras
  • Introduction to Modules; Modules over a PID
  • Normal Forms; The Rational Canonical Form
  • Topology
  • A Detour On Fractals
  • Differential Calculus
  • Extrema of Real-Valued Functions
  • Newton’s Method and its Generalizations

Book Details

Author(s): Jean Gallier
Publisher: –
Format(s): PDF
File size: 3.44 MB
Number of pages: 845
Link: Basics of Algebra, Topology, and Differential Calculus [PDF]

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