Mathematics

Introduction

In 2001, I began retaking calculus to refresh my mathematics skills before taking courses in statistics; I also took a course in linear algrebra. These are the mathematics books I’ve accumulated. I provide a separate page for probability and statistics.

Publisher’s information Comments
Algebra & Trigonometry
6th Edition
by Michael Sullivan
2002
Prentice Hall
ISBN 0-13-091465-7

This is a beautifully produced, full-color text that covers the following topics:

  • equations and inequalities
  • graphs
  • functions and their graphs
  • polynomial and rationa functions
  • zeros of a polynomial function
  • exponential and logarithmic functions
  • trigonometric functions
  • analytic geometry
  • applications of trigonometric functions
  • polar coordinates; vectors
  • analytic geometry
  • systems of equations and inequalities
  • sequences; inductions; the binomial theorem
  • counting and probability
Calculus Concepts and Contexts
2nd Edition
by James Stewart
2001
Brooks/Cole
ISBN 1-534-37718-1

This is another beautifully produced, full-color text. At Boston University, this text was used for a three-semester series in calculus.

The text covers the following topics:

  • functions and models
  • limits and derivatives
  • differentiation rules
  • applications of differentiation
  • integrals
  • applications of integration
  • differential equations
  • infinite sequences and series
  • vectors and the geometry of space
  • vector functions
  • partial derivatives
  • multiple integrals
  • vector calculus
Differential Equations
2nd Edition
by Paul Blanchard, Robert L. Devaney, and Glen R. Hall
2002
Brooks/Cole
ISBN 0-534-38514-1

This text provides a modern treatment of differential equations. In addition to covering the few differential equations that can be solved analytically, this book covers in detail qualitative and numerical techniques for attacking differential equations. The text is the product of the National Science Foundation Boston University Differential Equations Project.

The text covers the following topics:

  • first-order differential equations
  • first-order systems
  • linear systems
  • forcing and resonance
  • nonlinear systems
  • LaPlace transforms
  • numerical methods
  • discrete dynamical systems

The text is printed in two colors, blue and black.

Elementary Real and Complex Analysis
by Georgi El Shilov
translated and edited by Richard A. Silverman
1973
Dover Publications, Inc.
ISBN 0-486-68922-0

This inexpensive text is aimed at undergraduates in math, science, and engineering.

The chapters are:

  1. Real numbers
  2. Sets
  3. Metric spaces
  4. Limits
  5. Continuous functions
  6. Series
  7. The derivative
  8. Higher derivatives
  9. The integral
  10. Analytic functions
  11. Improper integrals
Linear Algebra and Its Applications
3rd edition
by David C. Lay
2003
Addison Wesley
ISBN 0-201-70970-8

This is a 21st-century linear algebra book, full of theory and applications. The book begins with systems of linear equations and finishes with the singular value decomposition and principal component analysis.

The applications, which are conveniently listed with page numbers on the inside of the front cover, include:

  • biology and ecology
  • business and economics
  • computers and computer science
  • control theory
  • electrical engineering
  • engineering
  • mathematics
  • numerical linear algebra
  • physical sciences
  • statistics

The book’s chapters are:

  1. Linear equations in linear algebra
  2. Matrix algrebra
  3. Determinants
  4. Vector spaces
  5. Eigenvalues and eigenvectors
  6. Orthogonality and least squares
  7. symmetric matrices and quadratic forms

This is an excellent book.

Matrices and Linear Algebra
2nd edition
by Hans Schneider and George Phillip Barker
1973
Dover Publications, Inc.
ISBN 0-486-66014-1

This book covers the theory of linear algebra without applications. The chapters are:

  1. The algebra of matrices
  2. Linear equations
  3. Vector spaces
  4. Determinants
  5. Linear transformations
  6. Eigenvalues and eigenvectors
  7. Inner product spaces
  8. Applications to differential equations