Recommended Books in the Mathematical Sciences

Views expressed here and the recommendations here, are those of J. M. Cargal and do not reflect the views of any organizations or journals to which he is associated.  (Other views are incorrect.)  This site does not take money from publishers, authors, or their agents.  It is funded entirely by J. M. Cargal

Write to jmcargal@sprintmail.com or James M. Cargal, PO Box 242548, Montgomery AL 36124.

This is the most recent photograph of James M. Caral (used with permission).
 
Edition 1.53, September 1, 2013. One book each on Information Theory, Matroids (in section on linear algebra) and General Physics.
 
Edition 1.52 April 1, 2012. Three books added on real analysis. One on advanced calculus. Two on combinatorics. One on group theory. Edition 1.5 October 14, 2011: An essay:
 
Elements of Boolean Algebra (22 pages) Note that there is also a chapter on Boolean Algebra in the Lectures on algorithms, number theory, probability and other stuff link below.
Edition 1.49  January 26, 2009:   One book on General Advanced Mathematics.  One book on General Applied Mathematics.  Three books added to Combinatorics ‒ two on  Fibonacci numbers (the other is very strong on Fibonacci numbers as well). One book on evolution.

 
Edition 1.4 (Jan 19, 2006):  Due to the efforts of Bob Hofacker I have added ISBN numbers to most books here.  However, these are here only as an aid.  It is easy to switch them around or have the wrong edition.  Also added here are two books on Abstract Algebra and one on Logic.

Edition 1.31 (June 7, 2003):  Cargal's lecture on The EOQ Formula for manufacturing (added to section on Inventory).    

Aitions in 1.3 (Jan 22, 2003) :  Two books in Number Theory.  Also a new section: Lectures on algorithms, number theory, probability and other stuff.

Site Created December 1998.
Copyright © 1998-2012
You can copy, but with proper attribution.


Top

Principles_of_Learning_a_Mathematical_Discipline

Principles of Learning Calculus

Calculus Pedagogy

Principles of Teaching and Learning Mathematics

Study it Twice

Ask Questions

Two Books for Undergraduates in the Mathematical Sciences

Pre-Calculus Algebra

Trigonometry

Calculus

Linear Algebra

Multivariable Calculus

Differential Equations (ODE's and PDE's) 

Difference Equations

Dynamical Systems and Chaos

Real Analysis

Infinitesimal Calculus (modern theory of infinitesimals)

Complex Analysis

Vector Calculus, Tensors, Differential Forms

General Applied Math

General Mathematics

General Advanced Mathematics

General Computer Science

Combinatorics (including Graph Theory)

Numerical Analysis

Fourier Analysis

Number Theory

Abstract Algebra

Geometry

Topology

Set Theory

Logic and Abstract Automata

Foundations

Algorithms

Coding and Information Theory

Probability

Fuzzy Stuff (logic and set theory)

Statistics

Operations Research (and linear, non-linear, integer programming, and simulation)

Game Theory

Stochastic Processes (and Queueing)

Inventory Theory and Scheduling

Investment Theory

General Physics

Mechanics

Fluid Mechanics

Thermodynamics and Statistical Mechanics

Electricity and Electromagnetism

Quantum Mechanics

Relativity

Waves

Evolution

Philosophy

Science Studies

Lectures on algorithms, number theory, probability and other stuff

Related Sites for Mathematical Resources 


Principles of Learning a Mathematical Discipline

If you have not had the prerequisites in the last two years, retake a prerequisite. The belief that it will come back quickly has scuttled thousands of careers.


Principles of Learning Calculus

Calculus Pedagogy

Principles of Teaching and Learning Mathematics

Study it Twice!

 

Ask Questions!

Serious students ask questions.  Half or more of all questions are stupid.  Good students are willing to ask stupid questions.  Generally, willingness to ask stupid questions is a sign of intelligence.

 

Two Books for Undergraduates in the Mathematical Sciences

Pre-Calculus Algebra

Trigonometry

Calculus 

         First, see Principle of Learning Calculus

          Regular Calculus Texts

Linear Algebra

 

Matroids

Multivariable Calculus

Back to Top

Differential Equations

  The Laplace Transform

  Partial Differential Equations

Difference Equations

Dynamical Systems and Chaos

Real Analysis

Infinitesimal Calculus (modern theory of infinitesimals)

Complex Analysis

The following book is a primer on complex numbers that ends with a short introduction to Complex Analysis.  It is a perfect book for the sophomore in math or engineering.  Great book:

Vector Calculus, Tensors, Differential Forms

General Applied Math

 

General Mathematics

General Advanced Mathematics