Online Books and Lecture Notes in Mathematics

< Algebra | Analysis | Geometry & topology | Logic & set theory | Probability & statistics | Applications >

Algebra

Abstract Algebra

Paul Garrett has 200 pages of lecture notes on abstract algebra.
Fundamental Problems in Algorithmic Algebra by Chee Yap.
Abstract Algebra:The Basic Graduate Year
Workbook in Higher Algebra by David Surowski

Algebraic geometry

J.S. Milne has comprehensive course notes on Algebraic Geometry.
Igor V. Dolgachev's lecture notes
Algebraic Geometry Seminar
Notes from Hartshorne's Algebraic Geometry Course, taken by William A. Stein.
Séminaire de Géometrie Algébrique
Algebraic Geometry: A Total Hypertext Online System Discusses varieties, schemes, module theory and differential forms. In DVI and HTML formats.

Category theory

Combinatorics

Elementary Algebra and Trigonometry

Precalculus textbook
A short course in trigonometry
Ken Kubota's college algebra notes. College algebra done right.

Field theory and Galois theory

Milne's lecture notes on fields and Galois theory
Introduction to Galois Theory, by David Wilkins

Geometric Algebra

Graph theory

The GTM book Graph Theory by Reinhard Diestel can be downloaded in PDF format. Unfortunately, printing has been disabled.

Group theory

J.S. Milne's lecture notes on group theory
Group Theory - Classics Illustrated
Buildings, BN-pairs, Hecke algebras, classical groups
Miscellaneous facts about Coxeter groups (Howlett)
An Elementary Introduction to Groups and Representations
Mirrors and Reflections: The Geometry of Finite Reflection Groups
Introduction to Group Theory A simple introduction to group theory, culminating in an (as yet incomplete) solution to Rubik's cube.

K-theory

An introduction to algebraic K-theory by Charles Weibel
Vector Bundles and K-theory by Allan Hatcher

Lie groups and Lie algebras

Isometric Actions of Lie Groups and Invariants

Linear algebra

Number theory

Introduction to Number Theory
The Prime Page (An Index of Information on Prime Numbers)
Robin Chapman - A Guide to Arithmetic
Milne's course notes on algebraic number theory
J.S. Milne, Course notes on elliptic curves
Course notes from Mazur's lectures on Euler Systems
The Mathematics of Fermat's Last Theorem
Igor Dolgachev has some lecture notes on modular forms.
The Pi Pages
An Introduction to p-adic Numbers and p-adic Analysis (University of Manchester final year Honours course)
Elliptic Curve Handbook, a book in preparation by Ian Connell. The first five chapters are available in postscript, DVI, and LaTeX formats.

Universal algebra

Analysis

Analysis

Practical Analysis in One Variable, by D. Estep and C. Johnson
Mathematical Methods of Engineering Analysis
Elements of Linear and Real Analysis
Manifolds, Tensors, Analysis, and Applications by Jerrold Marsden.

Chaos theory

Complex analysis

Differential equations

Dynamics

Fourier analysis

Functional analysis

Numerical analysis

Numerical Recipes Home Page

Real analysis

Wavelets

Wavelet tutorial

Geometry and topology

Differential Geometry

Euclidean Geometry

Euclid's Elements, Introduction

Knot theory

The Knot Theory MA3F2 page

Topology

Algebraic Topology, Solomon Lefschetz
G6522_ Topology of Manifolds
Allen Hatcher's home page has online books on Algebraic Topology, Vector Bundles and K-theory, and 3-manifolds.
Introduction to Smooth Manifolds
Textbook in problems on elementary topology by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and N.Y.Netsvetaev.
Algebraic Topology -- A Computational Approach
Crystallographic Topology
Topology of mechanical linkages

Logic and set theory

Logic

Foundations of mathematics

Practical Foundations of Mathematics

Probability and Statistics

Probability

Introduction to Probability is a text for a first course in probability, written by Charles M. Grimstead and J. Laurie Snell. The book is 520 pages, and it is in PDF format. Among the topics covered are discrete and continuous probability distributions, permutations and combinations, conditional probability, the central limit theorem, generating functions, Markov chains and random walks.
Probability Theory The Logic Of Science by Ed Jaynes
Noel Vaillant's Probability Tutorials

Statistics

Applications to other sciences

Algorithms and computation

Cryptography

Digital Signal Processing

Information theory

Gregory J. Chaitin's Home Page

Linear programming

Mathematical programming and optimization

Mathematical Programming Glossary
Lectures in Mathematical Optimization by U.T. Zimmerman.

Physics