Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra” by Ray M. Bowen and C.-C. Wang can be downloaded in pdf format. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. …

## Basic Topology of 3-Manifolds

Free book **“Basic 3-Manifold Topology”** by Allen Hatcher can be downloaded in pdf and postscript formats. The three chapters here are to a certain extent independent of each other. …

## Spectral Sequences in Algebraic Topology

This is intended to be a readable introduction to spectral sequences, with emphasis on their applications to algebraic topology. …

## Numerical Recipes in Fortran 90

You can download the each chapter of this free book “Numerical Recipes in Fortran 90: The Art of Scientific Computing” in pdf format. …

## Vector Bundles & K-Theory

The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. …

## Templates for the Solution of Algebraic Eigenvalue Problems

This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. …

## The Complexity of Boolean Functions

This free book presents a large number of recent research results previously unavailable in book form. Initially deals with the wee-known computation models, and goes on to special types of circuits, parallel computers, and branching programs. Includes basic theory as well recent research findings. Each chapter includes exercises. …

## Mathematical Tools for Physics

This book is for the undergraduate level, providing a one-semester bridge between some of the introductory math courses and the physics courses in which we expect to use the mathematics. This is the course typically called Mathematical Methods in Physics. …

## Worked examples in the Geometry of Crystals

The free book deals with the mathematical crystallography of materials. It is intended for use by students and by anyone interested in phase transformations or interfaces. …

## Directions in Infinite Graph Theory and Combinatorics

This free online book consists of invited surveys of various fields of infinite graph theory and combinatorics, as well as a few research articles. It aims to give some indication of the variety of problems and methods found in this area, but also to help identify what may be seen as its typical features, placing it somewhere between finite graph theory on the one hand and logic and set theory on the other. …