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This free book gives a gentle introduction to the set theoretic tools needed by anyone who comes into contact with modern Mathematics.

You can download the each chapter of this free book “Numerical Recipes in FORTRAN 77: The Art of Scientific Computing” in pdf format. This book, like its predecessor edition, is supposed to teach you methods of numerical computing that are practical, efficient, and (insofar as possible) elegant.

This free book is written primarily for students who are at freshman level or do not take a full 3-credit hour course in Linear/Matrix Algebra, or are wanting a contemporary and applied approach to Matrix Algebra.

The aim is to provide an introduction to higher local fields (more generally complete discrete valuation fields with arbitrary residue field) and render the main ideas of this theory (Part I), as well as to discuss several applications and connections to other areas.

Group Theory by Predrag Cvitanovic can be downloaded in pdf and postscript formats free of charge. If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional.

You can download generatingfunctionology by Herbert S. Wilf in pdf format free of charge. The generatingfunctionology is one of the best mathematics books ever written. Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis.

This free book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers.

This free ebook carefully leads the student through the basic topics of undergraduate real analysis. This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis. Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

Free pdf book Calculus by Gilbert Strang is a useful resource for educators and self-learners alike.

Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis by Ray M. Bowen and C.-C. Wang can be downloaded in pdf format. This is the second volume of a two-volume work on vectors and tensors. Volume 1 is concerned with the algebra of vectors and tensors, while this volume is concerned with the geometrical aspects of vectors and tensors. This volume begins with a discussion of Euclidean manifolds.