This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

This text is a basic introduction to those areas of discrete mathematics used by stu dents of mathematics and computer science.

Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated.

The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.

Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research.

New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the ...

These essays don’t share any common program or ideology. The standard for admission was: Nothing boring! Nothing trite, nothing tr- ial! Every essay is challenging, thought-provoking, and original.

Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others.

The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB, Mathematica, and Maple A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical ...

Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and ...