Designed to be suitable for a one-term course on modelling for advanced undergraduates, this text explains the process of modelling real situations to obtain mathematical problems that can be analyzed. Presentation is in the form of case studies, which are

Describes billiards and their relation with differential geometry, classical mechanics, and geometrical optics. This book covers such topics as variational principles of billiard motion, and symplectic geometry of rays of light and integral geometry. It is

Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. The book begins with an

This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to such areas as manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, and intersection indexes.

Diophantine analysis, an area of number theory that helps to discover hidden treasures and truths within the numbers by exploring rational numbers, comprises two different but interconnected domains - diophantine approximation and diophantine equations. This book presents the fundamental ideas and theorems from diophantine approximation.

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry...

Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric t

Ramanujan is recognized as one of the great number theorists of the twentieth century. This book provides an introduction to his work in number theory. It also examines subjects that have a rich history dating back to Euler and Jacobi, and they continue to

This is the sequel to Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (volume 4 in the AMS series, the Student Mathematical Library). As in the first volume, this book is divided into two parts. The first is a collection of exercises and problems, and the second contains their solutions. The book mainly deals with real functions of one real variable. Topics include: properties of continuous functions, intermediate value property, uniform continuity, mean value theorems, Taylor's formula, convex functions, sequences and series of functions.

Surfaces are among the most common and easily visualized mathematical objects. This book covers various ways of representing surfaces, combinatorial structure and topological classification of surfaces, topology and smooth structure, and much more.