Everyone knows some of the basics of probability, perhaps enough to play cards. In this book, the author has made the limit theorems accessible by stating everything in terms of a game of tossing of a coin: heads or tails. It is suitable for those wishing

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

This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications.

An introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate and introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas.

The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. In this book, Fischer looks at the classic entry point to the subject: plane algebraic curves. Here one quickly sees the mix of algebra and geometry, as well as analysis and topology, that is typical of complex algebraic geometry, but without the need for advanced techniques from commutative algebra or the abstract machinery of sheaves and schemes.

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

Presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is il

Learning about cryptography requires examining fundamental issues about information security. Questions abound and answering them requires an understanding of basic cryptography. This book, written by Russian cryptographers, explains those basics. Chapters are independent and can be read in any order. The introduction gives a general description of all the main notions of modern cryptography: a cipher, a key, security, an electronic digital signature, a cryptographic protocol, etc. Other chapters delve more deeply into this material. This text should be suitable for advanced high school...

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 volume is based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute. It is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the programme. The material is co-ordinated so that some of the major computer simulations relate to topics covered in the first ten chapters.