Bøger i Student Mathematical Library serien

Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

We have been curious about numbers - and prime numbers - since antiquity. One notable direction this century in the study of primes has been the influx of ideas from probability. This book intends to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness.

Introducing the heat equation and the closely related notion of harmonic functions from a probabilistic perspective, this book includes chapters on: the discrete case, random walk and the heat equation on the integer lattice; the continuous case, Brownian motion and the usual heat equation; and martingales and fractal dimension.

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. There have been striking developments in the mathematics of 3-dimensional manifolds. This book introduces some of these important developments.

Provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well.

Presents problems in abstract algebra for strong undergraduates or beginning graduate students. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations); rings (including basic ideal theory and factorization in integral domains); linear algebra (emphasizing linear transformations); and fields (including Galois theory).

Tries to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem. This book focuses on aperiodic tilings; the best-known example is the 'kite and dart' tiling.

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 tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes.