Tolerance graphs can be used to quantify the degree to which there is conflict or accord in a system and can provide solutions to questions in the form of "optimum arrangements." Arising from the authors' teaching graduate students in the U.S. and Israel, this book is intended for use in mathematics and computer science, where the subject can be applied to algorithmics. The inclusion of many exercises with partial solutions will increase the appeal of the book to instructors as well as graduate students.

Volume 2 provides a comprehensive review of integral analysis in multidimensional Euclidean space.

Based on a graduate course taught at Utrecht University, this book provides a short introduction to the theory of Foliations and Lie Groupoids to students who have already taken a first course in differential geometry. Ieke Moerdijk and Janez Mrcun include detailed references to enable students to find the requisite background material in the research literature. The text features many exercises and worked examples.

Arising from a summer school course taught by Janos Kollar, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Kollar's original course has been developed, with his co-authors, into a state-of-the-art treatment of the classification of algebraic varieties. The authors have included numerous exercises with solutions, which help students reach the stage where they can begin to tackle related contemporary research problems.

The study of combinatorial isoperimetric problems exploits similarities between discrete optimization problems and the classical continuous setting. Based on his many years of teaching experience, Larry Harper focuses on global methods of problem solving. His text will enable graduate students and researchers to quickly reach the most current state of research in this topic. Harper includes numerous worked examples, exercises and material about applications to computer science.

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex...

The techniques used to solve nonlinear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems and principles from first principles, this textbook gives upper undergraduates and graduate students a thorough understanding using as little background material as possible.

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular, their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan,...

Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The Appendix provides a summary of the basic properties of each Lie algebra of finite and affine type.

Requiring only an understanding of differentiable manifolds, Isaac Chavel covers introductory ideas followed by a selection of more specialized topics in this second edition. He provides a clearer treatment of many topics, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. Among the classical topics shown in a new setting is isoperimetric inequalities in curved spaces. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the...