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This book emerged from a set of lecture notes used by one of the authors to teach a 200 level course in Nature of Mathematics. The course was introduced as a bridge from traditional Calculus I, II, III courses to higher level courses of Mathematics, such as Abstract Algebra and Advanced Calculus. The book introduces basic notions from set theory, symbolic logic, functions and relations, number theory, combinatorics and graph theory. It also gives an introduction to more abstract mathematical proofs. The techniques discussed in the book include: direct proof, in particular proof by...

This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an...