Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.

This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

With exercises and projects, Exploring Mathematics supports an active approach to the transition to upper-level theoretical math courses.

A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed...

This first textbook on experimental mathematics that gives a comprehensive introduction to the application of computer programs in mathematical innovation.

Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of...

This text offers a friendly and concise introduction to algebra, with an emphasis on its real-world applications. It is intended for students who are less theoretically inclined. This text can be used for an undergraduate course in abstract algebra or modern algebra for mathematics, engineering, and computer science majors.

Rigorous yet engaging, Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course.