Graduate Texts in Mathematics
2 primary works
Book 146
Aimed at mathematicians and computer scientists who will only be exposed to one course in this area, Computability: A Mathematical Sketchbook provides a brief but rigorous introduction to the abstract theory of computation, sometimes also referred to as recursion theory. It develops major themes in computability theory, such as Rice's theorem and the recursion theorem, and provides a systematic account of Blum's complexity theory as well as an introduction to the theory of computable real numbers and functions. The book is intended as a university text, but it may also be used for self-study; appropriate exercises and solutions are included.
Book 174
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications. Of special interest are the 750 exercises, many with guidelines for their solutions, applications and extensions of the main propositions and theorems, pointers to new branches of the subject, and difficult challenges for the very best students.