Physical and digital books, media, journals, archives, and databases.
Results include
  1. Basic set theory

    Shen, A. (Alexander), 1958-
    Providence, R.I. : American Mathematical Society, c2002.

    The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own dedicated treatment.This book provides just that in the form of a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of "naive" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.

    Online American Mathematical Society

  2. Computable functions

    Shen, A. (Alexander), 1958-
    Providence, RI : American Mathematical Society, c2003.

    In 1936, before the development of modern computers, Alan Turing proposed the concept of a machine that would embody the interaction of mind, machine, and logical instruction. The idea of a 'universal machine' inspired the notion of programs stored in a computer's memory. Nowadays, the study of computable functions is a core topic taught to mathematics and computer science undergraduates. Based on the lectures for undergraduates at Moscow State University, this book presents a lively and concise introduction to the central facts and basic notions of the general theory of computation.It begins with the definition of a computable function and an algorithm and discusses decidability, enumerability, universal functions, numberings and their properties, $m$-completeness, the fixed point theorem, arithmetical hierarchy, oracle computations, and degrees of unsolvability. The authors complement the main text with over 150 problems. They also cover specific computational models, such as Turing machines and recursive functions. The intended audience includes undergraduate students majoring in mathematics or computer science, and all mathematicians and computer scientists who would like to learn basics of the general theory of computation. The book is also an ideal reference source for designing a course.

    Online American Mathematical Society

  3. Computer science--theory and applications : 6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011 : proceedings

    Berlin ; Heidelberg ; New York : Springer, ©2011.

    Annotation This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.

    Online SpringerLink

Guides

Course- and topic-based guides to collections, tools, and services.
No guide results found... Try a different search

Library website

Library info; guides & content by subject specialists
No website results found... Try a different search

Exhibits

Digital showcases for research and teaching.
No exhibits results found... Try a different search

EarthWorks

Geospatial content, including GIS datasets, digitized maps, and census data.
No earthworks results found... Try a different search

More search tools

Tools to help you discover resources at Stanford and beyond.