Towards Higher Categories (The IMA Volumes in Mathematics and its Applications)
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory.
Introduction to Calculus and Classical Analysis (Undergraduate Texts in Mathematics)
Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.
Fibre Bundles, Third Edition (Graduate Texts in Mathematics 20)
Dale Husemoller is Professor of Mathematics at Haverford College (PA). Most of his research has been in algebraic topology, homological algebra, and related fields. Together with John Milnor, Husemoller is author of Symmetric Bilinear Forms (Springer-Verlag, 1973). He is also the author of Elliptic Curves (Springer-Verlag, 1987) and cyclic homology (Tata Lecture notes, 1991). Visits abroad include the IHES (Institut des Hautes Etudes Scientifiques) in France, Universität Bonne and Universität Heidelberg in Germany, ETH in Zürich, Switzerland, and the Tata Institute of Fundamental Research in Bombay, India.
Kurt Goedel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Goedel's incompleteness theorems.
