An Introduction to Mathematical Reasoning by Cambridge University Press $128.00
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be...

Sets for Mathematics by Cambridge University Press $63.00
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the...

Knowledge and the Flow of Information by Center for the Study of Language and Inf $30.00
An attempt to develop a theory of knowledge and philosophy of mind using ideas derived from the mathematical theory of communication developed by Claude Shannon. Information is seen as an objective commodity defined by the dependency relations between distinct events. Knowledge is then analyzed as information caused belief. Perception is the delivery of information caused belief. Perception is...

Principia Mathematica: Volume 1 by Cambridge University Press
An Unabridged, Digitally Enlarged Printing Of Volume I of III: Part I - MATHEMATICAL LOGIC - The Theory Of Deduction - Theory Of Apparent Variables - Classes And Relations - Logic And Relations - Products And Sums Of Classes - Part II - PROLEGOMENA TO CARDIANL ARITHMITIC - Unit Classes And Couples - Sub-Classes, Sub-Relations, And Relative Types - One-Many, Many-One, And One-One Relations -...

Building Models by Games (London Mathematical Society Student Texts) by Cambridge University Press $22.95
This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions...

Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum) by Cambridge University Press $103.99
This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses. The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While it was apparent that the conjecture must be...

An Introduction to the Theory of Surreal Numbers (London Mathematical Society Lecture Note Series) by Cambridge University Press $69.00
The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the...

Turing's World 3.0: An Introduction to Computability Theory (Center for the Study of Language and Information - Lecture Notes) by Center for the Study of Language and Inf $22.95
Turing's World is a self-contained introduction to Turing machines, one of the fundamental notions of logic and computer science. The text and accompanying diskette allow the user to design, debug, and run sophisticated Turing machines in a graphical environment on the Macintosh. Turning's World introduces users to the key concpets in computability theory through a sequence of over 100 exercises...

Logic for Mathematicians by Cambridge University Press $21.95
Intended for logicians and mathematicians, this text is based on Dr. Hamilton's lectures to third and fourth year undergraduates in mathematics at the University of Stirling. With a prerequisite of first year mathematics, the author introduces students and professional mathematicians to the techniques and principal results of mathematical logic. In presenting the subject matter without bias...

Principia Mathematica to *56 (Cambridge Mathematical Library) by Cambridge University Press $92.00
The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is...