The Queen Of Mathematics

Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem. We have made the proofs of these theorems as elementary as possible. Unique to The Queen of Mathematics are its presentations of the topic of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem.

This book takes the unique approach of examining number theory as it emerged in the 17th through 19th centuries. It leads to an understanding of today's research problems on the basis of their historical development. This book is a contribution to cultural history and brings a difficult subject within the reach of the serious reader.

"This picture book traces the impressive career of Sophie Kowalevski, the first woman to receive a doctorate in mathematics requiring original research. As a girl, Sophie is fascinated by the equations her father uses to wallpaper her room. She proves herself a prodigy, and tutors are impressed enough to give her private lessons. Despite universities that refuse to allow women on campus or to pay them to teach, Sophie is able to distinguish herself with her research into partial differential equations. Sophie receives a doctorate and becomes the first female professional mathematician in Northern Europe. The book mentions several of Kowalevski's mathematical contributions and closes with an encouraging message about women in mathematics"--

Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.

An absorbing account of pure and applied mathematics from the geometry of Euclid to that of Riemann, and its application in Einstein's theory of relativity. The twenty chapters cover such topics as: algebra, number theory, logic, probability, infinite sets and the foundations of mathematics, rings, matrices, transformations, groups, geometry, and topology. Mathematics was republished in 1987 with corrections and an added foreword by Martin Gardner.

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.