An Adventurer's Guide to Number Theory (Dover Books on Mathematics)

Written for readers with an understanding of arithmetic and beginning algebra, this book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss. In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as:   Primes and divisibilityBeginning algebra, geometry, and discussions of Euclid's Elements, calculus, and set theoryQuadratic forms and residue arithmetic and quadratic reciprocity and related theorems Moreover, the author has included a number of unusual features to challenge and stimulate students: The original problems in Diophantus' Arithmetica Proofs of Fermat's Last Theorem for the exponents 3and 4Two proofs of Wilson's TheoremAlso included is a Table of Theorems grouped into categories according to subject, and an Index of Mathematicians. Readers with a mathematical bent will enjoy and benefit from these entertaining and thought-provoking adventures in the fascinating realm of number theory. Mr. Friedberg is a theoretical physicist who has contributed to a wide variety of problems in mathematics and physics, including mathematical logic, number theory, solid state physics, general relativity, particle physics, quantum optics, genome research, and the foundations of quantum physics.Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.   Read more