Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes New in this edition are coverage ofp adic numbers, Hensel s lemma, multiple zeta values, and elliptic curve methods in primality testing Key topics and features include a solid introduction to analytic number theory, including full proofs of Dirichlet s Theorem and the Prime Number Theorem concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user friendly style, historical context, and wide range of exercises that range from simple to quite difficult with solutions and hints provided for select exercises make Number Theory An Introduction via the Density of Primes ideal for both self study and classroom use Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra All necessary concepts from abstract algebra and complex analysis are introduced where needed Dunbar s number Wikipedia Dunbar s number is a suggested cognitive limit to the number of people with whom one can maintain stable social relationships relationships in which an individual knows who each person is and how each person relates to every other person VARIOUS NUMBER THEORISTS Various Number Theorists Home Pages Departmental listings Complete listing A B C D E F G H I J K L M N O P Q R S Real number Wikipedia In mathematics, a real number is a value of a continuous quantity that can represent a distance along a lineThe adjective real in this context was introduced in the th century by Ren Descartes, who distinguished between real and imaginary roots of polynomials The Official String Theory Web Site It s the st century Time to feed your mind Basics So what is string theory For that matter, what the heck are elementary particles Theory of Development MSS Research Theory of Development by Garry Jacobs, Robert Macfarlane, and N Asokan presented to Pacific Rim Economic Conference, Bangkok, Jan , Introduction to Modern Literary Theory Kristi Siegel Dr Kristi Siegel Associate Professor, English Dept Director, English Graduate Program Chair Languages, Literature, and Communication Division Human Intelligence biographical profiles, current This site includes biographical profiles of people who have influenced the development of intelligence theory and testing, in depth articles exploring current controversies related to human intelligence, and resources for teachers General Systems Theory StatPac Index General Systems Theory , David S Walonick, PhD General systems theory was originally proposed by biologist Ludwig von Bertalanffy in Since Descartes, the scientific method had progressed under two related assumptions The Prime Pages prime number research, records and More prime resources Conjectures and Open Problems A short list of conjectures and open problems relating to primes The Riemann Hypothesis One of the most important conjectures in prime number theory Deduction Induction Social Research Methods In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches Deductive reasoning works from