Difference between revisions of "Number theory"

Revision as of 17:21, 25 October 2007

Number theory is the field of mathematics associated with studying the properties of real numbers.

Number theory is a broad topic, and may cover many diverse subtopics, such as:

Some branches of number theory may only deal with a certain subset of the real numbers, such as integers, positive numbers, natural numbers, rational numbers, etc. Some algebraic topics such as Diophantine equations are occasionally considered number theory.

Introductory topics in number theory
- Covers different kinds of integers such as prime numbers, composite numbers, and their relationships (multiples, divisors, and more). Also includes base numbers and modular arithmetic.
Intermediate topics in number theory
Olympiad topics in number theory
Advanced topics in number theory

Introductory
- the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
General Interest
- Fermat's Enigma by Simon Singh (details)
- Music of the Primes by Marcus du Sautoy (details)

@@ Line 1: / Line 1: @@
-'''Number theory''' is the field of [[mathematics]] associated with studying the [[integers]].
+'''Number theory''' is the field of [[mathematics]] associated with studying the properties of [[ real number]]s.
+==Overview==
+Number theory is a broad topic, and may cover many diverse subtopics, such as:
+*[[Modular arithmetic]]
+*[[Inequalities]]
+*[[Field theory]]
+*[[Ring theory]]
+Some branches of number theory may only deal with a certain subset of the real numbers, such as [[integer]]s, [[positive]] numbers, [[natural number]]s, [[rational number]]s, etc. Some [[algebra]]ic topics such as [[Diophantine]] equations are occasionally considered number theory.
 == Student Guides to Number Theory ==