Difference between revisions of "Number theory"
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== Student Guides to Number Theory == | == Student Guides to Number Theory == | ||
| − | * [[Number theory/Introduction | Introductory topics in number theory]] | + | * [[Number theory/Introduction | Introductory topics in number theory]] -- Covers different kinds of integers such as [[prime number]]s, [[composite number]]s, and their relationships ([[multiples]], [[divisors]], and more). Also includes [[base number]]s and [[modular arithmetic]]. |
* [[Number theory/Intermediate | Intermediate topics in number theory]] | * [[Number theory/Intermediate | Intermediate topics in number theory]] | ||
* [[Number theory/Olympiad | Olympiad number topics in number theory]] | * [[Number theory/Olympiad | Olympiad number topics in number theory]] | ||
Revision as of 12:57, 24 July 2006
Number theory is the field of mathematics associated with studying the integers.
Contents
Student Guides to 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 number topics in number theory
Advanced Topics in Number Theory
Algebraic Number Theory
Algebraic number theory studies number theory from the perspective of abstract algebra. In particular, heavy use is made of ring theory and Galois theory. Algebraic methods are particularly well-suited to studying properties of individual prime numbers. From an algebraic perspective, number theory can perhaps best be described as the study of 
. Famous problems in algebraic number theory include the Birch and Swinnerson-Dyer Conjecture and Fermat's Last Theorem.
Analytic Number Theory
Analytic number theory studies number theory from the perspective of calculus, and in particular real analysis and complex analysis. The techniques of analysis and calculus are particularly well-suited to studying large-scale properties of prime numbers. The most famous problem in analytic number theory is the Riemann Hypothesis.
Elliptic Curves and Modular Forms
(I don't really feel like writing this right now. Any volunteers?)
Resources
Books
- Introductory
- the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
- General Interest
Miscellaneous
- Intermediate
- Olympiad
Other Topics of Interest
These are other topics that aren't particularly important for competitions and problem solving, but are good to know.
