Difference between revisions of "Number theory"
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== Intermediate Topics == | == Intermediate Topics == | ||
| + | An intermediate level of study involves many of the topics of introductory number theory, but involves an infusion of [[mathematical problem solving]] as well as [[algebra]]. | ||
* [[Diophantine equations]] | * [[Diophantine equations]] | ||
| − | * [[Euler's | + | * [[Euler's Theorem]] |
| − | * [[Fermat's | + | * [[Fermat's Little Theorem]] |
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
| − | * [[Wilson's | + | * [[Wilson's Theorem]] |
== Olympiad Topics == | == Olympiad Topics == | ||
| + | An Olympiad level of study involves familiarity with intermediate topics to a high level, a few new topics, and a highly developed [[proof writing]] ability. | ||
* [[Diophantine equations]] | * [[Diophantine equations]] | ||
| − | * [[Euler's | + | * [[Euler's Theorem]] |
| − | * [[Fermat's | + | * [[Fermat's Little Theorem]] |
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
| − | * [[Wilson's | + | * [[Wilson's Theorem]] |
Revision as of 02:01, 18 June 2006
Number theory is the field of mathematics associated with studying the integers.
Introductory Topics
The following topics make a good introduction to number theory.
- Counting divisors
- Diophantine equations
- Greatest common divisor
- Least common multiple
- Modular arithmetic
- Prime factorization
- Sieve of Eratosthenes
Intermediate Topics
An intermediate level of study involves many of the topics of introductory number theory, but involves an infusion of mathematical problem solving as well as algebra.
Olympiad Topics
An Olympiad level of study involves familiarity with intermediate topics to a high level, a few new topics, and a highly developed proof writing ability.
