Difference between revisions of "Number theory"
(→Intermediate Topics) |
(major edits to Intro section and Interm section) |
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== Introductory Topics == | == Introductory Topics == | ||
The following topics make a good introduction to number theory. | The following topics make a good introduction to number theory. | ||
| − | * [[Counting divisors]] | + | * [[Prime number | Primes]] |
| + | ** [[Sieve of Eratosthenes]] | ||
| + | ** [[Prime factorization]] | ||
| + | * [[Composite number | Composite numbers]] | ||
| + | * [[Divisibility]] | ||
| + | ** [[Divisors | Divisors]] | ||
| + | *** [[Common divisor | Common divisors]] | ||
| + | **** [[Greatest common divisor | Greatest common divisors]] | ||
| + | *** [[Counting divisors]] | ||
| + | ** [[Multiples]] | ||
| + | *** [[Least common multiple | Least common multiples]] | ||
| + | * [[Base numbers]] | ||
* [[Diophantine equations]] | * [[Diophantine equations]] | ||
| − | |||
| − | |||
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
| − | |||
| − | |||
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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]]. | 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]] | ||
| − | |||
| − | |||
* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
| − | * [[Wilson's Theorem]] | + | ** [[Euler's Totient Theorem]] |
| + | ** [[Fermat's Little Theorem]] | ||
| + | ** [[Wilson's Theorem]] | ||
| + | |||
== Olympiad Topics == | == Olympiad Topics == | ||
Revision as of 02:36, 19 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.
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.
