Difference between revisions of "Number theory/Introduction"
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| + | [[Number theory]] is the study of [[integers]] and an introductory study of number theory involves exploring many common relationships between integers. | ||
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| + | == Introductory Topics in Number Theory == | ||
The following topics make a good introduction to [[number theory]]: | The following topics make a good introduction to [[number theory]]: | ||
* [[Prime number | Primes]] | * [[Prime number | Primes]] | ||
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**** [[Greatest common divisor]]s | **** [[Greatest common divisor]]s | ||
*** [[Counting divisors]] | *** [[Counting divisors]] | ||
| − | ** [[ | + | ** [[Multiple]]s |
*** [[Common multiple]]s | *** [[Common multiple]]s | ||
**** [[Least common multiple]]s | **** [[Least common multiple]]s | ||
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* [[Modular arithmetic]] | * [[Modular arithmetic]] | ||
** [[Linear congruence]] | ** [[Linear congruence]] | ||
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| + | == Introductory Number Theory Resources == | ||
| + | === Books === | ||
| + | * ''the Art of Problem Solving Introduction to Number Theory'' by [[Mathew Crawford]] [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=10 (details)] | ||
| + | * General Interest | ||
| + | ** ''Fermat's Enigma'' by Simon Singh [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 (details)] | ||
| + | ** ''Music of the Primes'' by Marcus du Sautoy [http://www.amazon.com/exec/obidos/ASIN/0066210704/artofproblems-20 (details)] | ||
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| + | === Classes === | ||
| + | * [[Introduction to Number Theory Course]] is part of the [[AoPS Online School]]. [http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesS.php#begnum Details] | ||
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| + | == See also == | ||
| + | * [[Number theory/Intermediate | Intermediate number theory]] | ||
| + | * [[Number theory/Olympiad | Olympiad number theory]] | ||
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| + | [[Category:Introductory Mathematics Topics]] | ||
| + | [[Category:Number theory]] | ||
Latest revision as of 16:20, 2 March 2008
Number theory is the study of integers and an introductory study of number theory involves exploring many common relationships between integers.
Contents
Introductory Topics in Number Theory
The following topics make a good introduction to number theory:
- Primes
- Composite numbers
- Divisibility
- Division Theorem (the Division Algorithm)
- Base numbers
- Diophantine equations
- Modular arithmetic
Introductory Number Theory Resources
Books
- the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
- General Interest
Classes
- Introduction to Number Theory Course is part of the AoPS Online School. Details
