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 15:20, 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
[hide]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