Difference between revisions of "Number theory"
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| − | '''Number theory''' is the field of [[mathematics]] associated with studying the properties of [[ | + | '''Number theory''' is the field of [[mathematics]] associated with studying the properties and identities of [[ integer]]s. |
==Overview== | ==Overview== | ||
| Line 5: | Line 5: | ||
*[[Modular arithmetic]] | *[[Modular arithmetic]] | ||
*[[Prime number]]s | *[[Prime number]]s | ||
| − | Some branches of number theory may only deal with a certain subset of the real numbers, such as [[integer]]s, [[positive]] numbers, [[natural number]]s, [[rational number]]s, etc. Some [[algebra]]ic topics such as [[Diophantine]] equations are | + | Some branches of number theory may only deal with a certain subset of the real numbers, such as [[integer]]s, [[positive]] numbers, [[natural number]]s, [[rational number]]s, etc. Some [[algebra]]ic topics such as [[Diophantine]] equations as well as some theorems concerning integer manipulation (like the [[Chicken McNugget Theorem ]]) are sometimes considered number theory. |
== Student Guides to Number Theory == | == Student Guides to Number Theory == | ||
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* Introductory | * Introductory | ||
** ''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)] | ** ''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)] | ||
| − | ** ''Elementary Number Theory: A Problem Oriented Approach | + | ** ''Elementary Number Theory: A Problem Oriented Approach '' by [[Joe Roberts]] [http://www.amazon.com/exec/obidos/ASIN/0262680289 (details)] Out of print but if you can find it in a library or used, you might love it and learn a lot. Writen caligraphically by the author. |
| − | [http://www.amazon.com/exec/obidos/ASIN/0262680289 (details)] Out of print but if you can find it in a library or used, you might love it and learn a lot. | ||
* General Interest | * General Interest | ||
** ''Fermat's Enigma'' by Simon Singh [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 (details)] | ** ''Fermat's Enigma'' by Simon Singh [http://www.amazon.com/exec/obidos/ASIN/0385493622/artofproblems-20 (details)] | ||
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=== E-Book === | === E-Book === | ||
| − | * [ | + | * [https://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf ''Problems in Elementary Number Theory'' by Hojoo Lee] |
| − | * [http:// | + | * [http://artofproblemsolving.com/articles/files/SatoNT.pdf Number Theory by Naoki Sato] |
| − | === | + | === Online Courses=== |
| + | * Introduction | ||
| + | ** [https://artofproblemsolving.com/school/course/catalog/intro-numbertheory Introduction to Number Theory] | ||
* Intermediate | * Intermediate | ||
| − | ** [ | + | ** [https://artofproblemsolving.com/school/course/catalog/intermediate-numbertheory Intermediate Number Theory] |
== Other Topics of Interest == | == Other Topics of Interest == | ||
Revision as of 15:35, 2 March 2020
Number theory is the field of mathematics associated with studying the properties and identities of integers.
Contents
Overview
Number theory is a broad topic, and may cover many diverse subtopics, such as:
Some branches of number theory may only deal with a certain subset of the real numbers, such as integers, positive numbers, natural numbers, rational numbers, etc. Some algebraic topics such as Diophantine equations as well as some theorems concerning integer manipulation (like the Chicken McNugget Theorem ) are sometimes considered number theory.
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 topics in number theory
- Advanced topics in number theory
Resources
Books
- Introductory
- the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
- Elementary Number Theory: A Problem Oriented Approach by Joe Roberts (details) Out of print but if you can find it in a library or used, you might love it and learn a lot. Writen caligraphically by the author.
- General Interest
E-Book
Online Courses
- Introduction
- Intermediate
Other Topics of Interest
These are other topics that aren't particularly important for competitions and problem solving, but are good to know.
