Difference between revisions of "Number theory"
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| − | '''Number theory''' is the field of [[mathematics]] associated with studying the [[ | + | '''Number theory''' is the field of [[mathematics]] associated with studying the properties and identities of [[ integer]]s. |
| + | ==Overview== | ||
| + | Number theory is a broad topic, and may cover many diverse subtopics, such as: | ||
| + | *[[Modular arithmetic]] | ||
| + | *[[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 as well as some theorems concerning integer manipulation (like the [[Chicken McNugget Theorem ]]) are sometimes considered number theory. | ||
| − | == | + | == Student Guides to Number Theory == |
| − | + | * '''[[Number theory/Introduction | Introductory topics in number theory]]''' | |
| − | * [[ | + | ** Covers different kinds of integers such as [[prime number]]s, [[composite number]]s, [[perfect square]]s and their relationships ([[multiple|multiples]], [[divisor|divisors]], and more). Also includes [[base number]]s and [[modular arithmetic]]. |
| − | ** | + | * '''[[Number theory/Intermediate | Intermediate topics in number theory]]''' |
| − | + | * '''[[Number theory/Olympiad | Olympiad topics in number theory]]''' | |
| − | + | * '''[[Number theory/Advanced topics | Advanced topics in number theory]]''' | |
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| + | == Resources == | ||
| + | === Books === | ||
| + | * Introductory | ||
| + | ** ''the Art of Problem Solving Introduction to Number Theory'' by [[Mathew Crawford]] [https://artofproblemsolving.com/store/book/intro-number-theory (details)] | ||
| + | ** ''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. | ||
| + | * 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)] | ||
| + | ** ''104 Number Theory Problems'' by Titu Andreescu, Dorin Andrica, Zuming Feng | ||
| + | === E-Book === | ||
| + | * [https://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf ''Problems in Elementary Number Theory'' by Hojoo Lee] | ||
| + | * [https://numbertheoryguy.com/publications/olympiad-number-theory-book/ ''Intermediate Number Theory'' by Justin Stevens] | ||
| + | * [http://artofproblemsolving.com/articles/files/SatoNT.pdf ''Number Theory'' by Naoki Sato] | ||
| − | == | + | === Online Courses=== |
| − | + | *Introductory Number Theory | |
| − | + | ** [https://thepuzzlr.com/courses/introduction-to-number-theory-course/ Introduction to Number Theory] | |
| − | + | * Intermediate | |
| − | + | ** [https://artofproblemsolving.com/school/course/catalog/intermediate-numbertheory Intermediate Number Theory] | |
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== Other Topics of Interest == | == Other Topics of Interest == | ||
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* [[Fermat's Last Theorem]] | * [[Fermat's Last Theorem]] | ||
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=== Famous Unsolved Number Theory Problems === | === Famous Unsolved Number Theory Problems === | ||
| + | * [[Birch and Swinnerton-Dyer conjecture]] | ||
| + | * [[Collatz Problem]] | ||
| + | * [[Goldbach Conjecture]] | ||
| + | * [[Riemann Hypothesis]] | ||
* [[Twin Prime Conjecture]] | * [[Twin Prime Conjecture]] | ||
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| + | [[Category:Number theory]] | ||
| + | [[Category:Definition]] | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 22:08, 8 January 2024
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, perfect squares 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
- Problems in Elementary Number Theory by Hojoo Lee
- Intermediate Number Theory by Justin Stevens
- Number Theory by Naoki Sato
Online Courses
- Introductory Number Theory
- Intermediate
Other Topics of Interest
These are other topics that aren't particularly important for competitions and problem solving, but are good to know.
