Video source

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). In this #numbertheroy course following topics hav been explained in a very comprehensive way.

⭐️ Table of Content ⭐️

⌨️ (00:00) Introduction to number theory

⌨️ (02:07) The principle of mathematical induction

⌨️ (06:04) Basic representation theorem

⌨️ (10:14) The division algorithm

⌨️ (13:49) The divisibility

⌨️ (17:31) The euclidean algorithm

⌨️ (22:48) Linear Diophantine Equations

⌨️ (26:03) The fundamental theorem of arithemetic

⌨️ (30:38) Permutations and combinations

⌨️ (36:10) Fermat’s Little theorem

⌨️ (38:51) Wilson’s Theorem

⌨️ (42:42) Computer Programming

⌨️ (49:18) Basic properties of congruences

⌨️ (52:51) Residue Systems

⌨️ (58:12) Linear Congruences

⌨️ (1:01:54) Fermat’s little theorem and wilson’s theorem

⌨️ (1:06:31) The Chinese remainder theorem

⌨️ (1:10:50) The Eular Phi Function Part 1

⌨️ (1:14:34) The Eular Phi Function Part 2

⌨️ (1:19:12) Multiplicative function

⌨️ (1:23:51) The mobious inversion formula

⌨️ (1:28:08) Order of Elements

⌨️ (1:33:49) Primitive roots modolo

⌨️ (1:37:03) The prime counting function

⌨️ (1:41:39) The Eular’s criterion

⌨️ (1:45:44) The Legendre symbol

⌨️ (1:48:42) Quadratic Reciprocity part 1

⌨️ (1:53:17) Quadratic Reciprocity part 2

⌨️ (1:59:33) Application of quadratic reciprocity

⌨️ (2:02:13) Consicutive Residues

⌨️ (2:06:54) Consicutive triples of Residues part 1

⌨️ (2:09:03) Consicutive triples of Residues part 2

⌨️ (2:13:40) Sums of two squares

⌨️ (2:16:02) Sums of four squares

⌨️ (2:22:16) Gauss circle problem

⌨️ (2:25:38) Dirichlet’s devisor problem

⌨️ (2:29:55) Infinity Conclusion

⭐️ Credit ⭐️

Author of this Course: Aaron Wong, Nevada State College

Visit The Math Repository: https://www.youtube.com/channel/UCBvO3V-CAyAaoQP3Ekd9ZDA

License: Creative Commons Attribution license (reuse allowed)

⭐️ Join Us ⭐️

Join our FB Group: https://www.facebook.com/groups/cslesson

Like our FB Page: https://www.facebook.com/cslesson/

Website: https://cslesson.org

Video source