Number Theory for Beginners - Full Course

Learn about Number theory (or arithmetic or higher arithmetic in older usage) in this full course for beginners. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions.
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Learn about Number theory (or arithmetic or higher arithmetic in older usage) in this full course for beginners. Number theory 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 number theroy 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

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[Thegreattalks-ib]

Very good for high school freshies like me!

[NoobplaysMC]

Thanks for this Video very helpfull for Competetive exam

[Thegreattalks-ib]

Oh, and is it possible to make the video into sections?

[M-YasasVardhan]

About which book is he telling in the video

[zeldajerk]

The formula breaks when s equals t, because you sum from 0 to negative 1. Therefore a representation of n does not always give a representation of n - 1 in terms of that formula. It would need an extra case where you prove that representations of n with a zeroth power term give a representation of n-1.