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1
) Introduction to number theory
2
) The principle of mathematical induction
3
) Basic representation theorem
4
) The division algorithm
5
) The divisibility
6
) The euclidean algorithm
7
) Linear Diophantine Equations
8
) The fundamental theorem of arithemetic
9
) Permutations and combinations
10
) Fermat's Little theorem
11
) Wilson's Theorem
12
) Computer Programming
13
) Basic properties of congruences
14
) Residue Systems
15
) Linear Congruences
16
) Fermat's little theorem and wilson's theorem
17
) The Chinese remainder theorem
18
) The Eular Phi Function Part 1
19
) The Eular Phi Function Part 2
20
) Multiplicative function
21
) The mobious inversion formula
22
) Order of Elements
23
) Primitive roots modolo
24
) The prime counting function
25
) The Eular's criterion
26
) The Legendre symbol
27
) Quadratic Reciprocity part 1
28
) Quadratic Reciprocity part 2
29
) Application of quadratic reciprocity
30
) Consicutive Residues
31
) Consicutive triples of Residues part 1
32
) Consicutive triples of Residues part 2
33
) Sums of two squares
34
) Sums of four squares
35
) Gauss circle problem
36
) Dirichlet's devisor problem
37
) Infinity Conclusion
Description:
Dive into a comprehensive 2.5-hour video course on number theory, exploring the fascinating world of integers and their properties. Learn about prime numbers, mathematical induction, division algorithms, and advanced concepts like Fermat's Little Theorem and the Chinese Remainder Theorem. Master key topics including linear Diophantine equations, congruences, Euler's phi function, and quadratic reciprocity. Discover applications in computer programming and delve into intriguing problems like the Gauss circle problem and Dirichlet's divisor problem. Gain a solid foundation in this fundamental branch of pure mathematics, essential for understanding cryptography, computer science, and advanced mathematical concepts.

Number Theory Full Course - A to Z

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#Mathematics #Number Theory #Computer Science #Algorithms #Geometry #Congruence #Mathematical Proofs #Mathematical Induction
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) Introduction to number theory