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.
Overview
Syllabus
) Introduction to number theory.
) The principle of mathematical induction.
) Basic representation theorem.
) The division algorithm.
) The divisibility.
) The euclidean algorithm.
) Linear Diophantine Equations.
) The fundamental theorem of arithemetic.
) Permutations and combinations.
) Fermat's Little theorem.
) Wilson's Theorem.
) Computer Programming.
) Basic properties of congruences.
) Residue Systems.
) Linear Congruences.
) Fermat's little theorem and wilson's theorem .
) The Chinese remainder theorem.
) The Eular Phi Function Part 1.
) The Eular Phi Function Part 2.
) Multiplicative function.
) The mobious inversion formula .
) Order of Elements.
) Primitive roots modolo.
) The prime counting function.
) The Eular's criterion.
) The Legendre symbol.
) Quadratic Reciprocity part 1.
) Quadratic Reciprocity part 2.
) Application of quadratic reciprocity .
) Consicutive Residues.
) Consicutive triples of Residues part 1.
) Consicutive triples of Residues part 2.
) Sums of two squares.
) Sums of four squares.
) Gauss circle problem.
) Dirichlet's devisor problem.
) Infinity Conclusion.
Taught by
Academic Lesson
