This course on number theory aims to provide a comprehensive understanding of various topics such as mathematical induction, prime numbers, linear Diophantine equations, congruences, and quadratic reciprocity. By the end of the course, learners will be able to apply these concepts to solve problems related to integers and integer-valued functions. The teaching method includes lectures and explanations of key theorems and algorithms. This course is intended for individuals interested in deepening their knowledge of number theory and its applications in mathematics.
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
