Number Theory
Dive into a comprehensive 16-hour course on Number Theory, exploring fundamental concepts and advanced topics. Begin with mathematical induction and progress through division algorithms, greatest common divisors, and the Euclidean algorithm. Examine prime numbers, modular arithmetic, and divisibility rules before delving into linear congruences and the Chinese Remainder Theorem. Study Euler's Theorem, Wilson's Theorem, and Hensel's Lemma, then investigate primitive roots and their applications. Explore quadratic residues, reciprocity, and forms, before concluding with an introduction to integer partitions, generating functions, and Ramanujan's Theta Functions. Master key theorems and conjectures while developing problem-solving skills in this in-depth exploration of number theory.