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The foundation -- Number Theory 1

Mathematical Induction -- Number Theory 2

The division algorithm -- Number Theory 3

The Greatest Common Divisor -- Number Theory 4

The Euclidean Algorithm -- Number Theory 5

Primes and Composites -- Number Theory 6

Proofs and Conjectures involving primes -- Number Theory 7

Modular Arithmetic -- Number Theory 8

Divisibility Rules -- Number Theory 9

Solving linear congruences -- Number Theory 10

Chinese Remainder Theorem -- Number Theory 11

Euler's Theorem -- Number Theory 12

Euler's Totient Function -- Number Theory 13

Wilson's Theorem -- Number Theory 14

Hensel's Lemma -- Number Theory 15

The order of an integer modulo n -- Number Theory 16

Primitive Roots -- Number theory 17

More about primitive roots -- Number Theory 18

Applications of primitive roots -- Number Theory 19

Indices (the discrete log) -- Number Theory 20

Decimal Representations -- Number Theory 21

Quadratic Residues -- Number Theory 22

Quadratic Reciprocity proof -- Number Theory 23

Quadratic Reciprocity Examples -- Number Theory 24

Square roots mod p -- Number Theory 25

Sums of squares -- Number Theory 26

Quadratic Forms -- Number Theory 27

Introduction to Integer Partitions -- Number Theory 28

Generating Functions -- Number Theory 29

How to use generating functions with integer partitions -- Number Theory 30

Introduction to product-sum identities -- Number Theory 31

Ramanujan's Theta Functions -- Number Theory 32

Ramanujan's famous (mod 5) congruence -- Number Theory 33

Difference 2 at distance 1 -- Number Theory Video 34

Description:

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.

Number Theory

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#Mathematics #Number Theory #Discrete Mathematics #Generating Functions #Algebra #Linear Algebra #Quadratic Forms #Mathematical Proofs #Mathematical Induction #Modular Arithmetic #Chinese Remainder Theorem

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