The millennium prize problems You can also check the book "The Millennium problems: the seven greatest unsolved mathematical puzzles of our time" by K. Devlin. Math stacks QA93 .D485 2002

Proof writing tips.

Lesson 1Chapter 1 . Connectives

Lesson 2Chapter 2. Biconditional, truth tables.

Lesson 3 Chapter 1/2. More about conditional, negation rules. Three proof methods.

Lesson 4. Chapter 3/ 4. Examples of proofs.

Lesson 5Chapter 3/4/5. More proofs. Induction.

Lesson 6.Chapter 5. More proofs by induction

Lesson 7. Chapter 5. Strong induction. Recursive definitions. Fibonacci 's numbers.

Lesson 8 Chapter 5. Fibonacci numbers. Review of induction

Lesson 9Chapter 6. Sets

Lesson 10 Chapter 6 .Sets

Lesson 11Cartesian products and power sets.

Lesson 12. Chapter 7. Quantifiers. Chapter 8. Functions.

Lesson 13. Chapter 9. Injective, surjective functions

Lesson 14. More about functions. Inverses.

Lesson 15. Chapter 14. Cardinality.

Lesson 16. Chapter 14. Cardinality.

Lesson 17. Chapter 14 .Cantor 's diagonalization proof.

Lesson 18. Chapter 15-18 Review.

Lesson 19.Chapter 19. Congruence mod m, congruence classes, Computing mod m

Lesson 20. Applications. Computing powers by repeated squaring.Zm

Lesson 21 .Chapter 16,17,18, 19. Cancellation laws. euclideal algorithm. Diophantine equations.

Lesson 22 Chapter 20. Linear congruences.

Lesson 23 Chapter 21. Inverses

Lesson 24Chapter 22. Equivalence relations.

Lesson 25 Chapter 23. Prime numbers

Bounded gap between primes article

Lesson 26 Chapert 24. Fremat 's little theorem.