Having switched to WordPress for all my mathematical notes from now on, my first post here is a list of links to some mathematical notes I made on social media in the past, now stored as pdf files on my website.

1. Oscillatory price behaviour in mathematical economics: a simple numerical example

2. How Big Does a Near-Light-Speed Impactor Have to be to Wipe Out Life on Earth?

3. A little finding regarding Mersenne prime numbers

4. A little finding regarding the middle-half Cantor set

5. Some pretty pictures of quadratic forms

7. Elementary but fun problems

8. Two ways of proving a famous result regarding Fermat primes, side by side

9. Examples of ‘Unlimited Register Machine’ programs for Turing-computable functions

10. How the ‘Riemann sphere’ makes the distinction between lines and circles disappear

11. A catalogue of proofs that various sets, functions and relations are ‘primitive recursive’

12. A formal mathematical language for constructing ‘machine-checkable’ proofs, with MANY examples…

13. Memo on continued fractions

14. Collection of rules, techniques and theorems for solving polynomial congruences

15. Mathematical Induction, Greatest Common Divisor, Euclidean Algorithm, and Diophantine Equations

17. A quicker proof of the equivalence of the principle of induction and the well-ordering principle

18. M823 Revision problems for Chapter 1: The fundamental theorem of arithmetic

19. An example in which using zero as an actual divisor gives a unique and meaningful answer

21. M823 Revision problems for Chapter 2: Arithmetical functions and Dirichlet multiplication

22. The big oh notation and asymptotic equality of functions

26. Interesting problem involving groups of order p^2 where p is prime

27. Advanced Number Theory Note #3: Partial sums of Dirichlet convolutions, with some applications

28. M823 Revision problems for Chapter 3: Averages of arithmetical functions

30. Advanced Number Theory Note #5: Proof of an important ‘Tauberian theorem’ and some applications

36. Advanced Number Theory Note #8: Dirichlet’s theorem on primes in arithmetic progressions

38. M823 Revision problems for Chapter 5: Congruences

39. M823 Revision problems for Chapter 6: Finite abelian groups and their characters

40. M823 Revision problems for Chapter 7: Dirichlet’s Theorem on Primes in Arithmetical Progressions

41. M823 Revision problems for Chapter 9: Quadratic Residues and the Quadratic Reciprocity Law

42. Conversation with Tom Bailey about how a photon can have momentum even though it has zero mass

43. Using the ABC conjecture to prove Fermat’s Last Theorem

45. Ideal class group for the ring of integers in an imaginary quadratic field, Part I

51. Using a Residue Theorem from Complex Analysis to solve an improper integral

52. Time dilation formula from metric of special relativity

53. Conversation with Marc Fleury about the incompatibility of quantum theory and general relativity