Mathematical miniatures

1. A telescoping sum

2. Lagrange's identity

3. Perfect squares

4. Lest common multiples

5. Trig substitutions

Coffee break 1

6. Popoviciu's theorem

7. Catalan's identity

8. Several inequalities

9. Vectors

10. Mathematical induction at work

Coffee break 2

11. A highly divisible determinant

12. Hermite's identity

13. Complete sequences

14. Three polynomials

15. More about induction

Coffee break 3

16. A classical identity

17. Multiplicative functions

18. The "arbitrary" Proizvolov

19. Hölder's inequality

20. Symmetry

Coffee break 4

21. He knows I know he knows

22. A special inequality

23. Two inductive constructions

24. Some old-fashioned geometry

25. Extremal arguments

Coffee break 5

26. The AMS inequality

27. Helly's theorem for one dimension

28. Two approaches

29. Radical axis

30. The pigeonhole principle

Coffee break 6

31. The three jug problem

32. Rectifying trajectories

33. Numerical systems

34. More on polynomials

35. Geometric transformations

Coffee break 7

36. The Game of life problem

37. Tetrahedra with a point in common

38. Should we count

39. Let's count now

40. Some elementary number theory

Coffee break 8

41. Euclid's game

42. Perfect powers

43. The 2n-1 problem

44. The 2n+1 problem

45. The 3n problem

Coffee break

46. Pairwise sums

47. Integer progressions

48. Incomparable sets

49. Morse's sequence

50. A favorite of Erdös.