Introduction

I. Elementary mathematics

1. Fundamental operations on rational numbers

2. Higher arithmetical operations

3. Development of the number system

4. Algebraic equations

5. Functions

6. Percentages, interest and annuities

7. Plane geometry

8. Solid geometry

9. Descriptive geometry

10. Trigonometry

11. Plane trigonometry

12. Spherical trigonometry

13. Analytic geometry of the plane

II. Steps towards higher mathematics

14. Set theory

15. The elements of mathematical logic

16. Groups and fields

17. Linear algebra

18. Sequences, series, limits

19. Differential calculus

20. Integral calculus

21. Series of functions

22. Ordinary differential equations

23. Complex analysis

24. Analytic geometry of space

25. Projective geometry

26. Differential geometry, convex bodies, integral geometry

27. Probability theory and statistics

28. Calculus of errors, adjustment of data, approximation theory

29. Numerical analysis

30. Mathematical optimization

III. Brief reports on selected topics

31. Number theory

32. Algebraic geometry

33. Further algebraic structures

34. Topology

35. Measure theory

36. Graph theory

37. Potential theory and partial differential equations

38. Calculus of variations

39. Integral equations

40. Functional analysis

41. Foundation of geometry - Euclidean and non-Euclidean geometry

42. Foundations of mathematics

Tables