Table of Contents

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.