Soviet studies on teaching of university mathematics

Chapters in this book

1. I-XX I
2. Opening Lecture
3. Wie Gauß die alte Göttinger Mathematik schuf 1
4. Plenary Addresses
5. Functional integration; a semi-historical perspective 17
6. Existence of lattice structures in a class of magnetic phase transitions 25
7. The Fibonacci numbers and the Arctic Ocean 41
8. Section 0: Mathematical Education
9. Interplay of ideas in teaching mathematics 85
10. Soviet studies on teaching of university mathematics 97
11. The role of microworlds for constructing mathematical concepts 101
12. Section 1: History of Mathematics
13. "Gaußsche Quadrate" or Knut Vik designs—the history of a combinatorial structure 121
14. Die Mathematik und ihre Assistenten an der TH München (1868-1918) 135
15. An afterthought of Gauss on cyclotomy 147
16. Harmony and cosmos: mathematics serving a teleological understanding of the world 151
17. Gauß' Arbeiten über kürzeste Linien aus der Sicht der Variationsrechnung 167
18. Implizite gruppentheoretische Denkformen in den „Disquisitiones arithmeticae" von Carl Friedrich Gauß 179
19. Section 2: Mathematical Logic
20. Programs from classical proofs 187
21. Semantics for some constructors of type theory 201
22. Loop-free construction of counter-models in intuitionistic propositional logic 225
23. Section 3: Algebra and Number Theory
24. G-Cogalois field extensions and primitive elements 233
25. Sums of three squares, from Gauß to modular forms 241
26. Local Galois module structure and Hopf orders 249
27. Recipes for lattice dicing 257
28. Representations of Lie algebras with triangular decomposition 275
29. Local class field theory for metabelian extensions 287
30. Convexity theories 0 cont.—foundations 301
31. Banach spaces and superconvex modules 323
32. Affine categories which are varieties 339
33. A geometrical approach to rational solutions of the classical Yang-Baxter equation. Part I 347
34. Section 4: Geometry
35. Necessary conditions for the existence of conservation laws for systems of partial differential equations 359
36. A new decoration of the Socolar-Steinhardt tilings; an initial model for quasicrystals 377
37. A skew-symmetric curvature operator in Riemannian geometry 391
38. Development of non-Euclidean geometries since Gauß 397
39. Recent results in elementary geometry, part II 419
40. A curvature operator in Riemannian geometry 445
41. Section 5: Analysis of Several Complex Variables
42. The theorem of Gauß-Bonnet in complex analysis 451
43. On the origins of p-adic analysis 459
44. Section 7: Algebraic Topology
45. Certain properties of minimal triangulations of spheres 475
46. Stiefel-Whitney polynomials 485
47. On spherically generated rational spaces 491
48. Approximating spaces by polyhedra 499
49. Finite determinacy phenomena for finitely presented groups 507
50. Section 8: Quantum Groups and q-Deformation
51. Modular properties of ribbon abelian categories 529
52. Hopf-Galois extensions of graded algebras 581
53. Section 9: Computational Physics
54. Massive parallelism as the new track for scientific computing 591
55. Section 10: Relativistic Celestial Mechanics: Astrophysics and Cosmology
56. Relativistic celestial mechanics 599
57. Timelike incompleteness of spacetimes 611
58. The Lyman α forests and the universal bubble structure 617
59. Nonradial oscillations of neutron stars: a new branch of strongly damped normal modes 627
60. Testing Einstein's theory of gravity by lunar laser ranging 637
61. The gravitational fields of rotating bodies as minimal surfaces 649
62. The general relativistic two-body-problem. Theory and experiment 667
63. The solution of the second post-Newtonian two-body problem 681
64. Section 11: Gauß and Geomagnetism
65. Magnetospheres: the external magnetic field 695
66. Section 12: General
67. An inequality for the Kummer confluent hypergeometric function 715
68. Complete systems of Kummer and Weber-Hermite functions in spaces of holomorphic functions 723
69. Epimorphisms of topological groups and Z-sets in the Hilbert cube 733
70. Alphabetical List of Contributors 739
71. Author Index 745