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Chapter I | Set Theory | |
1. | Introductory remarks | 1 |
2. | The operation of direct product | 3 |
3. | Product-isomorphisms and some generalizations | 5 |
4. | Generalized projective sets | 9 |
4a. | Relations between products of different orders | 11 |
5. | Projective algebras | 12 |
6. | Generalized logic | 13 |
7. | Some problems on infinite sets | 15 |
8. | Measure in abstract sets | 16 |
9. | Nonmeasurable projective sets | 17 |
10. | Infinite games | 23 |
11. | Situations involving many quantifiers | 24 |
12. | Some problems of P. Erdos | 25 |
Chapter II | Algebraic Problems | |
1. | An inductive lemma in combinatorial analysis | 29 |
2. | A problem on matrices arising in the theory of automata | 30 |
3. | A fundamental transformation in the "theory of equations" | 30 |
4. | A problem on Peano mappings | 32 |
5. | The determination of a mathematical structure from a given set of endomorphisms | 32 |
6. | A problem on continued fractions | 32 |
7. | Some questions about groups | 33 |
8. | Semi-groups | 35 |
8a. | Topological semi-groups | 35 |
9. | A problem in the game of bridge | 36 |
10. | A problem on arithmetic functions | 36 |
Chapter III | Metric Spaces | |
1. | Invariant properties of trajectories observed from moving coordinate systems | 37 |
2. | Problems on convex bodies | 38 |
3. | Some problems on isometry | 39 |
4. | Systems of vectors | 39 |
5. | Other problems on metrics | 40 |
Chapter IV | Topological Spaces | |
1. | A problem on measure | 43 |
2. | Approximation of homeomorphisms of E[superscript n] | 43 |
2a. | On the approximability of transformations in three dimensions by compositions of cylindrical mappings | 44 |
3. | A problem on the invariance of dimension | 45 |
4. | Homeomorphisms of the sphere | 46 |
5. | Some topological invariants | 46 |
6. | Quasi-fixed points | 48 |
7. | Connectedness questions | 50 |
8. | Two problems about the disk | 50 |
9. | Approximation of continua by polyhedra | 51 |
10. | The symmetric product | 51 |
11. | A method of proof based on Baire category of sets | 53 |
12. | Quasi-homeomorphisms | 54 |
13. | Some problems of Borsuk | 55 |
Chapter V | Topological Groups | |
1. | Metrization questions | 57 |
2. | Universal groups | 58 |
3. | Basis problems | 59 |
4. | Conditionally convergent sequences | 61 |
Chapter VI | Some Questions in Analysis | |
1. | Stability | 63 |
2. | Conjugate functions | 69 |
3. | Ergodic phenomena | 70 |
4. | The Frobenius transform | 73 |
5. | Functions of two variables | 75 |
6. | Measure-preserving transformations | 76 |
7. | Relative measure | 77 |
8. | Vitali-Lebesque and Laplace-Liapounoff theorems | 78 |
9. | A problem in the calculus of variations | 79 |
10. | A problem on formal integration | 80 |
11. | Geometrical properties of the set of all solutions of certain equations | 80 |
Chapter VII | Physical Systems | |
1. | Generating functions and multiplicative systems | 83 |
1a. | Examples of mathematical problems suggested by biological schemata | 85 |
2. | Infinities in physics | 89 |
3. | Motion of infinite systems, randomly distributed | 91 |
4. | Infinite systems in equilibrium | 96 |
5. | Random Cantor sets | 97 |
6. | Dynamical flow in phase space | 104 |
7. | Some problems on electromagnetic fields | 107 |
8. | Nonlinear problems | 109 |
Chapter VIII | Computing Machines as a Heuristic Aid | |
1. | Introduction | 115 |
2. | Some combinatorial examples | 116 |
3. | Some experiments on finite games | 118 |
4. | Lucky numbers | 120 |
5. | Remarks on computations in mathematical physics | 121 |
6. | Examples from electromagnetism | 122 |
7. | The Schrodinger equation | 123 |
8. | Monte Carlo methods | 125 |
9. | Hydrodynamical problems | 128 |
10. | Synergesis | 135 |
Bibliography | 145 |
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Add Problems in Modern Mathematics, Ulam, famous for his solution to the difficulties of initiating fusion in the hydrogen bomb, devised the well-known Monte-Carlo method. Here he presents challenges in the areas of set theory, algebra, metric and topological spaces, and topological groups., Problems in Modern Mathematics to the inventory that you are selling on WonderClubX
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Add Problems in Modern Mathematics, Ulam, famous for his solution to the difficulties of initiating fusion in the hydrogen bomb, devised the well-known Monte-Carlo method. Here he presents challenges in the areas of set theory, algebra, metric and topological spaces, and topological groups., Problems in Modern Mathematics to your collection on WonderClub |