Mathematics++: selected topics beyond the basic courses
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2015]
|
| Series: | Student mathematical library
volume 75 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 343 Seiten Diagramme |
| ISBN: | 9781470422615 |
Staff View
MARC
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| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2015] | |
| 264 | 4 | |c © 2015 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Measure and Integral 1
§1. Measure 6
§2. The Lebesgue Integral 22
§3. Foundations of Probability Theory 31
§4. Literature 36
Bibliography 37
Chapter 2. High֊Dimensional Geometry and
Measure Concentration 39
§1. Peculiarities of Large Dimensions 41
§2. The Brunn-Mirukowski Inequality and Euclidean
Isoperimetry 44
§3. The Standard Normal Distribution and the Gaussian
Measure 53
§4. Measure Concentration 61
§5. Literature 81
Bibliography 82
Chapter 3. Fourier Analysis 85
§1. Characters 87
§2. The Fourier Transform 94
v
VI
Contents
§3. Two Unexpected Applications
§4. Convolution
§5. Poisson Summation Formula
§6. Influence of Variables
§7. Infinite Groups
§8. Literature
Bibliography
Chapter 4. Representations of Finite Groups
§1. Basic Definitions and Examples
§2. Decompositions into Irreducible Representations
§3. Irreducible Decompositions, Characters, Orthogonality
§4. Irreducible Representations of the Symmetric Group
§5. An Application in Communication Complexity
§6. More Applications and Literature
Bibliography
Chapter 5. Polynomials
§1, Rings, Fields, and Polynomials
§2. The Schwartz—Zippel Theorem
§3. Polynomial Identity Testing
§4. Interpolation, Joints, and Contagious Vanishing
§5. Varieties, Ideals, and the Hilbert Basis Theorem
§6. The Nullstellensatz
§7. Bezout’s Inequality in the Plane
§8. More Properties of Varieties
§9. BezouUs Inequality in Higher Dimensions
§10. Bounding the Number of Connected Components
§11. Liter atur e
Bibliography
99
106
109
113
124
137
138
141
142
145
150
160
163
168
169
173
173
175
176
180
185
188
195
200
219
226
232
232
Contents
vu
Chapter 6. Topology
§1. Topological Spaces and Continuous Alaps
§2. Bits of General Topology
§3. Compactness
§4. Homotopy and Homotopy Equivalence
§5. The Borsuk—Ulam Theorem
§6. Operations on Topological Spaces
§7. Simplicial Complexes and Relatives
§8. Non-embedd ability
§9. Homotopy Groups
§10. Homology of Simplicial Complexes
§11. Simplicial Approximation
§12. Homology Does Not Depend on Triangulation
§13. A Quick Harvest and Two More Theorems
§14. Manifolds
§15. Literature
Bibliography
235
236
240
247
253
257
262
271
283
289
301
309
314
318
321
330
330
Index
333
|
| any_adam_object | 1 |
| author | Kantor, Ida 1981- Matoušek, Jiří 1963-2015 Šámal, Robert 1977- |
| author_GND | (DE-588)1077873549 (DE-588)124638457 (DE-588)1077873689 |
| author_facet | Kantor, Ida 1981- Matoušek, Jiří 1963-2015 Šámal, Robert 1977- |
| author_role | aut aut aut |
| author_sort | Kantor, Ida 1981- |
| author_variant | i k ik j m jm r š rš |
| building | Verbundindex |
| bvnumber | BV042948557 |
| callnumber-first | Q - Science |
| callnumber-label | QA11 |
| callnumber-raw | QA11.2 |
| callnumber-search | QA11.2 |
| callnumber-sort | QA 211.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 |
| ctrlnum | (OCoLC)932194544 (DE-599)GBV823463257 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| series | Student mathematical library |
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| spelling | Kantor, Ida 1981- Verfasser (DE-588)1077873549 aut Mathematics++ selected topics beyond the basic courses Ida Kantor, Jiří Matoušek, Robert Sámal Mathematics ++ Providence, Rhode Island American Mathematical Society [2015] © 2015 xii, 343 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 75 Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Mathematics : Study and teaching (Graduate) Computer science : Mathematics Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s Harmonische Analyse (DE-588)4023453-8 s Endliche Gruppe (DE-588)4014651-0 s Polynom (DE-588)4046711-9 s Geometrische Topologie (DE-588)4156724-9 s DE-604 Matoušek, Jiří 1963-2015 Verfasser (DE-588)124638457 aut Šámal, Robert 1977- Verfasser (DE-588)1077873689 aut Erscheint auch als Online-Ausgabe 978-1-4704-2623-1 Student mathematical library volume 75 (DE-604)BV013184751 75 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028374768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kantor, Ida 1981- Matoušek, Jiří 1963-2015 Šámal, Robert 1977- Mathematics++ selected topics beyond the basic courses Student mathematical library Geometrische Topologie (DE-588)4156724-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd Endliche Gruppe (DE-588)4014651-0 gnd Integrationstheorie (DE-588)4138369-2 gnd Polynom (DE-588)4046711-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
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| title | Mathematics++ selected topics beyond the basic courses |
| title_alt | Mathematics ++ |
| title_auth | Mathematics++ selected topics beyond the basic courses |
| title_exact_search | Mathematics++ selected topics beyond the basic courses |
| title_full | Mathematics++ selected topics beyond the basic courses Ida Kantor, Jiří Matoušek, Robert Sámal |
| title_fullStr | Mathematics++ selected topics beyond the basic courses Ida Kantor, Jiří Matoušek, Robert Sámal |
| title_full_unstemmed | Mathematics++ selected topics beyond the basic courses Ida Kantor, Jiří Matoušek, Robert Sámal |
| title_short | Mathematics++ |
| title_sort | mathematics selected topics beyond the basic courses |
| title_sub | selected topics beyond the basic courses |
| topic | Geometrische Topologie (DE-588)4156724-9 gnd Harmonische Analyse (DE-588)4023453-8 gnd Endliche Gruppe (DE-588)4014651-0 gnd Integrationstheorie (DE-588)4138369-2 gnd Polynom (DE-588)4046711-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Geometrische Topologie Harmonische Analyse Endliche Gruppe Integrationstheorie Polynom Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028374768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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