A physicist's introduction to algebraic structures: vector spaces, groups, topological spaces and more

✍ Scribed by Pal, Palash B

• Publisher: Cambridge University Press
• Year: 2019
• Tongue: English
• Leaves: 717
• Category: Library

✦ Table of Contents

Cover......Page 1
Front Matter......Page 3
A Physicist’s Introduction to Algebraic Structures: Vector Spaces, Groups, Topological Spaces and More......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Figures......Page 21
Preface......Page 23
Part A: General Introduction......Page 25
1 Rules of Logic......Page 27
2 Sets and Functions......Page 42
3 Algebraic Structures......Page 61
Part B Vector Spaces......Page 89
4 Basics......Page 91
5 Operators on VectorSpaces......Page 112
6 Infinite Dimensional VectorSpaces......Page 150
Part C Group Theory......Page 177
7 General Properties ofGroups......Page 179
8 Finite Groups......Page 211
9 Representation of FiniteGroups......Page 251
10 Symmetries of RegularGeometrical Objects......Page 305
11 Countably Infinite Groups......Page 335
12 General Properties of LieGroups......Page 350
13 Rotations and Translations......Page 382
14 Unitary Groups and TheirRepresentations......Page 417
15 Orthogonal Groups andTheir Representations......Page 444
16 Parameter Space of LieGroups......Page 482
17 Representations of theLorentz Group......Page 496
18 Roots and Weights......Page 527
19 Some Other Groups andAlgebras......Page 572
Part D: Topology......Page 619
20 Continuity of Functions......Page 621
21 Topological Spaces......Page 631
22 Homotopy Theory......Page 655
23 Homology......Page 679
Part E: Appendices......Page 699
APPENDIXA. Books and Papers......Page 701
APPENDIXB. Answers to Selected Exercises......Page 703
APPENDIXC. Index......Page 711

✦ Subjects

Algebra, Abstract;Algebraische Struktur;Algebras, Linear;Mathematical physics;Mathematische Physik;Moduli theory;Topological spaces