Question

I want to learn symmetry in Mathematics. Can anyone suggest me a nice intuitive book on it.

Answer 1

Geometric symmetry? Groups?

Answer 2

All I guess, needed it to go deep into Quantum mechanics and particle physics

Answer 3

Symmetry Rules: How Science and Nature Are Founded on Symmetry (The Frontiers Collection)

by: Joseph Rosen

Contents

1 The Concept of Symmetry
1.1 The Essence of Symmetry
1.2 Symmetry Implies Asymmetry
1.3 Analogy and Classification Are Symmetry
1.4 Summary

2 Science Is Founded on Symmetry
2.1 Science
2.2 Reduction Is Symmetry
2.2.1 Reduction to Observer and Observed
2.2.2 Reduction to Quasi-Isolated System and Environment
2.2.3 Reduction to Initial State and Evolution
2.3 Reproducibility Is Symmetry
2.4 Predictability Is Symmetry
2.5 Analogy in Science
2.6 Symmetry at the Foundation of Science
2.7 Summary

3 Symmetry in Physics
3.1 Symmetry of Evolution
3.2 Symmetry of States
3.3 Reference Frame
3.4 Global, Inertial, and Local Reference Frames
3.5 Gauge Transformation
3.6 Gauge Symmetry
3.7 Symmetry and Conservation
3.7.1 Conservation of Energy
3.7.2 Conservation of Linear Momentum
3.7.3 Conservation of Angular Momentum
3.8 Symmetry at the Foundation of Physics
3.9 Symmetry at the Foundation of Quantum Theory
3.9.1 Association of a Hilbert Space with a Physical System
3.9.2 Correspondence of Observables to Hermitian Operators
3.9.3 Complete Set of Compatible Observables
3.9.4 Heisenberg Commutation Relations
3.9.5 Operators for Canonical Variables
3.9.6 A Measurement Result Is an Eigenvalue
3.9.7 Expectation Values and Probabilities
3.9.8 The Hamiltonian Operator
3.9.9 Planck’s Constant as a Parameter
3.9.10 The Correspondence Principle
3.10 Summary

4 The Symmetry Principle
4.1 Causal Relation
4.2 Equivalence Relation, Equivalence Class
4.3 The Equivalence Principle
4.4 The Symmetry Principle
4.5 Cause and Effect in Quantum Systems
4.6 Summary

5 Application of Symmetry
5.1 Minimalistic Use of the Symmetry Principle
5.2 Maximalistic Use of the Symmetry Principle
5.3 Summary

6 Approximate Symmetry, Spontaneous Symmetry Breaking
6.1 Approximate Symmetry
6.2 Spontaneous Symmetry Breaking
6.3 Summary

7 Cosmic Considerations
7.1 Symmetry of the Laws of Nature
7.2 Symmetryof theUniverse
7.3 No Cosmic Symmetry Breaking or Restoration
7.4 The Quantum Era and The Beginning
7.5 Summary

8 The Mathematics of Symmetry: Group Theory
8.1 Group
8.2 Mapping
8.3 Isomorphism
8.4 Homomorphism
8.5 Subgroup
8.6 Summary

9 Group Theory Continued
9.1 Conjugacy, Invariant Subgroup, Kernel
9.2 Coset Decomposition
9.3 Factor Group
9.4 Anatomy of Homomorphism
9.5 Generator
9.6 Direct Product
9.7 Permutation, Symmetric Group
9.8 Cayley’sTheorem
9.9 Summary

10 The Formalism of Symmetry
10.1 System,State
10.2 Transformation, Transformation Group
10.3 Transformations in Space, Time, and Space-Time
10.4 State Equivalence
10.5 Symmetry Transformation, Symmetry Group
10.6 Approximate Symmetry Transformation
10.7 Quantification of Symmetry
10.8 Quantum Systems
10.9 Summary

11 Symmetry in Processes
11.1 Symmetry of the Laws ofNature
11.2 Symmetry of Initial and Final States, the General Symmetry Evolution Principle
11.3 The Special Symmetry Evolution Principle and Entropy
11.4 Summary

12 Summary of Principles
12.1 Symmetry and Asymmetry
12.2 Symmetry Implies Asymmetry
12.3 No Exact Symmetry of the Universe
12.4 Cosmological Implications
12.5 The Equivalence Principle
12.6 The Symmetry Principle
12.7 The Equivalence Principle for Processes
12.8 TheSymmetry Principle for Processes
12.9 The General Symmetry Evolution Principle
12.10 The Special Symmetry Evolution Principle

Answer 4

Will it be sufficient?

Answer 5

This will do to start with, it includes an intro to group theory.

There are references for when you need to go further (which sounds as if it may be a while yet).

Answer 6

Herman Weyl's book "Symmetry" is an enjoyable read. It is not a textbook, and has a rather odd combination of elementary and advanced concepts. But it will be fun; I had lots of enjoyment from it, and even found a mention of an architectural detail that I hope to visit someday.

Answer 7

I've been reading Rosen's book "Symmetry Rules". It takes a while to get into, but chapter 5 "Application of Symmetry" finally has some material of genuine interest. The discussion of Mach's experience with the compass needle (which I read about in Weyl's book) was quite helpful.