PART I – IN THE BEGINNING 

Foreword 
Chapter 1 
Introduction 

– 
The Symmetry of Reality 
PART II – FIRST STEPS 
Chapter 2 
What is a Group? 

– 
A Collective Noun 

– 
Setting a Good Example 

– 
Smooth Operators 

– 
The Formal Answer to “What is a Group?” 

– 
In Addition it May be Noted… 

– 
Modular Arithmetic 

– 
The Symmetry Angle 
Chapter 3 
Shifting Shapes 

– 
Let’s Get Physical 

– 
Turning Triangles 

– 
On Further Reflection… 

– 
Movers and Shakers 

– 
Turtles all the Way Down 

– 
Cavorting Cubes 
PART III – EXTENDING THE CONCEPT OF NUMBER 
Chapter 4 
Rationality and Reality 

– 
Multiplying the Multitude 

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Divide and Conquer 

– 
A Magic Mirror 

– 
Expanding our Horizons 
Chapter 5 
Tabular Amasser 

– 
The Matrix is Everywhere 

– 
What have Matrices ever done for us? 

– 
Laying our Cards on the Table 

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The Perennial Question 
Chapter 6 
Matrix Revolutions 

– 
Turning the Tables 

– 
Direction of Travel 

– 
Generic Gyrations 

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From Dihedral to Orthogonal 

– 
Moveable Mirrors 
Chapter 7 
Imaginary Battleships 

– 
Mare Complexionis, The Sea of Complexity 

– 
Fleet Manoeuvres 

– 
‘Fessing Up 

– 
The Complex Numbers as a Group 

– 
amo, amas, amat… 

– 
Nonimaginary Numbers 

– 
The Sign of the Four 
PART IV – GROUP DECOMPOSITION 
Chapter 8 
Simplicity 

– 
Subsets and Subgroups 

– 
Exceptions to the Rule 

– 
Primed for Action 
Chapter 9 
Normality 

– 
What Passes for Normal Round Here 

– 
The Deciding Factor 

– 
Subgroups and Cosets 

– 
Using Cosets to Create Quotient Groups 
Chapter 10 
Profundity 

– 
A Simple Algorithm 

– 
The Quotient Group of a Maximal Normal Subgroup 

– 
Multiplication Redux 
PART V – SOLUTIONS OF POLYNOMIAL EQUATIONS 
Chapter 11 
Root of the Problem 

– 
Many Names, Many Numbers 

– 
Roots of Unity 

– 
From Algebra to Geometry… 

– 
From Geometry to Trigonometry… 

– 
From Trigonometry to Group Theory… 
[Chapter 12 
Mont Évariste] 

– 
TBC 
PART VI – UNITARY & SPECIAL UNITARY GROUPS 
Chapter 13 
First Contact – U(1) 

– 
To Infinity and Beyond… 

– 
Grandes Complications 

– 
1 × 1 is Complex… 

– 
U(1), SO(2) and Isomorphism 
Chapter 14 
Determination – U(2) & SU(2) 

– 
2 × 2 is more Complex… 

– 
The Shape of Things U(2) Come 

– 
U(2) Can be a Group 

– 
Singular Determination 

– 
SU(2) a Worked Example 

– 
A Study in Quartet 
PART VII – VECTOR SPACES & VECTORS 
Chapter 15 
It’s Space Jim… 

– 
The Red Arrows 

– 
How do we Group Vectors? 

– 
Tipping the Scales 

– 
Being Productive 
Chapter 16 
…But not as we know it 

– 
Pastures New 

– 
The Nature of Space (not Time) 

– 
Back to Bases 

– 
Exempli Locis 
Chapter 17 
Matrices Redux 

– 
More Marvellous Matrix Multiplications 

– 
Establishing Ownership 

– 
A Good Characteristic 

– 
Eigenlob für Eigenvalues 
PART VIII – LIE ALGEBRAS & LIE GROUPS 
Chapter 18 
The Lie of the Land 

– 
Getting Crotchety 

– 
Crossing Space 

– 
Skews me! 

– 
A Singularly Uncommon Algebra? 

– 
Without a Trace 
Chapter 19 
Making Connections 

– 
su(2) 

– 
su(3) 

– 
u(1) 

– 
As Smooth as Silk 

– 
Going off on a Tangent 
Chapter 20 
Power to Truth 

– 
There and Back Again 

– 
What difference does it make? 

– 
In Summary 

– 
Euling the Wheels 
[Chapter 21 
SU(3) and the Meaning of Lie] 

– 
SU(3) Unmasked 

– 
Putting a New Spin on Things 

– 
The Journey of a Thousand Miles… 

– 
TBC 
PART IX – SYMMETRY AND THE QUANTUM REALM 
[Chapter 22 
Probable Cause] 

– 
Chances Are… 

– 
As Easy as π 

– 
A Lack of Discretion 

– 
Chain Reactions 

– 
Improbable Complexity 

– 
Of Bras and Kets and Quantum States… 

– 
…of Double Slits and Things 
[Chapter 23 
Plceholder] 

– 
TBC 
Chapter 24 
Emmy 

– 
Emmy’s Life and Hard Times 

– 
Lights… Camera… Action! 

– 
Going Green 

– 
The Amazing Theorem 
[Chapter 25 
The Final Frontier] 

– 
TBC 
PART X – CLOSING THOUGHTS 

[Epilogue] 

Acknowledgements 

About the Author 