| PART I – IN THE BEGINNING |
| |
Foreword |
| Chapter 1 |
Introduction |
|
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The Symmetry of Reality |
| PART II – FIRST STEPS |
| Chapter 2 |
What is a Group? |
|
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A Collective Noun |
|
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Setting a Good Example |
|
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Smooth Operators |
|
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The Formal Answer to “What is a Group?” |
|
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In Addition it May be Noted… |
|
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Modular Arithmetic |
|
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The Symmetry Angle |
| Chapter 3 |
Shifting Shapes |
|
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Let’s Get Physical |
|
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Turning Triangles |
|
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On Further Reflection… |
|
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Movers and Shakers |
|
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Turtles all the Way Down |
|
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Cavorting Cubes |
| PART III – EXTENDING THE CONCEPT OF NUMBER |
| Chapter 4 |
Rationality and Reality |
|
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Multiplying the Multitude |
|
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Divide and Conquer |
|
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A Magic Mirror |
|
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Expanding our Horizons |
| Chapter 5 |
Tabular Amasser |
|
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The Matrix is Everywhere |
|
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What have Matrices ever done for us? |
|
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Laying our Cards on the Table |
|
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The Perennial Question |
| Chapter 6 |
Matrix Revolutions |
|
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Turning the Tables |
|
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Direction of Travel |
|
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Generic Gyrations |
|
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From Dihedral to Orthogonal |
|
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Moveable Mirrors |
| Chapter 7 |
Imaginary Battleships |
|
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Mare Complexionis, The Sea of Complexity |
|
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Fleet Manoeuvres |
|
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‘Fessing Up |
|
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The Complex Numbers as a Group |
|
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amo, amas, amat… |
|
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Non-imaginary Numbers |
|
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The Sign of the Four |
| PART IV – GROUP DECOMPOSITION |
| Chapter 8 |
Simplicity |
|
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Subsets and Subgroups |
|
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Exceptions to the Rule |
|
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Primed for Action |
| Chapter 9 |
Normality |
|
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What Passes for Normal Round Here |
|
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The Deciding Factor |
|
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Subgroups and Cosets |
|
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Using Cosets to Create Quotient Groups |
| Chapter 10 |
Profundity |
|
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A Simple Algorithm |
|
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The Quotient Group of a Maximal Normal Subgroup |
|
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Multiplication Redux |
| PART V – SOLUTIONS OF POLYNOMIAL EQUATIONS |
| Chapter 11 |
Root of the Problem |
|
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Many Names, Many Numbers |
|
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Roots of Unity |
|
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From Algebra to Geometry… |
|
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From Geometry to Trigonometry… |
|
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From Trigonometry to Group Theory… |
| [Chapter 12 |
Mont Évariste] |
|
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TBC |
| PART VI – UNITARY & SPECIAL UNITARY GROUPS |
| Chapter 13 |
First Contact – U(1) |
|
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To Infinity and Beyond… |
|
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Grandes Complications |
|
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1 × 1 is Complex… |
|
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U(1), SO(2) and Isomorphism |
| Chapter 14 |
Determination – U(2) & SU(2) |
|
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2 × 2 is more Complex… |
|
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The Shape of Things U(2) Come |
|
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U(2) Can be a Group |
|
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Singular Determination |
|
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SU(2) a Worked Example |
|
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A Study in Quartet |
| PART VII – VECTOR SPACES & VECTORS |
| Chapter 15 |
It’s Space Jim… |
|
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The Red Arrows |
|
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How do we Group Vectors? |
|
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Tipping the Scales |
|
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Being Productive |
| Chapter 16 |
…But not as we know it |
|
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Pastures New |
|
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The Nature of Space (not Time) |
|
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Back to Bases |
|
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Exempli Locis |
| Chapter 17 |
Matrices Redux |
|
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More Marvellous Matrix Multiplications |
|
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Establishing Ownership |
|
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A Good Characteristic |
|
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Eigenlob für Eigenvalues |
| PART VIII – LIE ALGEBRAS & LIE GROUPS |
| Chapter 18 |
The Lie of the Land |
|
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Getting Crotchety |
|
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Crossing Space |
|
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Skews me! |
|
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A Singularly Uncommon Algebra? |
|
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Without a Trace |
| Chapter 19 |
Making Connections |
|
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su(2) |
|
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su(3) |
|
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u(1) |
|
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As Smooth as Silk |
|
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Going off on a Tangent |
| Chapter 20 |
Power to Truth |
|
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There and Back Again |
|
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What difference does it make? |
|
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In Summary |
|
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Euling the Wheels |
| [Chapter 21 |
SU(3) and the Meaning of Lie] |
|
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SU(3) Unmasked |
|
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Putting a New Spin on Things |
|
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The Journey of a Thousand Miles… |
|
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TBC |
| PART IX – SYMMETRY AND THE QUANTUM REALM |
| [Chapter 22 |
Probable Cause] |
|
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Chances Are… |
|
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As Easy as π |
|
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A Lack of Discretion |
|
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Chain Reactions |
|
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Improbable Complexity |
|
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Of Bras and Kets and Quantum States… |
|
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…of Double Slits and Things |
| [Chapter 23 |
Plceholder] |
|
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TBC |
| Chapter 24 |
Emmy |
|
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Emmy’s Life and Hard Times |
|
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Lights… Camera… Action! |
|
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Going Green |
|
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The Amazing Theorem |
| [Chapter 25 |
The Final Frontier] |
|
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TBC |
| PART X – CLOSING THOUGHTS |
| |
[Epilogue] |
| |
Acknowledgements |
| |
About the Author |