Shears

by Antikythera

A Survey of Magical Fields and Attendant Mathematical Theory, Table of Contents (Interlude)

A Survey of Magical Fields and Attendant Mathematical Theory, Sixth Edition
by Spectral Melody, Wavefront, and Pivot Point

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Table of Contents

I Introduction & Background Requirements
II Changes from Fifth Edition
III Suggested Reading Orders
IV Notes on Spell Categorization

1 Animation (Force Magic)
1.1 Kinematics
1.2 Dynamics
1.3 First- & Second- Order Differential Equations
1.4 Isostatic Force
1.5 Thrust & Impulse
1.6 Telekinesis
1.7 Harmonic Oscillatory Motion
1.8 Higher-Order Differential Equations
1.9 Calculus of Variations
1.10 Coupled Oscillators
1.11 Nonlinear Systems

2 Projection (Barrier Magic)
2.1 Flat 2-Topes
2.2 Flat 3-Topes
2.3 (Approximately) Inelastic Collisions
2.4 Hyperplane Arrangements & Region-Counting
2.5 Curved Surfaces

3 Conjuration
3.1 Lattice Theory
3.2 Finite Distributive Lattices
3.3 Solid Conjuration
3.4 The Ideal Gas Law & Tracks-Well's Relations
3.5 Gas Conjuration
3.6 Fire Conjuration
3.7 Fluid Dynamics
3.8 Liquid Conjuration
3.9 Other Conjurations

4 Vivification
4.1 Integration of Surfaces
4.2 Complex Analysis
4.3 Thaumic Radiation (Electromagnetic & Magical)
4.4 The Magic Spectrum
4.5 MR Signatures
4.6 Magic Flux
4.7 EMR/MR Conversion
4.8 Illumination Magic
4.9 Magic Transference
4.10 Magic Fountains & Batteries, Natural & Artificial

5 Illusion
5.1 Plane Geometry
5.2 Linear Algebra
5.3 Visual Illusions
5.4 Kernel Convolution
5.5 Fourihay Series
5.6 Fourihay Transformation
5.7 Audio Illusions
5.8 Other Illusions

6 Mutation (Infusion)
6.1 Mutation Overview
6.2 Spell Interaction
6.3 Eigenvalues & Eigenspaces
6.4 Simplicial Complices
6.5 Suspension
6.6 Smooth Deformations & Homeomorphisms
6.7 Marked Hoof Chain Interpolation
6.8 Alteration
6.9 Infusion Interactions by Spell Type

7 Translocation (Space Magic)
7.1 Discrete Calculus
7.2 Nondifferentiable Symmetry Algebras
7.3 Teleportation (Objects)
7.4 Teleportation (Caster)
7.5 Smooth Topologies
7.6 Differentiable Symmetry Algebras
7.8 Spatial Deformation & Expansion

8 Identification (Metrics)
8.1 Information Theory
8.2 Error Propagation
8.3 Spatial Metrics
8.4 Chronometry
8.5 Spectrometry
8.6 Material Composition Metrics
8.7 Microstates, Macrostates, & Entropy
8.8 Thermometry
8.9 Magic Detection
8.10 Theoretical Limits on Certainty

9 Abstraction (Metamagic)
9.1 Spell Revision & Cancellation
9.2 Intermediate Logic
9.3 Sequencing
9.4 Conditional Structures & Passive Metrics
9.5 Subspells & Superspells
9.6 Enumerative Combinatorics
9.7 The Twelvefold Way
9.8 Rooted Trees & Hierarchical Spell Composition

10 Uncategorized, Non-Reproducible, or Otherwise Anomalous Magic

11 Noteworthy Open Problems
11.1 Materialism & the Physicality of Magic
11.2 Horn Physiology
11.3 Natural Magic Regeneration
11.4 Corrections to Energy/Momentum Conservation
11.5 Abjuration of Non-Magical Material
11.6 Non-Commutative Spatial Deformation
11.7 Divination
11.8 Temporal Magic
11.9 Non-Unicorn Magic

A Closing Remarks, Credits, & Thanks
B Bibliography
C Index
D List of Tables

Comments

[Reese]

Ooh, neat. :D
Though also very dense-looking. I'm not sure I'd be quite as enthused as Twilight to make the whole thing leisure reading. :)

Hm. Now I'm wondering if it's actually possible to conjure a true ideal gas. I'm guessing probably not, but it's an interesting idea. And some of my old professors joked about the stores selling the massless strings, frictionless pulleys, and the like used in examples... :)

Hm, horn physiology is an open problem? Interesting. Very interesting. What aspect(s) of it, I wonder? And "Materialism & the Physicality of Magic" makes me curious.

...As is the entirety of non-unicorn magic, it appears. :D

So, yeah, in short, a nice interlude, I think.

[Geminii]

"Marked Hoof chain", snerk. :)

[at least I amuse myself]

having a compendium of magical knowledge is good, but this seems like too many topics for one book. It's like if you had geology and neuroscience in the same text; I can't help but feel it's either hopelessly dense and good only as a reference for the already-knowledgeable (but such ponies would have better specialized books on everything they were interested in anyway), or unhelpfully general and good only for making the reader feel like they know a lot (much like the science books I read for leisure as a child).

[TheButcher]

How much thought went into where in the magic theory what Math goes. I remember on my last read through spending quite some time trying to guess the relevance.
6937185 There's some really cool books about as dense. Sure, non-autistic people are mostly unable to properly appreciate it, but I remember a really cool book titled "Analysis" had a similar ToC and I read that start to finish. This could be the textbook for a multi semester University course, like three modules.

My analysis professor was... Mean. Really mean. Maybe he was autistic and couldn't connect to the problems of his students. He was used by our university to separate the wheat from the chaff and probably was bitter about those of us who didn't put in enough work and treated his students unkindly and looked at us as if we were disgusting worms. But he gave us this book and it was excellent and his lectures were good, just hard and not at all optimized for ease of learning.

It's just everything he taught us was correct and beautiful and his proofs, especially those he did himself and didn't copy from elsewhere, were clever and fun. When, after surviving his exams a few times we asked intelligent questions he became a different person, bloomed in the math.

[Cursed Quill]

I wanna read it. Even this ToC is a balm.