Here's my (pharpend) basic outline for the book. It's extremely rough at this point and will probably be gutted and slaughtered in its entirety.
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Chapter 1, Introduction
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Chapter 2, functions and types
- Define types
- Define functions
- Comprehension notation
- Domain & codomain
- Functions that output types
- Functions that output other functions
- Currying
- Injective functions and surjective functions
- Inverting functions
- Useful functions
- id
- (.)
- flip
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Chapter 3, Propositions
- Proofs are functions
- Types are propositions
- The life and times of Haskell Brooks Curry
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Chapter 4, Special sets
- Magmas
- Semigroups
- Categories
- Monoids
- Groups
- Rings
- Fields
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Chapter 5, fancy functions
- Homomorphisms
- Isomorphisms
- Endomorphisms
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Chapter 6, monomials
- Examples
- How to manipulate them algebraically
- Graphs of lines
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Chapter 7, polynomials
- Examples
- How to manipulate them algebraically
- Graphs of lines
- Quadratic formula
Let us make this our goal for now, then we will move on.
- Chapter 8, exponential functions
- Chapter 9, logarithms
- Chapter 10, trig functions
This is a good segue to talk about Complex numbers
- Chapter 11, complex and imaginary numbers
- Chapter 12, Complex functions
- Chapter 13, Complex algorithms
Good segue to talk about the concept of dimensions
- Chapter 14, Dimensions
- Chapter 15, Parametric functions
- Chapter 16, Complex parametric functions
- Chapter 17, functions that go from F^n to F, where F is a field.
- Chapter 18, functions that go from F to F^n, where F is a field.
- Chapter 19, functions that go from F^n to F^m, where F is a field.
We'll next want to approach systems of equations. first\ matrices
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Chapter 20, Matrices
- Matrix addition, multiplication, etc
- Matrices as linear functions
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Chapter 21, Systems of equations
- What is a system of equations
- using matrices to solve for them
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Chapter 22, Vector spaces
... Basically go through linear algebra
- Chapter 35, calculus
... Go through calculus and differential equations
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Chapter 52, Statistics
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Appendix B - boring stuff
- Introduction of the primary authors (Peter Harpending, Randy Brown).
- Book license
- How to contribute