The most interesting “Category Theory” （范畴论) for Programmers course** III **by Dr. Bartosz Milewski , a follow-up of last year’s course II.

**Prerequisites**:

- Fundamental of Category Theory: Functor, Natural Transformation, etc. (Course II Series)
- (Nice to have) : Basic Haskell Functional Programming Language. (Quick Haskell Tutorial)

1.1: **Overview Part 1**

Category Theory (CT) = Summary ofALLMathematics

Functional Programming = Application of CT

Philosophical Background:

- Math originated 3,000 years ago in Geometry by Greek Euclid with
**Axioms**and deductive （演译）**Proof-driven****Logic**. - Geometry = Geo (Earth) + Metry (Measurement).
- Math evolved from 2-dimensional Euclidean Geometry through 17 CE French Descartes’s
**Cartesian Geometry**using the 13CE Arabic invention “**Algebra**” in**Equations**of n dimensions: $latex (x_1, x_2,…, x_n) $, $latex (y_1, y_2,…, y_n) $ - Use of Algebra: 1) Evaluation of algebraic equations (in CT: “Functor”) ; 2) Manipulation. eg. Substitution (in CT :…

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