Formalising lecture notes from 1st year Imperial Mathematics course.
Currently planning to refactor M40002 with comments.
Chapter 1 - Sets and Logic
- C1. Law of the Excluded Middle
- C1. De Morgan's Laws
- C1. Transitivity, Contrapositives, and Distirbutivity
- C1. De Morgan's Laws for Sets
- C1. "For all" and "There exists"
Chapter 2 - Functions and Equivalence Relations
- C2. Function Composition
- C2. Injective, Surjective, and Bijective
- C2. Binary Relations
- C2. Predicates on Binary Relations
- C2. Quotients and Equivalence Classes
- C2. Well-Ordered Principle
- C2. Countability
- C2. Bounds, Supremums and Infimums
- C2. Completeness Axiom and its Corrollaries
- C3. Convergence of Sequences
- C3. Some Properties of Sequences
- C3. Algebra of Limits for Sequences
- C3. Subsequences
- C3. Cauchy Sequence
- C4. Definition of Convergent Series
- C4. Properties of Finite Sums
- C4. Properties of Infinite Sums
- C4. Different Tests for Convergence
- C5. Definitions of Continuity
- C5. Sequential Continuity
- C5. Algebra of Limits for Functions
- C5. Continuity of Polynomials
- C5. Intermediate Value Theorem
- C5. Open and Closed Sets
- C5. Uniform Continuity and Convergence
- C6. Definition of Differentiation
- C6. Some Basic Propterties of Differentiation
- C6. Fermat's Theorem for Stationary Points