Mathematics in Lean
1. 引言
2. 基础
3. Logic
4. Sets and Functions
5. Elementary Number Theory
6. Structures
7. Hierarchies
8. Groups and Rings
9. Linear algebra
10. Topology
11. Differential Calculus
12. 积分和测度论
Index
Mathematics in Lean
Mathematics in Lean
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Mathematics in Lean
1. 引言
1.1. 入门指南
1.2. 概述
2. 基础
2.1. 计算
2.2. 证明代数结构中的等式
2.3. Using Theorems and Lemmas
2.4. More examples using apply and rw
2.5. Proving Facts about Algebraic Structures
3. Logic
3.1. Implication and the Universal Quantifier
3.2. The Existential Quantifier
3.3. Negation
3.4. Conjunction and Iff
3.5. Disjunction
3.6. Sequences and Convergence
4. Sets and Functions
4.1. Sets
4.2. Functions
4.3. The Schröder-Bernstein Theorem
5. Elementary Number Theory
5.1. Irrational Roots
5.2. Induction and Recursion
5.3. Infinitely Many Primes
6. Structures
6.1. Defining structures
6.2. Algebraic Structures
6.3. Building the Gaussian Integers
7. Hierarchies
7.1. Basics
7.2. Morphisms
7.3. Sub-objects
8. Groups and Rings
8.1. Monoids and Groups
8.2. Rings
9. Linear algebra
9.1. Vector spaces and linear maps
9.2. Subspaces and quotients
9.3. Endomorphisms
9.4. Matrices, bases and dimension
10. Topology
10.1. Filters
10.2. Metric spaces
10.3. Topological spaces
11. Differential Calculus
11.1. Elementary Differential Calculus
11.2. Differential Calculus in Normed Spaces
12. 积分和测度论
12.1. 初等积分
12.2. 测度论
12.3. 积分