跳转至

Discrete Mathematics Lecture Notes

Translation status

This is an English companion version generated for the bilingual site. It summarizes and translates the structure of the Chinese source while keeping key mathematical and technical notation intact. A full line-by-line translation can be generated later with scripts/translate.py after an API key is configured.

Source

What This Note Covers

Lecture notes for discrete mathematics, covering logic and proofs, sets and functions, algorithms, induction and recursion, counting, and relations.

Study Outline

  • Logic and Proofs: Propositional logic, predicate logic, inference rules, and proof strategies.
  • Basic Structures: Sets, functions, sequences, sums, and matrices as discrete objects.
  • Algorithms: Algorithmic thinking, complexity notation, and common analysis patterns.
  • Induction and Recursion: Mathematical induction, strong induction, recursive definitions, and structural reasoning.
  • Counting: Permutations, combinations, binomial coefficients, and counting strategies.
  • Advanced Counting: Recurrence relations, inclusion-exclusion, generating functions, and derangements.
  • Relations: Relations, closures, equivalence relations, partial orders, and partitions.

Preserved Notation Examples

The Chinese source contains mathematical notation and technical symbols. Examples preserved for cross-language lookup:

  • $p \to q$
  • $\forall x P(x)$
  • $O(n\log n)$
  • $x+1=4$
  • $x$
  • $p,q,r,\ldots$
  • $\neg p$
  • $p$
  • $p \land q$
  • $q$

How to Use This Page

Use this English page as a quick map before reading the Chinese lecture note. The Chinese page contains the complete detailed content, formulas, examples, tables, and course structure. This companion page makes the topic discoverable to English visitors and gives Biying enough English context to explain what the note is about.