This semester I am teaching a new course, Basic Concepts in Mathematics, at the Guangdong Technion – Israel Institute of Technology, Shantou.
The notes will be written as a diary for teachers.

The complete text of the course will be updated here:
Download PDF

Structure of the course

  • Methods of proving — parity, induction, invariants, pigeonhole principle.
  • Naive set theory — unions, intersections, Cartesian products, Venn diagrams.
  • Number theory and equivalence — remainders, congruences, countable/uncountable sets.
  • Orders and lexicographic induction — lexicographic order.

Collaboration and AI

Students were encouraged to collaborate and to use AI only as a reviewer, not as an author.
The diary includes a full section explaining how to:

  1. attempt each problem before asking for help,
  2. use AI to improve clarity,
  3. reflect on understanding and learning process.

Characters used on the cover:

辵 chuò walk, walking

遒 qiú powerful 道 dào road 達 dá extend

邑 yì city

邻 lín neighbour 郭 ɡuō outer city wall