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NUS Math Module Review: MA3205 Set Theory

Assessment Structure:

Homework: 4%

Midterm Exam #1: 23%

Midterm Exam #2: 23%

Final Exam: 50%

This is a pure math module that leads up to the path of mathematical logic in the pre-requisite tree (MA5219/MA5220 Logic and Foundations of Mathematics I/II require MA3205). The module’s topics include set and operations, pairing, products and relations, Russell’s paradox and proper classes, natural numbers, comparing size of sets, quasi/partial/linear/well-orders, countable and uncountable sets, ordinals and ordinal arithmetic, cardinals and cardinal arithmetic, and some applications of Axiom of Choice. There is no main textbook of reference.

Class size is small so lectures and tutorials are held in a classroom without webcast. Attendance is not compulsory for both, but one needs to submit their weekly homework during the tutorial session. Tutorial sessions simply involve Prof. Dilip explaining the solutions for tutorial problems.

Homework is split into 11 parts (one per tutorial session), and only the best 10 out of 11 will be graded and each are of equal weightage. Each homework consists of only one problem provided in the lecture notes (all tutorial/homework problems are contained in the lecture notes). However, I strongly recommend students of this module to try out all problems in the notes as they are very good practices which reinforce the concepts taught.

Concepts taught in set theory are generally extremely intuitive, but it guess less intuitive in the second half. The first half of the course is mostly a repeat of MA1100. After that comes orders and ordinals/cardinals, which were not introduced in MA1100. This module is notorious for the difficulty of understanding ordinal/cardinal arithmetic, so students should expect to spend more time understanding them. In this academic year, Prof. Dilip rearranged the order of the chapters taught, and started ordinal/cardinal arithmetic at around week 10, making it easier for students to understand the content.

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