"If his patterns are more permanent than theirs, it is because they are made with ideas." ~ G. H. Hardy
AY24/25 Sem 1 Lecturer: Prof. Goh Jun Le Tutor: Prof. Goh Jun Le Topics: - Logic ☹ - Proof techniques - Induction - Set theory ☹ - Functions - Number theory - Equivalence relations - Cardinality and choice ☹ - Real numbers Assessment: - Homework: 24% - Midterm: 26% - Final: 50%
Firstly, the fact that this module is titled Basic Discrete Mathematics is wrong, well reason being that a chapter on the real numbers is present here. Anyway, I liked the bulk of this module's contents (it is clear that I detest a few topics) as well as the interesting questions in tutorials, homework assignments, midterm, as well as the final examination.
When I study Mathematics, I am very much interested in intriguing results. Here are some notable questions that we encountered throughout the semester.
I have two detailed write-ups regarding the two interesting questions mentioned in Tutorial 7 which are titled Conjugacy and A Word on Projection Maps. These tie in very nicely with content from MA2202 (Algebra I) and MA3201 (Algebra II) respectively. To be precise, we only discuss the Ring Theory part of MA3201 in the write-up (in particular, the Chinese remainder theorem).
However, there were a number of things which I disliked and could not get used to in the module. Firstly, there is no known recommended reference text. Under Prof. Goh's iteration, I would say that the closest reference text to his materials would be Simon G. Chiossi's `Essential Mathematics for Undergraduates'. It is an extremely useful book which would be very handy for all four years of Undergraduate Mathematics. Also, Prof. Goh mentioned at the start of the semester that \(\mathbb{N}\), the set of natural numbers, would constitute all positive integers as well as zero. Sure, I would just take it as it is.
Also, there was the legendary \(e_a(p)\) and \(R_b(a)\) notation which appeared in Number Theory. Clearly, these are unconventional notations which mean the following: for any positive integer \(a\), its prime factorisation is given by \[a=\prod p^{e_a(p)}\] which is unlike the usual \[a=p_1^{\alpha_1}\ldots p_k^{\alpha_k}.\] Also, \(R_b(a)\) denotes the remainder when \(a\) is divided by \(b\), which is essentially the modulo \(b\) operation! Prof. Goh mentioned that he wanted us to strictly adhere to these notation and the results we deduced in class. Again, sure, I would just take it as it is.
Lastly, I do not see a purpose in studying Mathematical Logic and Set Theory in detail. I feel that it would be more useful and interesting if the bulk of these were replaced with Graph Theory, but then again the whole course on Discrete Mathematics would have significant overlap with CS1231S.
Expected grade: A- Final grade: A