Taught by: Kuldip Singh
Name: Deng Guoyao Steve Eric (@steveeeveveve)
Content (Structure/Organization): 4
The course started with an introduction to philosophical perspectives about how math is used to understand the world.
The bulk of the course recaps math concepts that most likely would have been taught in pre-university, such as set theory.
The final weeks include experiments to prove concepts like the value of g.
Manageability of Workload: 3
The assignment that takes the most time to complete are the essays, which can be up to 3000 words long.
The group projects are more manageable as each member needs to answer a few questions each that mainly revolve around math proofs.
Ease/Difficulty of Attaining Grades:
Since the only feedback I was given by Prof was about my first essay which was not really applicable for my second essay in my opinion and the only grade was for the in-class quiz, I cannot give a good estimate of how liberal Prof is in giving grades.
Learning Value/Recommendation: 2
This course was mainly unhelpful, given that I have already learnt most concepts recapped. Prof also always said that he understood that most of us would have learnt these math concepts.
However, the discussion about philosophical thought was interesting.
About the Instructor:
Prof knows how to break down concepts to make people understand, and even sets up experiments to demonstrate.
He also gave me readings to refer to to boost my essay.
However, given that most seminars are actually lectures, this course is definitely one of the least engaging NUSC courses
Name: Ng Jia Yeong (@jy_jaywhy)
Content (Structure/Organization): -
Prof has a broad structure in mind, as shown by the four units I mentioned above. The topics in the first two units are relatively fixed because they serve to build foundations for understanding the last two units. However, the exact topics covered, especially in the last two topics are more flexible and Prof may choose to include or remove certain concepts from the syllabus depending on what he wants to focus on. In this iteration, he covered symmetries and quantum mechanics.
Prof is also receptive to student participation and feedback when pacing the class. If we look confused about a certain topic for example, he'll spend more time going through that topic, possibly leaving out some future topic from the syllabus as a trade-off. He'll also check in on us regularly to ensure we're following whatever he's teaching. The amount of time spent on each topic and the exact topics covered are thus variable.
Accessibility and Assessment: 4
There are four units in this module: reality, mathematics, science, and "mathematics and reality". Mainly, we covered how mathematical and scientific knowledge are constructed and how they relate to the philosophy of reality (metaphysics and epistemology). These concepts can be abstract and/or esoteric but Prof Kuldip walks through them slowly, so the learning process is very friendly. Just be prepared to spend some time on advanced concepts that are more confusing, if you're really curious about the content. Still, you don't have to really understand everything in class to do well -- you just need to know enough to write your essays.
1. Mathematical derivation
We spent a lot of time deriving advanced mathematical concepts such as geometry, calculus, and trigonometry starting from a few axioms. The process of mathematical derivation is useful for people who're curious about how mathematicians and scientists do their work. While a lot of us would have done something similar in pre-university mathematics, doing this kind of derivation in extremely simple areas such as arithmetic does give you a newfound appreciation of how the entire field of mathematics can be constructed from axioms.
2. Philosophy
Philosophy requires clarity of thought and argument and some serious critical thinking, which in my opinion makes it a kind of technical skill in itself. Among the philosophical questions we discussed are the relationship between mathematics and reality and the nature of mathematical and scientific knowledge. Given that both essays for this module involve some degree of philosophical inquiry, the class discussions and preparation for the essay does train you in philosophy which can be good preparation for future modules.
Manageability of Workload: 4
Workload is very manageable. There are regular problem sets done in groups which take less than 2 hours per submission and there are two individual essays which don't demand a lot of time -- unless you're interested in some concept that requires you to read up more. There are some readings to do but they introduce the relevant concepts well and I recommend reading them before class so the philosophical concepts aren't so foreign when Prof goes through them.
Ease/Difficulty of Attaining Grades:
I think Prof grades reasonably. Everyone is likely to do well in the group problem sets, so your grade will likely be determined by your class participation and individual essays. Knowing this, I think a good grade can be achieved if you're good at writing essays in the context of his essay prompts. Having looked at the past few reviews of this module, it seems that Prof has responded by giving us feedback on our first essay after he has marked it, so you can use that feedback to write a good second essay.
Learning Value/Recommendation: 4
This module is a good introduction to the titular subjects of mathematics and reality for the unacquainted. The Prof is nurturing, the learning curve is gentle, and workload is manageable. The main areas of learning would be an appreciation for mathematics and science as fields of study and not just "tools", and an introduction to the philosophy of reality. Admittedly it's not easy to think of ways in which this module will be directly useful for future studies/work, since this module is quite academic and theoretical. However for those working with mathematics and science I think it's always useful to learn about its foundations, such as how knowledge is constructed. It certainly piqued my interest in the work of mathematicians.
More generally, given my review I think this module is a good "first inquiry/Making Connections module". In a sense, you can practise your writing/reasoning skills in this relatively less demanding module before moving on to more difficult or challenging inquiries/Making Connections modules.
About the Instructor:
Prof Kuldip's passion about the subject shows in his teaching and he explains the concepts quite clearly; I enjoyed his delivery of the content. He's also friendly and as I mentioned earlier, frequently checks in with us that we can follow the pace of the class. One thing however that I think is a weakness is that he tends to ramble -- he can go on tangents which are interesting but don't quite answer your question, which takes up time in class. Otherwise, I think he's a good teacher and is well-suited to teach this module.
Name: Tan Joe Wel (@BunyPiza)
Content (Structure/Organization): -
The structure described below is based on the structure of the module in AY21/22 semester 1. Apparently from talking to Prof Kuldip he does change the content that is taught from semester to semester so the structure would change as well.
The module had an overarching structure that Prof Kuldip follows. It seems like there is a set of concepts that Prof Kuldip wants to teach us, and then the classes are rather flexible as long as he can teach all the concepts before the end of the semester.
I may be wrong on this but even the decision to teach structural realism at the end of the semester as like the ""culmination"" of the things taught throughout the semester seemed to only be made halfway through the semester. I remember Prof Kuldip saying that we did not need knowledge of quantum mechanics early on, but then teach us quantum mechanics later on as requisite knowledge for understanding structural realism.
Accessibility and Assessment: 2
I would like to add a disclaimer that I came into this module having quite a bit of background in the subject domain, so this module was rather accessible for me. What I am writing here is my best effort in imagining what someone who is like a pure FASS/humanities student would experience.
I would say that someone with no background in the module's subject domain can pick up the content in this module pretty easily. The difficulty in this module comes from the need to think logically, reasoning out each step of a mathematical argument to construct a mathematical proof which was needed for homework assignments. However, since the homework assignments were given as groupwork, it should not be too difficult since the ones that are stronger in logical reasoning can not only help, but also teach the other groupmates.
This semester in particular Prof Kuldip taught the concept of structural realism, which was not in previous semesters to make up for the inability to perform in-class experiments. Structural realism required knowledge of quantum physics, which can be difficult to understand. However, the scope of the final essay was very broad, and we could choose not to use structural realism in the final essay. That being said, the final half of the semester was highly focused on the concept of structural realism and many classes were dedicated to building up the requisite mathematical and physical knowledge required to understand the core ideas behind structural realism.
The module teaches logical thinking and logical reasoning, being able to take a mathematical concept, expanding on it and manipulating it one step at a time with justification, until we have a mathematical result that is universally true and is new mathematical knowledge. I think this skill is not particularly useful in office environments but is very useful in academia in scientific fields, especially when the papers you write will be used as a basis for furthering scientific knowledge.
For students looking to go into higher-level scientific and mathematical fields, the knowledge of how mathematical knowledge is generated and how scientists generate scientific knowledge is also invaluable and is something that I think mainstream NUS modules will not teach as well as in this module.
Manageability of Workload: 4
Again, maybe my description may not be entirely accurate because I did not need to do much additional research or to watch videos to learn the concepts, but I try my best to judge based on someone who has some knowledge and is somewhat interested in the subject matter.
The module consisted of 2 essays, 5 group homework assignments and a presentation coupled with the final essay. From my experience the first essay did not require much research at all, and the research that I did do was simply for citation purposes. The second essay however is more technical in nature and hence does require quite a bit of work. Personally, I spent an entire week just focusing on the essay, setting aside studying for finals for my other mods, and I was still not happy with the quality of my essay.
The homework assignments can be very variable in terms of workload, if you or someone in your group is very strong in logical thinking, each homework assignment can be finished by one person in two hours. However, since the questions are quite hit-or-miss (like if you know you know if you don't know you don't know), the homework assignments can certainly take up a lot of time if the group does not have anyone that can solve the questions quickly.
The deadlines that Prof Kuldip gives are all very generous (~ 1 month for essays, 2 weeks for homework assignments) so as long as you start early the workload can definitely be spread out.
Ease/Difficulty of Attaining Grades:
For the homework assignments, I imagine most groups would get full marks for them as long as they put in the requisite amount of effort (the assignments are not easy by any means, but since they are mostly mathematical proofs you know when you have the right answer). In my semester homework assignments constituted 40% of total grades, so simply put if you want a decent grade your group must get full marks for the homework assignments.
The other 60% are essays, which is dependent on knowledge of subject matter but also many other skills, so if your research skills and essay writing skills are good, you still can do well in this module even if you know nothing about mathematics or physics.
Prof Kuldip to me is very lenient in marking essays, but I have had rather strict professors judge my previous essays so I do not know in the grand scheme if things if he is lenient or not.
Learning Value/Recommendation: 5
As someone who is considering a career in academia and wants to research something in the field of physics, this module has been very eye opening to how modern physicists currently view the universe around us and how physics as a whole has arrived at structural realism as the most popular view of the nature of reality.
Mainstream NUS modules can teach us the knowledge that physicists have discovered over the years, but this module has taught me how physicists generated that knowledge.
About the Instructor:
Prof Kuldip is not only extremely knowledgeable on the subject matter and also high-level mathematics and physics, he is able to explain the difficult and counterintuitive concepts underlying the field in a way that is both clear and understandable to people without prior knowledge of this field. As someone who is interested in mathematics and physics, I have tried to explain these concepts to students and even my parents, and I must say that the way Prof Kuldip is able to explain these concepts is something I don't know if I ever can achieve.
Prof Kuldip is also very understanding of how difficult the concepts he is teaching are, and tries very hard to engage the class to ensure that we understand what he has taught.
Additional Comments/Word of Advice:
I know this module is not very popular amongst USP students, with some mentioning that they are turned away by the involvement of mathematics and physics. But if you are even just slightly interested in the philosophy of maths and science; how we obtained the mathematical results and scientific knowledge that we take for granted today, I will say that the module is not unfriendly to people who have no prior knowledge of mathematics and physics, and is also an extremely interesting module that Prof Kuldip teaches very well.
Content (Structure/Organization): -
The module was structured as a series of seminars. Around two-thirds of the seminars involved discussions of a reading or problem set within small breakout groups of 3-4 people, while the rest were delivered lecture-style. (In general, Prof Singh's schedule followed the units as stated in the syllabus but left out some topics within the units, such as Godel's Incompleteness Theorem in Unit 2.)
Assessments included a group assignment which tackled a problem set, as well as two essays (1.5k words & 3k words). The difficulty of the group assignment and first essay is quite reasonable, although the second essay might pose a challenge to those who find the content dry due to the flexibility of the essay prompt.
Accessibility and Assessment: 4
The mathematical content is fairly accessible for students who have done H1/H2 Mathematics. Prof Singh tries to cater to everyone regardless of their background in mathematics and is quite happy to explain concepts from first principles, although some may be put off by his long derivations (which often come up in class but aren't necessary in the module's assessments). However, students in math-intensive fields might be bored by his explanations.
The philosophical content is also manageable. Prof Singh takes a couple of lessons to go through content that he squeezed into a single seminar for USS, so as to make sure that everyone has a good grasp of the concepts.
This module teaches some basic philosophy of mathematics and trains students to think from an axiomatic perspective. However, the mathematical content covered in the seminars should not be new to most students.
That said, the essay prompts may provide an opportunity to delve deeper into specific topics in philosophy of mathematics, mathematical logic or mathematics in the natural sciences.
Manageability of Workload: 3
The workload of the module is average. Seminars require a bit of preparation time (not more than an hour) and the two essays are of reasonable length. Beyond breakout group discussions, no class participation was required outside of seminar time.
Ease/Difficulty of Attaining Grades:
A decent grade should be attainable in the module, although I can't be sure about this as Prof Singh was not transparent with the grading and did not release any marks or written feedback for the assignments/essays. However, he scheduled individual consultation sessions for every student to provide feedback on the first essay and offer advice on the second essay.
Learning Value/Recommendation: 4
As a CS & Math student, I thought the module gave me a better appreciation of the nature of mathematics and its connection with the natural sciences, although I didn't find it to be particularly eye-opening.
About the Instructor:
Prof Singh is quite knowledgeable about the subject domain of the module, given that he is a mathematical physicist and has been teaching this module for many years. He is also enthusiastic about the content that he teaches, although he sometimes gets carried away with his explanations.
Personally, I would have preferred the module to be organised with more overlap between the units. The current organisation of the module feels a bit shallow and rushed in its coverage of the content.
Additional Comments/Word of Advice:
I would recommend this module to those who are interested in learning about mathematics but find the subject intimidating, as Prof Singh is very willing to help students better understand the content. IMO, math/physics majors should only take up this module if they are willing to write essays on the module's content, as many of the seminars would cover content that they already know.
Content (Structure/Organization): -
Two parts - Philosophy and Mathematics + Physics. Both are a more in depth cut from what he does in USS. He delivers lectures in a mix of narration from handwritten notes and whiteboard, as well as class discussions based on readings and/or proving stuff. He does not really follow his prescribed syllabus; at the tail end of the semester he delved more into Physics instead of Metamath as was stated in the syllabus.
Accessibility and Assessment: 4
He is excellent at dumbing down content. For the first part of the module which touched on philosophy, he went quite slowly yet in depth into the various schools of thought. In the second half he did everything from first principles which was familiar from secondary school Math and Physics.
You can definitely takeaway math skills as well as a greater understanding of the world at large, through a new lens of math and philosophy. As I do math myself, this module was refreshing as I get to view both pure and applied math to view the world in different ways. However, if you are looking for an in depth Mathematics module - this is not really one.
Manageability of Workload: 4
The workload was not laid out very well at the start - rather, he emails us every lesson. So we had 2 essays and 1 group homework. There was supposed to be a test but it was cancelled (probably for online sem). Until now I am not very sure what the weightages are oof.
Ease/Difficulty of Attaining Grades:
I did well but I don't know how, in general, does he mark. He gave us feedback on our first essay but that's it. Even after the final grades arrived, I still don't know the exact comments on my final essay and the group project.
Learning Value/Recommendation: 4
I managed to learn more about how both spheres of math as well as physics connect to my understanding of the world.
About the Instructor:
He is clearly extremely knowledgeable as he does mathematical physics and although I doubted his ability to impart pure math and philosophy knowledge on us due to his background, he does it and also dumbs down content well. However, the structure of the module does not allow collaboration or optimisation of learning much, though not strictly his problem - could be online classes.
Content (Structure/Organization): -
It wasn't very structured as Prof didn't stick to the course outline, but I think this was probably because of the difficulties of covid teaching. The first part of the mod was a lot of philo, and the second part was a lot of math. This is a math inquiry but there is really a lot of philo and I felt that the essays were quite philo-based!
Accessibility and Assessment: 3
Math knowledge isn't needed but the mod will be tedious and boring if you hate math :p A mathy background helps with appreciating the proofs/appreciating this mod in general. Being good at math helps with writing proofs, but this was a small part of the mod (I think).
No background knowledge is needed for the philo part!
Appreciating the logic and methodology of deriving of mathematical knowledge
Manageability of Workload: 4
Workload for readings were reasonable, and generally the workload is chill. The workload for the final essay is not at all chill though, but maybe this applies to all USP mods HAHA
Ease/Difficulty of Attaining Grades:
Not sure how it compares to other mods cos this is my first USP mod, but Prof Kuldip seems reasonable and understanding!
Learning Value/Recommendation: 3
It was overall quite interesting because the philosophical aspect of math isn't something you come across very often, or even realise that it exists. I think some parts could have been more interesting and engaging though
About the Instructor:
Prof Kuldip is super passionate about math and physics and philo, and the derivation of 1+1 and basic math operations was q mindblowing. Unfortunately he's also a bit dry at some parts. I think he explains concepts well, but the concepts are also quite dry sometimes.
Name: Tan Yee Jian (@swampertx)
Content (Structure/Organization): -
It is about 4 weeks of philosophy + 8 weeks of math. The philosophy section goes through the different school of thoughts that describe reality (realism, representation, antirealism etc) briefly and investigate their methods. The math part consists of Prof Kuldip going deriving high school math from a few set of axioms. These axioms are a mix and match; from my understanding it is some field axioms for defining natural and rational numbers (real numbers not covered), and euclid's axioms for geometry. With these help we derive most things from trigonometry to calculus.
The mathematical knowledge required is only A-Levels equivalent, which is true, as Prof Kuldip will review these by deriving the results for us, and not much out of the syllabus. As this is a e-learning sem, all lectures are a single-sided lecture with us watching him derive theorems, not far from a mathematics lecture.
Assessment wise, two essays at the end of each sections. First essay was to give an example of a synthetic a priori statement and explain it; the second is a more open essay with some suggested topics, such as the beauty of mathematics, is reality mathematics etc.
Accessibility and Assessment: 4
If you have taken KI and likes math, this mod is probably too easy for you. But even if you are weak in both, the mod might not be very challenging either. So if you are in the middle, be ready for a chiller sem (other than essay writing weeks) if you take this.
It is about 4 weeks of philosophy + 8 weeks of math. The philosophy section goes through the different school of thoughts that describe reality (realism, representation, antirealism etc) briefly and investigate their methods. The math part consists of Prof Kuldip going deriving high school math from a few set of axioms. These axioms are a mix and match; from my understanding it is some field axioms for defining natural and rational numbers (real numbers not covered), and euclid's axioms for geometry. With these help we derive most things from trigonometry to calculus.
The mathematical knowledge required is only A-Levels equivalent, which is true, as Prof Kuldip will review these by deriving the results for us, and not much out of the syllabus. As this is a e-learning sem, all lectures are a single-sided lecture with us watching him derive theorems, not far from a mathematics lecture.
Assessment wise, two essays at the end of each sections. First essay was to give an example of a synthetic a priori statement and explain it; the second is a more open essay with some suggested topics, such as the beauty of mathematics, is reality mathematics etc.
Manageability of Workload: 5
Readings take about 1 hour at most per week for fast readers. For math lessons it is mostly sitting in and listen to lecture and nothing else. I would say pretty light for a USP mod.
Ease/Difficulty of Attaining Grades:
I got a very average grade for this module. The hardest part is that there is virtually no feedback for essays? I made the mistake (again) of not finishing drafts earlier to get feedback from the prof, but it could be also my writing is lackluster. Oh and math knowledge probably would not help you more than having given some thoughts about the beauty of mathematics and stuff. Coming from a math major who is really bad at writing :)
Learning Value/Recommendation: 2
I got to think a bit more about philosophy, but that is all. Mathematics knowledge is not too deep (again, I am a math student but I think there really is nothing beyond the A-Levels standard), so don't worry if you are weaker in math. Take it to think about philosophy stuff maybe.
About the Instructor:
Prof Kuldip puts in effort into teaching and does not use any comic sans slides for this module. Most mathematical derivations are handwritten, and I have no issues with the handwriting. You might fall asleep during the boring parts so try making some notes and copy down stuff to keep yourself awake. If there were more prompt feedback then it'd be better.