TEACHING PAGE OF DANIEL NG
Tutorials
In 2017 October-December, I taught Analysis 2A (Uniform convergence, metric spaces, compactness).
In 2018 February-April, I taught Algebra 1B (vectors and matrices) and Algebra 2B (rings and fields).
Algebra 1B
Spaceship: tutorial on spans, linear independence and bases. Also: how to write proofs.
Analysis: Summary of revision tutorial on continuity. Also: some 2017 past paper solutions.
Exam studying tips
Here are some techniques I gathered when I was studying at Cambridge.
- Start doing past papers as soon as possible!
If you've done the homework sheets throughout the term then you are more than ready to start doing past papers.
You don't need to know all the definitions by heart to start attacking your first paper. Here are 3 reasons why you should.
- The most common definitions/theorems will come up and those that are not important won't.
This naturally creates a space reptition system (SRS), which is a technique proven to be very effective for the human brain.
In this way, you will have a clearer of idea of what's important and what's not: e.g. do I need to learn this proof?
Do not be afraid to look up your notes when you do past papers. This is part of the learning process.
- It gives you the context in which the definitions/theorems come up. When they appear in context, you are more motivated to learn them.
- You will be less nervous during exams, having seen so many past papers already.
Note: this method only works if you do A LOT of past papers.
If there are no past papers/not enough, then look up past papers from another university and ask your tutor which questions are relevant.
Don't worry if the first past paper feels hard. By the time you get to your 10th it will be easy (easier).
- Don't start studying from the very first chapter. When you start revising, your motivation is the highest at the beginning.
By the time you get to the last chapter (that is, if you ever manage to get there), you will have been exhausted.
If you've actually been listening in lectures and tutorials during term, you already have a rough idea of what a "vector space" or a "ring" is, so it's okay to start studying from the middle/end.
Lecturers love setting 2/3 of the questions on the last 1/3 of the course. If you follow advice 1, then you follow this advice automatically because past papers don't start from chapter 1.
- Recommended order of revising: past papers, then redo example sheets, then learn compulsory theorem-proofs.
- Use your tutors! Email/message/whatsapp/snapchat them.
If there are no solutions for a certain past paper, you can ask your tutor.
Alternatively you can ask the smartest student in your tutorial group.