I start a maths degree in September and the first module is Foundations: logic, sets, relations, proof technique. Everyone in the year above says it broke them, and not one of them can tell me what specifically broke. I did well at A-level and have never written a proof longer than two lines in my life. Is the content hard, or is it the format that gets people?
I did it the stupid way: I memorised proofs. It worked for the first two sheets because the questions were close to the lecture examples, then the sheet with quantifiers landed and I had nothing, because I had never actually built anything myself. Cost me a resit and a summer. Write bad proofs early and get them shredded in office hours.
If you have programmed at all, the closest feeling is your first strongly typed language after a loose one. The rules are not clever, there are just more places where you are not allowed to hand-wave, and the compiler is a human with a red pen. Same as programming, the fix is volume of small exercises rather than staring at one big one.
Careful with that analogy past the first month. Types tell you when you are wrong immediately, whereas a wrong proof looks exactly like a right one until somebody reads it. That delay is the actual difficulty and it is why people need a marker or a study partner early.
I marked that module for three years. The first assessed sheet was always a bloodbath and the exam never was, which tells you it is a translation problem rather than a capability problem. The single most common way to lose marks was quietly assuming the thing you were asked to prove, usually about halfway down. If a marker can point at a line and ask why, you have not finished.
Mild disagreement with the top answer. Nested quantifiers are genuinely hard content, not just unfamiliar format - swapping the order of two quantifiers changes the statement completely and most people take a month to feel that rather than check it mechanically. Do a hundred true or false questions on quantifier statements before term starts and you will have removed the worst of it.
@proof_pilar · 2mo ago · 2 replies
The content of Foundations is the smallest of any module you will take that year. What changes is that nobody cares whether you got the answer any more - they care whether every line follows from the one above it, and that is a skill you have never been asked for. Expect three weeks of feeling stupid and one week where it clicks.
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@listener_lena · 2mo ago
Week five for me too, and the thing that flipped it was copying one proof from the notes by hand every morning and then closing the notes and trying to reproduce it. Not memorising it - reproducing it. The gaps you cannot fill are exactly the steps you did not understand.
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