Advice for Discrete Math Paper 3

[Kaito]

So I'm taking Math HL and I love it. It's really fun and challenging etc and the core isn't much of a problem. My school offers the discrete math option and as we all know finals are coming up. I've realized that there are about 70+ theorems/corollaries/proofs etc for number theory and a lot of terms to memorize for graph theory as well as a couple of algorithms. I understand most of it but I'm having a bit of trouble memorizing everything, not to mention some of the proofs.

Does anyone have any advice on what to focus on and what difficult proofs are worth memorizing for paper 3?

Thanks in advance.

[batmansmaster]

Quote

70+ theorems/corollaries/proofs

Are you sure you did not learn a significant amount of material outside of the syllabus? IIRC there were for sure less than 10 proof we might need to be able to know unless you are talking about the possible variation in questions they could ask. 

For number theory, I find it is useful to understand what tricks to use to be able to do the proof and in what different ways you are able to carry out mathematics in modular arithmetic. If you do have enough time and proof do not make sense to you it could make sense to memorize at least the start or the hard points so you could, in theory, do it, however, understand and practice the common thought processes are useful in my opinion. Also feel free to ask me about proof if you do not get them, I should be able to remember/pick it up quickly.

Tbh for graph theory, I do not remember there being many proofs, however, I do remember a common question was to proof a formula through reasoning, by drawing graphs with a certain number of vertices and nodes and further reason how adding vertices would verify the formula through some reason.

 

[Kaito]

13 hours ago, batmansmaster said:

Are you sure you did not learn a significant amount of material outside of the syllabus? IIRC there were for sure less than 10 proof we might need to be able to know unless you are talking about the possible variation in questions they could ask. 

For number theory, I find it is useful to understand what tricks to use to be able to do the proof and in what different ways you are able to carry out mathematics in modular arithmetic. If you do have enough time and proof do not make sense to you it could make sense to memorize at least the start or the hard points so you could, in theory, do it, however, understand and practice the common thought processes are useful in my opinion. Also feel free to ask me about proof if you do not get them, I should be able to remember/pick it up quickly.

Tbh for graph theory, I do not remember there being many proofs, however, I do remember a common question was to proof a formula through reasoning, by drawing graphs with a certain number of vertices and nodes and further reason how adding vertices would verify the formula through some reason.

 

Thanks for the advice!

Well, at my school we're using the Haese books and the book mentions about 70 theorems/corollaries and their proofs. I'm not entirely sure which ones I'm expected to know. I'm pretty good with modular arithmetic so I'm not too worried about that. However, while doing a past paper 3 I stumbled upon a question asking me to prove that GCD(m,n) * LCM(m,n) = mn.

I think I would be able to figure this one out on my own but I'm worried about the time limit. Usually with proofs I end up taking different approaches and then scrapping them and starting over and I feel like I don't really have time for that. So I was wondering which of the proofs are worth memorizing (at least to a certain degree) to help save time on paper 3.

 

[batmansmaster]

On 4/28/2018 at 12:53 PM, Kaito said:

Thanks for the advice!

Well, at my school we're using the Haese books and the book mentions about 70 theorems/corollaries and their proofs. I'm not entirely sure which ones I'm expected to know. I'm pretty good with modular arithmetic so I'm not too worried about that. However, while doing a past paper 3 I stumbled upon a question asking me to prove that GCD(m,n) * LCM(m,n) = mn.

I think I would be able to figure this one out on my own but I'm worried about the time limit. Usually with proofs I end up taking different approaches and then scrapping them and starting over and I feel like I don't really have time for that. So I was wondering which of the proofs are worth memorizing (at least to a certain degree) to help save time on paper 3.

 

 

I used the Cambridge book, which imo was great. I never looked the Haese option book though.  I did remember some proofs but roughly 1-2 and some of the number theory properties with divisibility, (1 was a graph theory one for sure) the rest you should be able to work yourself once you have the idea/strategy for most types of proofs.