Discrete maths option (HL)

[hanniexx]

I find with this option, it's split into 3 parts:

1. graph theory (like Prims, etc)

2. maths counting like Euclidein theory, etc.

3. proofs.

Basically, I get very stuck on how to approach the proofs. How do you guys approach it, so you not want proof you need to work with, etc?

Also, what do you guys think is the best way to revise for this exam - just question after question?

Thank you!

[soadquake981]

Well I agree with the first two parts that you mentioned (graph theory and number theory), but I believe that all the proofs on the exams fall under the category of number theory. Many of them have to do with divisibility (involving linear congruences and such). I believe that if you understand number theory well enough, which is by no means easy, you will do well on the proofs.

The only other studying method I can think of is to look at as many markschemes for previous tests as possible, and try to find common patterns in the way IB writes its proofs.

[hanniexx]

Hmmm yeah that is a good idea.

Sometimes I have seen the odd proof for graph theory too. Like there was one about different coloured lines and different coloured planar areas and you had to prove it had so many sections or something.

But yeah, I'll definitely look at markschemes and what not.

There's a like a few number theory proofs, liked the Chinaman proof, or something like that too. My textbook makes it look much more complicated than I think it is.

Are there any good websites you may know which are good at explaining/going over discrete maths?

Thank you!

[soadquake981]

Haha, you mean the "Chinese Remainder Theorem"?

And yes, now that you mention it, there are some proofs regarding graphs. However, as far as I can remember, they're usually pretty short and simple. A lot of them utilize Euler's relation v+e-f=2.

And no, unfortunately I don't know of any good website. Most of the review I've been doing is from past exams and review packets that my teacher has put together over the years. It's strange that there are no plain-language websites about discrete math!

[hanniexx]

Haha, yar woops, that's the one! XP

Ahh okay.

Yeah, 'tis rather annoying. But I'm guessing with Discrete being a pretty new side to maths, it's not too common to find lots of stuff on it. Unfortunately.

Are you using a textbook?

Thank you for your help darl, and good luck with it!! ^^

Oo I just found an OSC revision book for it. But it's 2006 - do you know if the Discrete syllabus has changed since then?

Edited May 11, 2010 by hanniexx

[soadquake981]

We used a textbook to initially learn all the material, but we borrowed those books from another school and we don't have them now.

And no, sorry, I don't know if the syllabus has changed since 2006. I wouldn't expect so!

[tdubthebassist]

I find with this option, it's split into 3 parts:

1. graph theory (like Prims, etc)

2. maths counting like Euclidein theory, etc.

3. proofs.

Basically, I get very stuck on how to approach the proofs. How do you guys approach it, so you not want proof you need to work with, etc?

Also, what do you guys think is the best way to revise for this exam - just question after question?

Thank you!

'maths counting' is wrong word of putting that.

I would mix 2 and 3 to call 'number theory'

[hanniexx]

I find with this option, it's split into 3 parts:

1. graph theory (like Prims, etc)

2. maths counting like Euclidein theory, etc.

3. proofs.

Basically, I get very stuck on how to approach the proofs. How do you guys approach it, so you not want proof you need to work with, etc?

Also, what do you guys think is the best way to revise for this exam - just question after question?

Thank you!

'maths counting' is wrong word of putting that.

I would mix 2 and 3 to call 'number theory'

I just forgot the name of it, that's why I said maths counting

[tdubthebassist]

I find with this option, it's split into 3 parts:

1. graph theory (like Prims, etc)

2. maths counting like Euclidein theory, etc.

3. proofs.

Basically, I get very stuck on how to approach the proofs. How do you guys approach it, so you not want proof you need to work with, etc?

Also, what do you guys think is the best way to revise for this exam - just question after question?

Thank you!

'maths counting' is wrong word of putting that.

I would mix 2 and 3 to call 'number theory'

I just forgot the name of it, that's why I said maths counting

don't worry about it. It is just Mathematician being super weird

[lightofthedawn]

Hi

I took Further Mathematics SL (which requires all the options, including Discrete Math). I'd suggest that the best way to get comfortable with the idea of proof is to first be thoroughly familiar with proofs that you find in textbooks. Granted, memorization on its own doesn't help you gain mastery, but after a while you will observe similarities in approaches. Even if you cannot immediately obtain a complete proof, you will have certain ideas how to start (and as you'll learn, IB is generous with its "method marks"). For instance, if you are given the fact that two numbers a and b are co-prime and are required to prove something about them, you will automatically think of using the fact that there exist integers x and y such that ax + by = 1. Stuff like that.

As for which textbooks, I highly recommend the Cambridge University Press one (http://www.cambridge.org/us/education/ib/maths.htm) if you can manage to get your hands on it. I borrowed mine from the library (and returned, and borrowed... repeat for 1.5 years haha).

All the best! It is not easy to jump from standard problem-solving drill type questions to rigorous proof, so don't be discouraged.

[Anxious070610]

Hi

I took Further Mathematics SL (which requires all the options, including Discrete Math). I'd suggest that the best way to get comfortable with the idea of proof is to first be thoroughly familiar with proofs that you find in textbooks. Granted, memorization on its own doesn't help you gain mastery, but after a while you will observe similarities in approaches. Even if you cannot immediately obtain a complete proof, you will have certain ideas how to start (and as you'll learn, IB is generous with its "method marks"). For instance, if you are given the fact that two numbers a and b are co-prime and are required to prove something about them, you will automatically think of using the fact that there exist integers x and y such that ax + by = 1. Stuff like that.

As for which textbooks, I highly recommend the Cambridge University Press one (http://www.cambridge.org/us/education/ib/maths.htm) if you can manage to get your hands on it. I borrowed mine from the library (and returned, and borrowed... repeat for 1.5 years haha).

All the best! It is not easy to jump from standard problem-solving drill type questions to rigorous proof, so don't be discouraged.

Do you know of any other great textbooks??

you know...like a version for dummies??

hahaha i'm having some issues to understand discrete maths..and i wish to be fully prepared, before i take the course