Preparation for MS221

So – I’m approaching the end of my third OU module, MS2211, and the exam is in a few days.  I missed all the local revision tutorials through being away with work2 and, despite some good intentions, I am woefully behind.  Consider this a crammer’s guide for learning university level mathematics in 3 and a half days 😉3.

MS221 consists of four blocks: block A covering sequences, conics and geometry; block B covering iteration and matrices; block C covering more complex4 integration and differentiation and Taylor Polynomials; and block D covering complex numbers, number theory, groups and logic and reasoning5.  The exam allows an annotated handbook and so it is fairly easy to prepare given a few days of dedicated effort, which (if you’re reading this in time, may help6. Continue reading Preparation for MS221

Proof by Induction

In my last post I talked a little about logic as it applies to generic statements.  Now it’s time to think about more mathematics proofs and different techniques.  As part of MS221 there are two proof types that we need to consider: proof by exhaustion and proof by induction.  This all lays the foundations for building more and more complex mathematical statements so it’s important to get the basics right.

Dominoes
Wikipedia: Domino effect

Firstly, proof by exhaustion.  This simply means that we try every possible valid input and check that the result is true.  A single false result would disprove our proposition.  So let’s consider an example:  Continue reading Proof by Induction

Proof and logic

The final part of block D in MS221 of my OU Maths degree is all about mathematical proofs and deduction, which I find absolutely fascinating.  A big part of this block was clarity on some logical fallacies that we encounter all the time and that many people use to trick us into agreeing with their arguments.

XKCD: CorrelationXKCD: Correlation

With one week to go until the General Election in the UK it seems like a good time to revisit logic and proof from both the political and mathematical sides.

Continue reading Proof and logic

Public-Private Keys

This morning I had a tutorial for module MS221 of my OU Maths degree.  In addition to complex numbers, groups, and proofs one of the topics we covered was RSA encryption and decryption.  As I’m a little behind in my study I’m going to use this post to explain how this type of encryption works (even though this is already covered elsewhere e.g. in wikipedia).   You’re going to need a little maths to follow this, but hopefully not too much!

Firstly, a quick recap.  Public-private key encryption means that you have a pair of keys – the public one you can give out without a care and anyone can use this to encrypt messages to you.  Without the private key to decrypt, it’s practically impossible to decipher the encrypted messages, so as long as you actually keep your private key private, everything is (relatively) safe.  As an aside, if your private key is obtained by someone else then they will be able to read your messages and you would never know.

Continue reading Public-Private Keys

Taking my degree seriously?

I have to say it – I’m three modules in to my OU degree and, while I regularly promise to set aside time for study, I always find myself doing no more that a three hour tutorial and then a further 3-6 hours doing the assignments and this has done the trick so far.  There’s always something that gets in the way and eats up that time – something I’d rather be doing… and it’s not because I’m not enjoying it – I love maths and am somewhat annoyed with myself that I’m missing out on the richness of the OU course by cutting straight to the specific examples I need to complete the coursework.

So why am I not doing the work?  Possibly the key reason is that I am currently able to get away with it.  Why spend more time when I can do what I’m doing and get distinctions?  Surely this is an efficient use of my time.  I’m hardly a role model to students anywhere by doing this… but I doubt I’m the first.

Continue reading Taking my degree seriously?