Tag: Mathematics

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

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