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.
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
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.
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.