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

An academic professional

I’m three days in to my new role and, while there is some run of the mill development that I’m managing there’s also a very exciting project just starting that I’ll be taking from the very beginning based on a discussion I had with the CEO on my first day.

This new secret project means I’ve got to become an expert in Deep Learning and also all the changes in AI and since I wrote my own thesis.  I discovered very quickly that the way I knew was the “old way” and that machine learning has come on very considerably in a short space of time. So the past few days I’ve regressed into academic mode.

Continue reading An academic professional

3D Printer Part 1 – binding

So, today I decided to make a start on the 3D printer project.  I’ve got 15 parts now, enough to get started and also to get to a point where I can have something that moves I hope (I have a plug and circuit board in these issues).  The first 12 issues cover “stage 1” and that’s what I hoped to be covering in this first guide.

I had the mantra “read everything carefully before starting” ingrained as a child so I have a Pavlovian response when opening a  kit to read the instructions. In this case the instructions are spread across several magazines and the logical thing to do was to put them all in the binder first.  The binder takes 15 issues and looks like this:

The unfilled binder
The unfilled binder

This instructions say:

  1. Open the top and bottom flaps
  2. Remove all pegs and insert into the holes in the spine
  3. Close the top flap clipping into place
  4. Open the magazine in the centre and slip the first peg into the top of the  centre fold
  5. Do the same at the bottom, pulling the peg out slightly first
  6. Close the bottom flap, clipping into place.

Continue reading 3D Printer Part 1 – binding

But is it correct?

I love science.  My parents fostered a great sense of curiosity in me and the need to learn.  Part of this was the ability to question what was presented and come to my own conclusions as to whether it was correct or not.  It was okay to change my mind as new evidence was presented, included my own experiences and this is how we grow as individuals.

At university we were taught to go to the primary sources for information – not the summaries or reviews but read the original papers and decide whether the research was sound for ourselves.  Corrections are regularly published for papers (or retractions made) and these are not always referenced when the original paper is cited, perpetuating the error.  (I don’t want to get into a discussion of specific examples as this will detract from the point of this post).

Continue reading But is it correct?

New Horizons

So, most people know by now that in a week’s time I start a new role.  After 12 years of working for established business both small and large I am joining a start up in an area at the current edge of what is possible in computer science.  I’m very much looking forward to having my technical and scientific abilities stretched as far as they’ll go and, not unsurprisingly, the immersion in a new venture where the focus is on the solution and not why things can’t be done (often the case in established companies).

I have a reading list as long as the references for my own thesis to get through in the next few weeks so I can become an expert in my new field: deep learning and artificial intelligence.  One of the first things I’ll be doing is attending the ReWorkDL summit in Boston, MA, which is just a fascinating line up of some of the leading people in this space.  All being well I will be presenting at the 2016 summit.

I’ll be tweeting throughout the event with thoughts and comments and will do a summary post afterwards.

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?

Creating a 3D printer

At the start of 2015 I saw an innocuous sponsored tweet in my twitter feed for a week by week build your own 3D printer.  I’ve wanted one for a while but never really felt I could justify the cost on a toy… and then I saw the opportunity to build one myself and spread the cost… I used to spend more on coffee in a week so the justification was made and I signed up.

The printer I’m building is from 3D Create and Print who haven’t endorsed or sponsored anything in this blog.  Each issue comes with a part for the printer and a magazine with a design, with occasional extra free gifts.  I now have the first 11 issues, which includes the power adapter, so it’s probably a good time to start putting the parts together.

I’ll be filming how to assemble the printer along with a blog of any gotchas since, as anyone who has ever assembled flat pack furniture knows, sometimes just following the instructions isn’t always enough 🙂