Following on from my previous video Ten Ways to Improve Your Chances of Success in GCSE Maths here is the next video in my Ten Ways series for A Level Maths and Further Maths.

As with my last video I’ve tried to focus more on the habits that I think a good A Level student needs to have to have a better chance of being successful in their studies. I didn’t want the video to just be a list of what I think are the most important topics to revise for A Level maths because I’m sure that there are a ton of videos already out there that do just that – personally I don’t think that you should necessarily prioritise any topics over others as they could all come up in your exams as ‘big questions’.

Also as with my last video this video has come about through my own personal observations as a professional maths tutor in Leeds of my A Level maths students and noticing common themes (I didn’t want to say denominator!) amongst those who do well and get the grades that they want and those who unfortunately don’t do so well. Believe me when I say it isn’t just down to knowing the topics – you have to have the right attitude to the subject to be successful at A Level maths.

I hope that you find the video useful – it’s a bit longer than I expected it to be but if you think it’s too long then … well … I guess just don’t watch it to the end, though I really hope you do watch it to the end because there might be some useful stuff for you. I’d love to know if you have any of your own tips and advice that you’d like to share with other A Level maths students. If I get enough suggestions then I might make another video to share some of your tips!

This is a video that I made recently which brings together some of what I’ve learned through my time as a professional maths tutor in Leeds tutoring GCSE maths students. I’ve noticed that each year there are a similar set of problems that many GCSE maths students will have to deal with so hopefully this video will give you a bit of advice about how you could avoid some of the pitfalls that some students end up falling into and how you can become a much more successful GCSE maths student that can go on to ace your GCSE maths exams!

The video is more about your habits and attitudes to maths as a subject and isn’t just a list of topics to revise and shortcut methods or anything like that. I do mention a couple of important topics that I think every GCSE maths students needs to know but there are so many videos and resources out there that cover the individual topics that there wasn’t really anything new that I could add – everything is already out there. What I certainly did think that I could add were my unique personal experiences as a tutor!

I’ve tutored lots of GCSE maths students – particularly for GCSE higher level – over the last half a decade and I’ve got some real insight into the things that trip students up. Working one to one with people means that I can really find out how they work, their strengths, weaknesses and what really causes them problems when it comes to GCSE maths.

I hope that this video will be useful to you. I plan to do some more videos on A Level maths and QTS Numeracy over the coming weeks – so keep an eye out for those. If you have any questions for me about your GCSE maths studies then just get in touch – I will get back to you as soon as I can with any answers that I can give.

I never really used to be interested in history in school – in fact I couldn’t wait to drop the subject. I just couldn’t see the point in thinking about the past when it just didn’t seem relevant to me or anything for that matter. Historians out there will be pleased to hear that I take a very different view of history now and, although I wouldn’t say that I’m a fully fledged historian, I do enjoy reading the odd history book.

My interest in mathematics and history come together when I read mathematics books written by some of the greatest mathematical thinkers in history. It’s amazing to see how problems were solved by the ancient Greeks using the technique of application of areas which is mostly a lost art now and has been replaced by algebraic techniques; or to see how philosophical issues have shaped the development of mathematics such as whether the Axiom of Choice is valid as an axiom.

Well here are my top historical mathematics books with a brief explanation of what’s inside

  • Principles of Mathematics – Bertrand Russell Bertrand Russell is one of my favourite philosophers and mathematicians in history. Not many can match Russell for his depth of knowledge – even today. Don’t be confused by the title – this is not a book on simple mathematics; it’s certainly not for the faint-hearted and will take a good chunk of time to plough through. Most of what is inside the book would now be considered a bit dated but at the time this was ground-breaking stuff.
  • Elements – Euclid Probably one of the most famous mathematics books ever written. I still think it’s incredible that this book was still the standard geometry textbook in most schools up until the 19th Century – about 2000 years after it was written in ancient Greece. Nowadays most textbooks are thrown out after a year to bring in the next lot of ‘updated’ textbooks. If any book shows how timeless mathematics is then this is it.
  • Treatise on Conic Sections – Apollonius of Perga This is another book by an ancient Greek but is nowhere near as well known as Elements. It’s a shame because inside this book are some of the most inventive uses of the technique known as application of areas to prove various properties of the conic sections – circles, ellipses, parabolas and hyperbolas. Again, although the technique has now been replaced with algebraic techniques the solutions are nothing short of beautiful.
  • Contributions to the Founding of the Theory of Transfinite Numbers – Georg Cantor Cantor is the father of the infinite in mathematics. His works took mathematics in a whole new direction – a very controversial direction at the time it would seem. When you read this book it all seems so straightforward to deal with the infinite but the imagination required to come up with some of the arguments and proofs is off the scale.
  • The Continuum – Hermann Weyl This is an unusual book as Weyl decided that he wasn’t happy with the way that mathematics was working at the time – he felt that mathematics had inadvertently created different ‘levels’ and there was a number system on each of these levels that comes about through the logic used and numbers on different levels were being combined when they shouldn’t be. He aims to demolish these levels and create a single number system but his logical system pays a price for this. It sounds like the plot to a novel! Weyl’s philosophy changed several times throughout his life and this gives a bit of insight into his personal philosophy at the time it was written. He later abandoned this work in favour of a diffeent philosophy but then, after a few years, he changed his mind and thought it was a good work after all.

So there you have it – some of my favourite maths books from history. I love reading these historical maths books because it feels like you’re reading the minds of some of the greatest mathematicians, philosophers and scientists to have ever lived. I’m sure there’s loads more of these books for me to read – I’ll be on the lookout for some good ones to read. By the way – some of these books are in the public domain now and you can download some of them for free from the internet. I prefer to buy copies of the actual book but just so you know.