To add to my previous blog-post on “what is the most important thing we learn at University”: the fact that mathematics graduates have learnt to think (as well as learnt to think logically, and critically) and have experience in learning complex difficult new material is one of the main attractions to employers. See this Cambridge Maths Admissions leaflet for some “destinations” information and data on average salaries.
Many mathematicians are very fond of saying that, and it is only too true! You cannot learn maths without doing maths. In this post I’m going to explain some different ways you can find and try of doing maths for different learning purposes.
Many students starting to study mathematics need some time until they realise the exact role of formal definitions in (esp. pure) mathematics. I love how Lara Alcock puts it: “when mathematicians state a definition, they really mean it.” (How to Study for a Mathematics Degree, OUP 2012, Chapter 3). Continue reading
This year, in my Groups IA course in Cambridge, I am trying to sprinkle my lectures with useful facts about how to think about mathematics, how to learn mathematics, and how to develop good intuitions as well as good working habits. I will try to post these thoughts on this blog as I go along. Most of these ideas come from a brilliant book by Lara Alcock, “How to Study for a Mathematics Degree”. To quote from her introduction: “Part 1 could be called ‘Things that your mathematics lecturer might not think to tell you.'”
As I have been preparing for the new academic year over the past summer, I have been discovering the concepts of growth mindset and maths mindset mainly through the book “Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching” by Jo Boaler from Stanford. It is an amazing read and I cannot recommend it highly enough!
in which we find out about permutation properties of Möbius maps and start looking at cross-ratios.
in which we view Möbius maps via matrices, and compose geometrically meaningful maps.
in which we meet the unitary group and start exploring Möbius maps as transformations of the Riemann sphere.
in which meet the orthogonal group and we rotate and reflect in two and three dimensions.
in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.