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.'”
This book is addressed to students, and I have in parallel found the book addressed to lecturers also very helpful, “Ideas from mathematics Education: An introduction for mathematicians” by Alcock and Simpson. This is free to download from Lara Alcock’s website.