What is Reddit's opinion of How to Think Like a Mathematician: A Companion to Undergraduate Mathematics?

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Houston's How To Think Like A Mathematician is pretty good. It covers pretty much all the basics (assuming you've at least made it through high-school math) and spends a lot of time focusing on how to think about the material, as opposed to just the material itself.

As someone just finishing their last year of Masters in maths undergrad, A lot of the stuff that you find in The Art of Problem Solving won't really show up until year 2 probably.

Here are the books I used in the summer before starting uni "How to think like a Mathematician" Bridging the Gap to University Mathematics A Consise introduction to Pure Mathematics

Those books were interesting reads for me so I would recommend them. I'll answer any questions you have if you want.

I can't think of a single book that captures this so cleanly. A few that have been useful:

• Kevin Houston's How to think like a mathematician?
• Lara Alcock's How to study as a Mathematics major? or any of her books on analysis.
• Polya's books on discovery.
• In general studying books that are Inquiry Based Learning focused. Example Burns's books on analysis/group theory/number theory or e.g. David Farmer's short books on group theory/knot theory. A lot of these books present theorems in a sequence of chunks which are intended to capture the process of how one would think of proofs for them.
• Oh I also like Devlin's book that someone else recommended.

https://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X

Look at Customers also bought, books about proofs, Real analysis, probability etc. Amazon suggests a bunch: Hammack, Courant/Robbins, Devlin, Polya: http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X/

Have a look at the courses that you'll be studying in your first year - find some introductory texts on them. Many universities publish course notes online - you might even be able to find some from your own university. Anything you do beforehand will make it easier once you get there.

Depending on your previous experience, there a couple of things to consider that will make the transition to university mathematics easier.

The main thing is proofs - if you're not comfortable setting out a (rigorous) proof, practise beforehand. Our recommended text was 'How to think like a mathematician' (Houston).

Another area is algebra - it helps to be very comfortable with standard algebra. You don't want to have any issues manipulating lots of Greek letters. For applied courses it helps to be sharp with standard derivatives and integrals, too.