How to Study for a Mathematics Degree

by Lara Alcock

Every year, thousands of students go to university to study mathematics (single honours or combined with another subject). Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more the mathematics shifts in focus fromcalculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a goodunderstanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

Genres: Mathematics, Nonfiction, Science, Academic, Self Help, Stem

289 pages, Kindle Edition

First published November 8, 2012

Reviews

[Ali · Rating 4 out of 5]

Yes, I read this book from cover to cover, and it was good but I got lost but Alcock told me it was okay to get lost as I wasn't an undergraduate yet and that made me feel good. This is definitely a good book to reference whilst studying, it doesn't just end if you will but keeps going with you. If you're a mathematics student that is.

[William Schram · Rating 4 out of 5]

Informative. The book goes over what to expect from your mathematics major. It explains that you must relearn or unlearn habits and ideas acquired through years of mathematics classes. It takes off the training wheels. There are fewer examples, you have to make do with less hand-holding, and you have to do as much as you need to without being told.

[juli · Rating 2 out of 5]

This book is significantly less helpful 3/4 of your way through a mathematics degree, and infinitely less interesting than whatever your lecturer is on about “smuggling drugs across the US-Mexican boarder.”

[Hannah · Rating 5 out of 5]

I found this book to be a comforting, insightful read which I believe has given me invaluable advice for the degree I am about to begin.
I enjoyed the fact that the book was constantly anticipating questions I might ask, as well as providing solutions to problems I hadn’t even considered I would have. Reading this felt like being given a hug, being given a lifeline, and I highly recommend it to any student nervous about starting their mathematics degree.

[Ninia · Rating 4 out of 5]

i DISSECTED this

[Alice Bell · Rating 4 out of 5]

An interesting read as a teacher of A level. Some useful insights, many relevant to studying A level too, which I will share with my students. A good read for anyone going off to study any mathematical type degree.

[Isaac · Rating 3 out of 5]

Good book on what to expect in university maths courses. If read prior to undergraduate studies you definitely be thinking correctly about your studies.

[Sebastian Szymczyk · Rating 3 out of 5]

The first 170 pages are informative because they truly explain how to start thinking like a Mathematician. This has been what I have been missing in my mathematics-heavy subjects at university, as my lecturers often took the approach of teaching us mathematics like (I am anologising here) a cookbook which ended up confusing the class a lot. This was because we didn't know how to treat the mathematics in an effective and proper way, which made it very difficult for understanding edge-cases or in trying to solve problems that differed from stereotypical ones that could be easily solved using a plug and chug approach. Definitely, the first 170 pages have helped me to approach mathematics more like a true Mathematician and not someone who simply wants to pass subjects.

I had given the book 3/5 stars, because I found that from page 170 onwards it started reading like a general guide to how to study for any degree. While the advice found in pages 170-270 may be useful for someone whose never studied at university before, for those that have, it can seem very redundant.

[Fotis Koutoulakis · Rating 5 out of 5]

Splendid little book on getting oneself ready for University level mathematics.

The first part was a small primer on some mathematical objects and proofs, alongside some rudimentary guidance on how to manipulate them.

The second part was less relevant to me, because it applied to students at a maths department (and how for instance, to catch up if they're behind, or manage their time before exams, etc), but I still went through it and find some interesting bits and pieces here and there.

[Mahad · Rating 5 out of 5]

A very clean book that clearly teaches students want to expect at university, and how to cope with the sudden jump from high-school maths to undergraduate modeules. Notably, the Panic chapter may be very helpful for anyone who is currently struggling for their degrees. I enjoyed a lot of the notes about how to learn from lectures and lecture notes, and in particular, the idea of making 'module concept maps' is very useful to me. Would recommend. :)

[Linnéa · Rating 4 out of 5]

skulle egentlig gjerne ha lest denne i/sommeren etter vg3, men den er uansett fin og informativ.
gir meg også ord på ting jeg har hatt i tankene selv, og som jeg kanskje kan vise til fremtidige elever i matematikk!

[Khalid Alqassimi · Rating 5 out of 5]

Alcock goes over all the necessary bits of information one would need to embark on a mathematical journey. Inspirational and short, she resonates with mathematicians-to-be. I wish I had read this book before entering university.

[Emilio Vilches · Rating 4 out of 5]

Good read before going to University

Its ok. Some good pieces of advice here and there, it was a quick read. If you are already deep in your university math degree maybe it's not worth the buy.

[Andrew · Rating 4 out of 5]

this book helped me adjust to the type of maths done in uni. I always expected my maths be like the type done in secondary/high school, so it was nice to learn that the big change from that type of maths to this was a common experience.

[Anita · Rating 5 out of 5]

Changed my attitude towards proofs and reading mathematics - excellent read

[Joao Almeida-Domingues · Rating 4 out of 5]

1.2 - Post Problem Questions
1.3
3. Definitions Appendix
7
— reading break down example
— concept maps
— Synthesis

[Emily Watts · Rating 5 out of 5]

A very good insight into what uni maths could require/ be like

[James Israel · Rating 5 out of 5]

A nice book that must be read before getting a math degree in college

[Caleb Osako · Rating 4 out of 5]

Definitely worth reading, but not always a page-turner. The way other chapters are referenced so frequently gets a bit annoying, but overall very helpful.

[Jasmine · Rating 5 out of 5]

A life-saver in the post first term panic! Highly highly recommend!

[Lukas Rubikas · Rating 2 out of 5]

Useful, informative book that I have no douby *will* be useful, at least in some small way, for anyone preparing to study for a mathematics degree.
However, there are a couple of reasons why this is not a five star book - first, that can fairly be attributed to the reader's own ignorance, this is geared towards undergraduates. I was a graduate student that got into a highly mathematical postgraduate course - so I assumed this was just perfect for me. And some ways it was, some ways it was not - throughout the book you will be assumed to be an undergraduate and will be given advice that is a couple of years late and you had learned it a hard way already. I just wished it emphasized its perfect target audience better, as the word "undergraduate" appeared only once on the 30-lines-long back cover of this book which I didn't read, something I got used to doing when reading fiction. So part of it is my mistake indeed.
However I believe the author stated in the book that the students from other disciplines that have to dive deeper into mathematics will still find the book useful. This is true and I probably would have read it even having knowledge I described in my first point. However, that viewpoint seems to be dropped throughout the book, around when introducing the correct notation and proofs and asking the reader "can you see why?" without giving the answer. I felt that was a bit ironic for a book that emphasizes on mathematical correctness and rigorousness does not state those answers, that would surely not take any significantly more pages as it's already a fairly long (taking into account its small print) read and, most importantly, claiming that the read is useful to students in other disciplines who chose maybe a few of mathematics modules. I absolutely doubt that those students will "see why" and will find it frustrating.

[Cody · Rating 4 out of 5]

Great guide to those transitioning from high school mathematics to university mathematics. It has lots of tips on how to do proofs, how to read and write mathematics, and how to interact with the lecturers and other students. Also, Lara Alcock describes aspects on what it's like being a lecturer or a mathematician, which I did not know before.

Recommended for anyone studying mathematics in university.

[Electric-guitar · Rating 5 out of 5]

Really enjoyed this book. Written as if Lara Alcocks is speaking directly to you. Book is inspirational and the advice can be applied to many other subjects or parts of life :)
Lots of tips and further web-links given.

Thanks

[Jessica Wang · Rating 5 out of 5]

A very real guide to what it will be like a university studying mathematics and how to adjust to it. The part about what to do when panicking about getting behind on work was really reassuring that it happens to everyone now and then. :)

[Maria · Rating 2 out of 5]

me pareceio un poco aburrido y superficial, pero fue un easy read la verdad

[eny · Rating 5 out of 5]

not me finally finishing this in my third yr 🫣

[Amanda · Rating 4 out of 5]

Is a great book that really prepared me for university, introducing me to some of the terms used in my first year.