How to Study for a Mathematics Degree

ISBN : 9780199661329

Lara Alcock
288 ページ
138 x 196 mm
  • Research-based advice on how to understand and learn undergraduate mathematics
  • Student-centred perspective that builds on the skills and expectations of typical new undergraduate mathematics students
  • Explicit discussion of common points of confusion about both mathematical concepts and the whole enterprise of proof-based mathematics
  • Practical guidance on how to keep up with lectures and manage the demands of multiple courses and tests
  • Challenging material presented in a friendly, accessible style

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 fundamental: the mathematics shifts in focus from calculation 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 good understanding 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.


Part 1: Mathematics
1: Calculation Procedures
2: Abstract Objects
3: Definitions
4: Theorems
5: Proof
6: Proof Types and Tricks
7: Reading Mathematics
8: Writing Mathematics
Part 2: Study Skills
9: Lectures
10: Other People
11: Time Management
12: Panic
13: (Not) Being the Best
14: What Mathematics Lecturers Do


Lara Alcock is a Senior Lecturer in the Mathematics Education Centre at Loughborough University. She studied mathematics to masters level at the University of Warwick, before going on to doctoral study in mathematics education at the same Institution. Prior to her present position, she spent four years as an Assistant Professor in Mathematics and the Graduate School of Education at Rutgers University in the USA, and two as a Teaching Fellow in Mathematics at the University of Essex in the UK. In her current role she teaches undergraduate mathematics, works with PhD students in mathematics education, and conducts research studies on the ways in which people learn, understand and think about abstract mathematics. She has been awarded National Teaching Fellows of 2015 by The Higher Education Academy.

Winner of the Annie and John Selden Prize for Research in Undergraduate Mathematics Education 2012

"one of the best books that a budding mathematician could read before going to university ... they will have a distinct advantage over those who don't bother to read it ... it is a very good and enjoyable read" - Graham Storr, The Mathematical Gazette

"Alcock's work will definitely join my list of recommended books for maths undergraduates during their first year." - Noel-Ann Bradshaw, Times Higher Education

"I would recommend this book to all students who are starting their studies of Mathematics as a major, but also those who are still in school and thinking about their choice of university subjects. It is a small, useful book." - Zuzana Hucki, London Mathematical Society

"I do recommend this book - it is an excellent source of information and advice for new and existing students about what to expect from a typical mathematics degree, and how and why they should be prepared." - Ken P. O'Neill AMIMA, Mathematics Today

"I suspect anyone reviewing this book will say they wished it had been available back in their day (indeed, the two quotes on the cover of my copy do exactly that). I, however, will go slightly further and say that not only do I wish this book had been available ten years ago, I also wish I would have had the sense to read it. The time between finishing school and starting university is short, and in all the excitement of buying your own kettle and secretly thinking how much you'll miss your old bedroom, it's easy to forget the main reason you're going. Reading one maths book won't ruin your whole summer (I hope!), and How to Study for a Mathematics Degree is a fairly short and rather enjoyable read which could give you a head-start in university life that pays off for years to come." - Michael Wallace, Significance

"I wish I had a book like this 20 years ago. It would have helped me manage my time and learn a lot more than I did at that age!" - Dr Magdalena D. Toda, Director of Undergraduate Studies Dept. of Mathematics and Statistics, Texas Tech University, USA

"This is an excellent book, which will be of great value to any sixth-former intending to embark on a mathematics-related university course, as well as to undergraduates already doing so. I cannot imagine a better book than this one for helping students to bridge the school-university gap. It would make an excellent gift for anyone thinking of studying mathematics at university and it belongs on every university reading list and in every school and university library." - Colin Foster, July Mathematical Gazette

"Making the transition from school-level to University-level mathematics is hard, in terms of the complexity of the subject matter, the rigour of thought, and the need to be able to study much more independently. This excellent and wide-ranging book engages with all these issues and more, giving a very helpful insight into what is coming for beginning undergraduates in mathematics or mathematics-related disciplines. I just wish this book had been available in my day!" - Dr Geoff Tennant, Senior Lecturer in Mathematics Education, Institute of Education, University of Reading, UK

"Great advice for students who want to study math. Actually, good advice for all students. And, good advice for adults and professionals too. Alcock's straightforward writing style and practical tips make the tallest mountains seem climbable with small steps." - Matthew Leingang, Courant Institute of Mathematical Sciences, New York University