Excelling in University-level Mathematics, and not Just Surviving


In this blog I discuss some of the critical study skills that students of mathematical disciplines such as engineering ought to acquire. A lot has been written on study skills, and I have gone through some of the key writings to distil the essential elements that a first year student embarking on a mathematically-oriented degree programme ought to know and make use of.

Acquiring Lifelong Study Skills

Most high school students are entirely dependent on their teachers to provide them with everything they need to succeed in their studies. Whilst this approach is effective at pre-university level, it is less effective at university, and fails entirely when the student graduates and starts practising as an engineer(Felder, 1993).  This is because on the job there are no teachers, lectures or homework. There are only problems, and there are only acceptable and unacceptable solutions. To thrive in such an environment, a student has to acquire the ability to identify problems, acquire relevant knowledge, both new and old, and apply this knowledge to the resolution of the problem. A student can acquire such an ability during university through identifying effective study techniques and honing them to perfection.  Such study skills, which include the ability to attack and resolve problems, enable students to become experts in their chosen professions(Chapman, 1946).

For you to succeed in your studies, and in your latter life, you must earnestly want to learn (Chapman, 1946). Equally important as well, you must apply some thought towards finding the best methods to carry out the most important activity in your life as a student, namely to study (Chapman, 1946). This includes gaining an understanding of the learning style that suits you best as an individual (Felder, 1993), as well as appreciating the most appropriate study techniques for your course. It is essential to note that unlike the humanities and social sciences, the study of mathematics is a process that requires progressive step-by-step learning of fundamentals, with each lecture building up on the previous lecture, and higher level courses being dependent on the fundamentals taught in lower level courses(Rosenkrantz, n.d.).

How to study university mathematics

University level mathematics is quite different from high school mathematics(University of Hull Skills Team, 2013). In pre-university courses a topic is developed and then usually followed by a period of practice, with the teacher present to consolidate learning. At university material is covered at a much faster pace, and in general, successive lectures normally move on to new topics. At university it is therefore essential that a student takes responsibility for keeping up with the work. In addition, as a student, you need to realise that most of the learning takes place outside the lectures, in private self-study, and in informal study groups as well as in tutorial workshops.


Make it a point to attend all lectures, and avoid cherry picking (Reeve, 2009), no matter how much you think of  the relevance or irrelevance of the lectures. During the lecture, think through what the lecturer is saying and writing.  Try to work through each step yourself, and if you don’t follow ask questions there and then. Don’t be afraid to ask, even if you think that the question is a silly one.  If it is not feasible to ask your question during the lecture, then make it a point to ask the lecturer at the end. As you are well aware, it is quite easy to lose concentration during lectures and to fall asleep. However, you should realise that maintaining concentration is solely a matter of practice and self-discipline, and you must work at it (University of Cambridge Faculty of Mathematics, 2014).

Pre-lecture Preparation

You understand a lecture best if you come to the lecture with some idea of its subject matter (Chapman, 1946). This means that prior to each lecture you need to preview the lecture material. This should be easy as most lecturers now post their lectures on the university virtual learning environment (VLE) well before the lecture. Try to formulate questions in your mind about the material to be covered. This enables you to better manipulate the lecture material and therefore to better understand it. Identify the key elements to be covered in the lecture, and note any new concepts, formulae and equations to be presented in the lecture(Hubin & Ridell, 1977).

Post-Lecture Activities

You will save an immense amount of time if you always get to grips with one lecture before going on to the next(University of Cambridge Faculty of Mathematics, 2014). Immediately after the lecture, find time to review and edit your notes. Look for important ideas and relationships in the work covered in the lecture, and also try to relate it to previous work, and to other course modules that you may be taking(Hubin & Ridell, 1977). Naturally, as you do this questions will emerge. Don’t regard university mathematics as a competitive sport(University of Cambridge Faculty of Mathematics, 2014). Rather, talk to fellow students, ask them questions and collaborate with them. However, remember that collaboration does not mean copying. Instead, view it as an equal partnership aimed at achieving more learning in the time available.  Those questions that you can’t answer with your friends, refer to the lecturer, workshop tutors, and postgraduate teaching assistants working on the course.

Tutorial Workshops

In most universities, lectures are supported by workshop tutorials. These are small, seminar-style classes, where you can work through problem sheets and discuss lecture topics  in small groups with the support of one or more academics and postgraduate teaching assistants. For these to be effective, you need to prepare by reading through your lecture notes, listing possible questions to ask during the workshop, working through problem sheets and identifying those problems that you need help on(Maier, Barney, & Price, 2013).

Concluding remarks

At university you have to take the initiative to keep ahead of your studies. This involves spending a considerable amount of time in independent self-study outside of lecture and workshop hours. This is hard work, but don’t give up, and keep on going. In addition, university study is about collaboration. Take time to prepare before lectures and workshops. Similarly after lectures and workshops, spend time reviewing the course material. Work consistently throughout the year. And importantly, learn to ask questions inside and outside of lectures, and make it a habit to always reflect on the progress of your studies. If you do this, then your stay at university will be comfortable, and you won’t need to go into panic mode whenever the exam period is around the corner. Good luck in your studies.


Chapman, S. (1946). How to Study Physics: Stanford University Press.

Felder, M. (1993). An Engineering Student Survival Guide CHapter One, 7  (3), pp. 42-44

Hubin, D. R., & Ridell, C. (1977). How to Study Physics  Retrieved 04 October, 2015, from https://web2.ph.utexas.edu/~turner/classes/HowToStudyPhysics.htm

Maier, P., Barney, A., & Price, G. (2013). Study Skills for Science, Engineering and Technology Students: Pearson UK.

Reeve, H. (2009). How to Study More Effectively for a Maths Degree – A Student View Retrieved 04 October, 2015, from http://maths.york.ac.uk/www/StudySkills

Rosenkrantz, P. R. (n.d.). How to Study Math, Science and Engineering.   Retrieved 04 October, 2015, from https://www.cpp.edu/~rosenkrantz/skills2.htm

University of Cambridge Faculty of Mathematics. (2014). Study Skills in Mathematics.   Retrieved 04 October, 2015, from http://www2014.maths.cam.ac.uk/undergrad/studyskills/text.pdf

University of Hull Skills Team. (2013). Study Skills in Mathematics.   Retrieved 04 October, 2015, from http://www2.hull.ac.uk/lli/skills-development/mathsstats/study_skills_maths.aspx

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