Mathematical Issues for Physicists and Engineers
Mathematics is critical to the study of physics and
engineering; indeed, historically the development of mathematics,
physics and engineering have often gone hand in hand.
The physicist or engineeer needs to embrace mathematics in order
to get the most from their studies. Unfortunately, students often
struggle with the mathematical aspects of their physics or
engineering degree course: 8 key reasons for this are provided
below.
stemNRICH was specially
designed to address these 8 problem areas by providing meaningful,
rich and interesting mathematical science problems for students to
engage with prior to arrival at university.
Background Mathematics
There is a great deal of mathematical content knowledge which a
physicist or engineer needs to know. Some of the more advanced
skills required are
Mathematics 
Applications 
Equations 
All of physics! 
Calculus and differential equations 
Dynamics 
Vectors 
Forces, statics 
Complex numbers 
Wave equations, frequency analysis 
Matrices 
Stress and strain, 3D graphics 
Logarithms 
Sound intensity 
Logic 
Digital circuits and computing 
Estimation and approximation 
Checking answers, setting up problems 
Statistics and probability 
Statistical physics 
Geometry 
Statics, mechanics 
... and problem solving skills 
Setting up any problem! 
In addition to this strong base of advanced skills, any
physicist or engineer needs to have very strong number, computation
and general maths skills. Unfortunately, even a good grade in maths
might not be sufficient to support the underlying physics once a
student begins university. Why is this?
Eight mathematical problem areas
Suppose that a physics or engineering student achieved a good
grade in GCSE mathematics or AS mathematics. Why would such
students struggle with the mathematical aspects of physics or
engineering? There are several possible reasons:
 Overly Procedural thinking
 Mathematics exams can often be passed by learning the content
procedurally. This means that students can answer certain
types of question by following a recipe. The problems with more
complex physical applications arise because even minor deviations
from the precise recipe cause the student to fail to know what to
do.
 Lack of ability to translate mathematical answers to
physical interpretation

 Even students who are very skilled at mathematics might have
trouble seeing how to relate the mathematical process to a
realworld context. An important part of this is interpreting
answers and realising when a mathematical description breaks down.
Lack of skill in this area hampers the use of common sense, so
valuable in quantitative science.
 Lack of ability to translate
physical situation into the correct mathematical
description

 The physical world is intrinsically mathematical and the
process of modelling the world involves extracting the correct
mathematical description from a physical scenario. This has always
been the most tricky part of physics and engineering, and a lack of
total confidence in the mathematics exacerbates the
difficulties.
 Lack of ability to make estimates or
approximations

 Physics and engineering contexts are often quite complicated.
In order to apply mathematics predictively, approximations will
often need to be made. To make approximations requires the student
to really understand the meaning and structure of the
mathematics.
 Lack of problem solving skills

 Physics and engineering problems are not usually clearly
'signposted' from a mathematical point of view. The physicist or
engineer must assess the situation, decide how to represent it
mathematically, decide what needs to be solved and then solve the
problem. Students who are not well versed in solving 'multistep'
problems in mathematics are very likely to struggle with the
application of their mathematical knowledge.
 Lack of experience with calculation or difficult
contexts

 There are two ways in which lack of practice can impact
mathematical activity in the all of the sciences, especially those
rooted in physics
 First is a lack of skill at basic numerical manipulation. This
leads to errors and holdups regardless of whether the student
understands what they are trying to do.
 Second is a lack of practice at thinking mathematically in
genuinely difficult scientific contexts.
 Lack of confidence

 Lack of confidence builds with uncertainty and failure, leading
to more problems. Students who freeze at the sight of numbers or
equations will most certainly under perform.
 Lack of mathematical interest
 Students are hopefully strongly driven by their interest in
science and its realworld applications. If mathematics is studied
in an environment independent of this then mathematics often never
finds meaning and remains abstract, dull and difficult.
If you are a student aiming to study physics or engineering at
university, do any of these areas seem like they might possible
cause you some problem? If so, why not take a look at some of the
stemNRICH problems and start thinking about these matters now?