UCL's University Preparatory Course in Science and Engineering
What the course is about :
Welcome. All of you come from a variety of different educational abilities, backgrounds and cultures.
As such you have been used to many different ways of being taught and you may have differing expectations
about how to be taught and how to learn. Before coming here most of you may have followed courses where much
of the process of studying and learning was organised for you. Specifically, you may have been told what
material to study, how much material to study, when you should study it. You may also have obtained good
marks for your work simply by repeating what the lecturer taught you in class, etc...
However, this is not the case in British universities. Here, much greater responsibility is placed on you
and you will find that much of your effort and work whilst studying here will involve you in going beyond
what you were taught in class. Many of the skills, abilities and experiences required to successfully
complete this course, and your future university degree, include being able to organise your own work and
time, participating, extending ideas, forming your own opinions, developing an independence of thought,
doing personal research, communicating effectively in writing and/or orally, or working as part of a group.
Study at this level is thus much broader than simply a matter of developing the necessary technical skills
needed to pass the course. Many of the tasks that you undertake as part of this course, and your future
degree, are designed to encourage you to think and reflect more deeply and widely about not only the topic
itself but also the way you learn and organise that topic.
Therefore, the motivation behind the whole UPCSE course, as well as the mathematics course, is to help you
make the transition to the level, abilities, attitudes and culture of education required for entry into 1st
year science and engineering course at British university.
The Mathematics Course :
Surprising as it may sound the learning of mathematics is not just about learning to 'get the right
answer'. It is also (amongst other things) about being able to think mathematically and read mathematically,
and then being able to show how you develop your ability, reading and thinking. Consequently, as part of the
coursework you will need not only to be able to do the mathematics set but also be able to describe exactly
the process by which you went about doing such mathematics.
Hence, throughout the course you will need to demonstrate your developing mathematical thinking, technical
and reading ability by :
- solving specific mathematical problems
- adopting the approach of reading mathematics. This will be done by interpreting technical text, mathematical expressions, solutions to mathematical problems, diagrams, etc...
- studying and learning how you go about working on, solving and hence, learning mathematics
Specifically, the course aims to help you develop the following abilities :
- the ability to solve appropriate mathematical problems
- the ability to construct appropriate mathematical proofs
- the ability to read mathematically by interpreting/describing mathematical text, expressions, solutions and/or proofs as appropriate, and demonstrate this through written and/or oral work
- think mathematically by identifying mathematical patterns and use these to extend given mathematics
- the ability to critically analyse and discuss issues in mathematics, as well as your learning of mathematics
- the ability to work individually and in groups on the topic of mathematics
- the ability to improve &/or extend any aspect of 1) - 6) above.
The Aims of the Lectures :
The aim of the lectures will be to introduce and explain the topic we will study during any specific
week. It is important to understand that much of your learning will come not simply as a result of working
during the lectures (and tutorial) but also from your own independent private study (see the introduction
above). Lectures should therefore not be seen as the only time in which to learn the relevant mathematics but as the
starting point which you will need to carry over into your own personal study time, revision, research,
reading, etc...
The Aims of the Tutorials :
From the introduction above, the general aim of our tutorial sessions will then be to help you :
develop your mathematical ability
as well as
develop the ability to read and think mathematically
in other words to be able to do mathematics and solve mathematical problems, as well as understand the
technical English, mathematical expressions and the solution to maths problems and/or proofs.
In order to show that you have understood the mathematics you have read and performed you will need to
interpret in plain English everything you read, namely
describe the meaning of mathematical text as well as describe the way in which
you solved maths problems and developed maths proofs
induction week 0 | notes and slides |
tutorials | sample tests and exam |
software