BSc/MEng Materials Science with an Integrated Foundation Year

Mathematics is both a language and a way of thinking. In this unit you’ll be introduced to the foundational logical that mathematics is built on; with the aim that you will use this to both accurately write down mathematical statements and prove them. 

ILO 1

Evaluate formulae of propositional logic, and identify equivalent formulae, by using truth tables.

ILO 2

Identify tautologies of propositional logic by using fundamental logical identities.

ILO 3

Analyse relations between sets using Boolean algebra.

ILO 4

Prove mathematical statements using, for example, proof by induction, proof by contradiction, and proof by contrapositive.

ILO 5

Apply the language of permutations to solve problems such as counting problems.

This unit begins with an introduction to the language of propositional logic, which is the basic formalism required for writing down mathematical statements. For instance, here we give mathematical interpretations for the words ‘and’, ‘or’, and ‘not’. To obtain a fully expressive language we will also introduce the quantifiers of predicate logic, expressed as ‘for all’ and ‘there exists’. With this in place, we will be able to formulate mathematical expressions and begin writing proofs.

We will then introduce the language of sets, which allows us to speak of collections of objects. This is a fundamental starting point for Pure Mathematics, where many initial objects of interest are sets. As an application will we consider the set of permutations of the integers 1 through n. Permutations are very useful and have applications to, for instance, counting problems. We will end the course by considering examples of such applications. 

New material will be taught asynchronously through videos and supplemented by the lecture notes. Each week there will be an in-person review session, focussing primarily on examples, as well as an in-person tutorial session. 

Continuous Assessment from Tutorials - 10 short multiple choice tests at the end of every tutorial class in Weeks 3-12. 9 best results are used to make 30% of the total mark for the course.

Examination. Weighting within unit 70%
 

M. Liebeck, A Concise Introduction to Pure Mathematics (Fourth Edition). CRC Press, Boca Raton, FL, 2016.

S. Lipschutz, Set Theory and Related Topics (Second Edition). McGrawHill, London, 1998.

J. Franklin and A. Daoud, Proof in Mathematics: An Introduction. Kew Books, Sydney, 2011.

R. Steege and K. Bailey, Schaum’s Outline of Intermediate Algebra (Third Edition). McGraw-Hill Education, New York, 2018.

R. Hammack, Book of Proof (Third Edition). MN Open Textbook Library, Minneapolis, 2013. 

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £29,200 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The Foundation Year Bursary is available to UK students who are registered on an undergraduate Foundation Year here and who has had a full financial assessment carried out by Student Finance.

Details of country-specific funding available to international students can be found within our International country profiles .

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability, therefore, we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships please visit our undergraduate student finance pages and the Department funding pages that you intend to progress to after successfully completing the Foundation Year.