BSc/MEng Materials Science with an Integrated Foundation Year

The course unit aims to provide a basic course in probability theory and vectors for Foundation Year students.

    
ILO 1: Define free and position vectors and perform basic arithmetic 
operations on vectors in 2D and 3D Cartesian coordinates.

ILO 2: Calculate the scalar and vector product of a pair of vectors.

ILO 3: Calculate the vector and Cartesian equations of lines and planes given 
any sufficient set of information.

ILO 4: Apply knowledge from the course to solve geometry problems.

ILO 5: Formulate and solve probability problems involving finite, equally-likely 
sample spaces.

ILO 6: Calculate the distributions of discrete random variables defined on 
sample spaces.

ILO7: Apply the binomial, geometric and Poisson distributions in probability 
models.

ILO8: Calculate normal distribution probabilities using the normal table, and 
apply the normal distribution in probability models. 

Eleven lectures: Vectors: Scalars and vectors. Magnitude and direction. Addition of vectors. Multiplication by a scalar. Scalar products and projections. Vector Products. 2D and 3D coordinate geometry. Position vectors and unit vectors. Parametric Equations. Vector equations of lines and planes. Shortest distance between two lines.

Five lectures : Probability: Experiments, outcomes. Sample spaces, events, complements and unions/intersections of events, use of combinations and permutations to evaluate probabilities on finite sample spaces. Conditional probability and independence.

Three lectures: Random variables: Discrete and continuous random variables. Displaying probability distribution functions. Probability distribution functions as the limits of relative frequency distributions. Mean and sample mean.

Three lectures: Standard distributions: Binomial, poisson and normal distributions with applications.

Exam; Weighting within the unit 80%

Multiple (e.g. 10) small online tests during the semester; Weighting within the unit 20%

STROUD, K.A, 2007. Engineering mathematics (6th ed.) Palgrave Macmillan, Baisingstoke. 
(ISBN9781137031204/ ISBN 9781137031228) 

SPIEGEL, M. & MEDDIS, R. 1980. Schaum's outline of theory and problems of probability and statistics 
(SI [Metric] ed.) McGraw-Hill, London. (ISBN0070843562 / ISBN9780070843561) 

MCCOLL, J. 1995. Probability (Modular mathematics). Edward Arnold, London. (ISBN0340614269 / 
ISBN9780340614266) 

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 will be £10,050 for the 2027/28 academic year. In England and Wales, tuition fees for home undergraduate students are subject to the Government fee cap, which the Government has announced will be £10,050 for the 2027/28 academic year.

Government policy is to increase the fee cap on an annual basis to reflect inflation (i.e. increasing costs), and the tuition fee home students pay in subsequent academic years will reflect any increases in the Government fee cap (which we will communicate to you as soon as we can in advance of the relevant academic year).

Tuition fees for international students will be £29,200 for the 2027/28 academic year. For subsequent academic years, the University reserves the right to increase the tuition fee by up to 7% each year, including to reflect rising costs associated with delivering our education and wider student experience.

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.