# BSc/MEng Materials Science with an Integrated Foundation Year / Course details

Year of entry: 2023

## Course unit details:Mathematics 0F2

Unit code MATH19842 10 Level 1 Semester 2 Department of Mathematics No

### Aims

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

### Learning outcomes

On completions of this unit, successful students will be able to:

find the vector between two points, and express it in various different forms.

use simple properties of vectors, including addition, scalar multiplication and modulus.

define the scalar product of two vectors, and use this to find the angle between two vectors, and the component of one vector in the direction of another.

define the vector product of two vectors, and use this to find, among other things, the area of a parallelogram and the moment of a force about a point.

find the equation of a straight line in Cartesian and vector forms, given two points on the line or one point and the line’s direction. Also, find the midpoint between any two points.

find the equation of a plane in Cartesian and vector forms, given any sufficient set of information.

find whether a line intersects a plane or another line, and find the intersection point if it exists; find also whether one line/plane is parallel to (or perpendicular to) another line/plane.

find the shortest distance between a point and a plane or a line, or between two lines.

formulate and solve probability problems involving finite, equally-likely sample spaces;

calculate the distributions of discrete random variables defined on sample spaces;

apply the binomial, geometric and Poisson distributions in probability models;

calculate normal distribution probabilities using the normal table, and apply the normal distribution in probability models.

### Syllabus

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.

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Coursework 1 (week 6) Weighting within unit 10%

Coursework 2 (week 11 ) Weighting within unit 10%

Examination  (semester 2) Weighting within unit 80%

BOSTOCK, L., & CHANDLER, S. 1981. Mathematics - the core course for A-level. Thornes, Cheltenham. (ISBN0859503062)

STROUD, K.A, 2007. Engineering mathematics (6th ed.) Palgrave Macmillan, Baisingstoke. (ISBN9781403942463 / ISBN1403942463)

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)

### Study hours

Scheduled activity hours
Lectures 24
Tutorials 11
Independent study hours
Independent study 65

### Teaching staff

Staff member Role
Sergei Fedotov Unit coordinator
Neil Walton Unit coordinator