 # Module IEA-1003:Mathematics 3

### Module Facts

Run by School of Computer Science and Electronic Engineering

10 Credits or 5 ECTS Credits

Semester 2

Organiser: Dr Maziar Nezhad

### Overall aims and purpose

To continue the process of equipping students with the mathematical skills required for Year 1 Engineering Courses and for progressing successfully to Year 2 Courses.

The module will consist of two main topics:

• Probability and statistics (1/3 of the semester)
• Matrices, vectors and vector fields (2/3 of semester)

The module will also teach the rudiments of using Matlab for statistics and matrix calculations.

### Course content

Probability and Statistics

• Arrangement of data; histograms; mean; mode; and median. Dispersion; range; standard deviation. Normal distribution; standardized normal curve. ; Probability; Independence; Mutually exclusive events; Probability density functions; The binomial distribution; The Poisson distribution; The Gaussian distribution.

Matrices

• Matrix definition; Operations on Matrices; Determinants; Matrix inversion; Solutions of linear equations using matrices;

Vectors and vector fields

• Vector definition; Operations on vectors. Vectors in 2D and 3D; Representation of lines and planes using vectors; Scalar and vector products of two vectors; Angle between two vectors; Scalar fields; Vector fields; Gradient of a scalar field

### Learning outcomes mapped to assessment criteria

threshold

40%

good

60%

excellent

70%

Know and understand probability and statistics. Be able to calculate averages and data spread. Be able to calculate the probability of different events.

Has knowledge and understanding of most of the material covered. In addition to the threshold requirements, understands the implications of the theory and is able to apply this to solving problems. Has basic knowledge of data arrangement, dispersion and distribution. Can calculate simple probabilities. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

Know and understand the basic operations of matrix algebra, determinants and their application in solving systems of linear equations.

Has knowledge and understanding of most of the material covered. In addition to the threshold requirements, understands the implications of the theory and is able to apply this to solving problems. Has basic knowledge and understanding of matrix algebra. Can calculate determinants of matrices. Can invert matrices. Knows the application of matrices to solving equations. In-depth understanding of all areas covered. Able to apply theory to unseen problems.

Know and understand the basic operations in vector algebra. Be familiar with Cartesian and geometric representations of vectors. Use vectors to represent lines and planes. Know the concept of a scalar field and a vector field. Calculate the gradient of a scalar field using partial derivatives.

Can describe a vector field and carry out simple vector operations. Knows the connection between matrices and vectors. Can calculate with lines and planes in three dimensions. Knows the concept of a scalar field and a vector field and can calculate the gradient of a scalar field. In addition to threshold requirements, can write more complex code. Has a good understanding of commands and can manipulate data with ease. Can do a basic level of debugging. In addition to previous skills is able to write complex code, self initiate a project and make the connection between different concepts. Has superior debugging skills and can develop/find new commands and concepts by reading the Matlab manual on their own.

Be acquainted with the use of Matlab for statistical, probabilistic and matrix calculations.

Is familiar with the Matlab environment and can do simple calculations in the Matlab interface. In addition can write simple Matlab scripts. In addition can import/export data and plot in 2D and 3D.

### Assessment Methods

Type Name Description Weight
:End of semester examination 55
Probability & Statistics in-class test 10
Matrices and Vectors in-class test 10
Vector Fields in-class test 10
Lab test 1- Probability and statistics 5
Lab test 2 - Matrices and Vectors 5
Lab test 3 - Vector fields 5

### Teaching and Learning Strategy

Hours
Lecture

2 x 2 hour Lectures over 12 weeks

48
Private study 52

### Transferable skills

• Literacy - Proficiency in reading and writing through a variety of media
• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Computer Literacy - Proficiency in using a varied range of computer software
• Information retrieval - Able to access different and multiple sources of information
• Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.

### Subject specific skills

• Apply underpinning concepts and ideas of engineering;
• Solve problems logically and systematically;
• Analyse and display data using appropriate methods and mathematical techniques;
• Demonstrate familiarity with relevant subject specific and general computer software packages.