## MA114-5-AU-CO:Matrices and Complex Numbers

The details
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Current
Thursday 08 October 2020
Friday 18 December 2020
15
14 July 2020

Requisites for this module
(none)
(none)
(none)
(none)

MA201, MA204, MA205, MA225, MA301, MA306, MA314, MA315, MA317

## Key module for

BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)

## Module description

The module introduces several important mathematical constructions, namely, complex numbers, vectors and matrices, and shows how they are employed in various areas of mathematics and statistics. Particular attention is paid to how matrices are used for data analytics.

## Module aims

The aim of this module is to introduce BSc Data Science and Analytics to several important mathematical constructions, namely, complex numbers, vectors and matrices, and show how matrices are used for data analytics.

## Module learning outcomes

On completion of the module students should be able to:

- understand the geometric and algebraic properties of vectors in two- and three-dimensional Euclidean space;
- perform simple operations on matrices;
- solve systems of linear equations using row operations;
- calculate the determinant and the inverse of a matrix;
- calculate the eigenvalues and eigenvectors of a matrix;
- diagonalize a symmetric matrix;
- understand linear mappings, projection matrices, singular value decomposition of quadratic forms;
- apply linear mappings, projection matrices, singular value decomposition of quadratic forms using data science software such Matlab;
- be able to add, subtract, multiply, and divide complex numbers in Cartesian form; - be able to plot complex numbers on an Argand diagram;
- be able to move between Cartesian and polar forms of complex numbers;
- be able to calculate arguments, moduli and complex conjugates;
- be able to multiply and divide complex numbers in polar form;
- be able to find complex nth roots.

## Module information

Syllabus

Complex numbers:

- Addition, subtraction, multiplication and division of complex numbers in both Cartesian and polar form;
- de Moivre's theorem;
- complex nth roots.

Vectors:

- Geometry and algebra of vectors in 2 & 3 dimensions;
- vector addition and scalar multiplication.

Matrices:

- systems of linear equations;
- Gaussian elimination, elementary row operations;
- identity and inverse matrices, determinants;
- eigenvalues and eigenvectors;
- diagonalization of symmetric matrices;
- applications to quadratic forms in two and three dimensions;
- matrices of linear mappings;
- projection matrices;
- singular value decomposition of quadratic forms.

## Learning and teaching methods

Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.

## Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

## Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Exam  Main exam: 180 minutes during Summer (Main Period)

### Exam format definitions

• Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
• In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
• In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
• In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Coursework Exam
0% 100%

### Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Jessica Claridge, email: jessica.claridge@essex.ac.uk.
Dr Jessica Claridge & Dr Alexei Vernitski
Dr Jessica Claridge (jessica.claridge@essex.ac.uk), Dr Alexei Vernitski (asvern@essex.ac.uk)

Availability
No
No
No

## External examiner

Prof Stephen Langdon
Brunel University London
Professor
Resources
Available via Moodle
Of 4163 hours, 9 (0.2%) hours available to students:
4154 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information

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