MA114-5-AU-CO:
Matrices and Complex Numbers
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Current
Thursday 03 October 2024
Friday 13 December 2024
15
03 January 2024
Requisites for this module
(none)
(none)
(none)
(none)
MA201, MA202, MA204, MA205, MA214, MA222, MA225, MA301, MA302, MA306, MA314, MA315, MA317
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)
This 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.
The aims of this module are:
- To introduce mathematical constructions which are used in a wide range of applications of mathematics, namely, complex numbers, vectors and matrices.
By the end of this module, students will be expected to:
- 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.
- 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.
- Use linear mappings and projection matrices in applications to data science.
- Use singular value decomposition of matrices in applications to data science.
- Use data science software such as MATLAB.
For students outside of the Department, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure whether you meet this criteria please contact maths@essex.ac.uk before attempting to enrol.
Indicative 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:
Matrix addition and multiplication
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
Teaching in the School will be delivered using a range of face to face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.
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: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period)
|
| Exam |
Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment 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.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Alexei Vernitski, email: asvern@essex.ac.uk.
Dr Alexei Vernitski
asvern@essex.ac.uk
No
No
No
Prof Stephen Langdon
Brunel University London
Professor
Available via Moodle
Of 35 hours, 22 (62.9%) hours available to students:
13 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.
Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can
be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements,
industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist
of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules.
The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.