MA114-5-PT-NW:
Matrices and Complex Numbers
2025/26
Mathematics, Statistics and Actuarial Science (School of)
Northwest University
Spring Special
Undergraduate: Level 5
Current
Monday 12 January 2026
Friday 26 June 2026
15
13 March 2026
Requisites for this module
(none)
(none)
(none)
(none)
MA201, MA202, MA204, MA205, MA214, MA222, MA225, MA301, MA302, MA306, MA314, MA315, MA317
BSC I26ENW Data Science and Analytics
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.
Indicative syllabus:
Complex numbers:
- Addition, subtraction, multiplication and division of complex numbers in both Cartesian and polar form
- Applications of complex numbers to trigonometry such as 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
Applications to data science:
- Linear mappings
- Projections
- Singular value decomposition
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 a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
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
maths@essex.ac.uk
No
No
No
No external examiner information available for this module.
Available via Moodle
No lecture recording information available for this module.
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