MA114-5-AU-CO:
Matrices and Complex Numbers
2019/20
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Undergraduate: Level 5
Current
Thursday 03 October 2019
Saturday 14 December 2019
15
09 April 2020
Requisites for this module
(none)
(none)
(none)
(none)
MA201, MA204, MA205, MA225, MA301, 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)
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.
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.
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
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;
- matrices of linear mappings;
- projection matrices;
- singular value decomposition of quadratic forms.
This module consists of one lecture and two labs per week which are shared with MA114-4, and one extra lab in each of the last five weeks of the term. There are four revision lectures in the summer term.
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 |
| Coursework |
E-assessment 1 |
|
|
| Coursework |
E-assessment 2 |
|
|
| Exam |
Main exam: 24hr 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.
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, email asvern@essex.ac.uk
Dr Alexei Vernitski (asvern@essex.ac.uk)
No
No
No
No external examiner information available for this module.
Available via Moodle
Of 167 hours, 40 (24%) hours available to students:
127 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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