MA114-4-AU-CO:
Matrices and Complex Numbers

The details
2019/20
Mathematical Sciences
Colchester Campus
Autumn
Undergraduate: Level 4
Current
Thursday 03 October 2019
Saturday 14 December 2019
15
01 October 2019

 

Requisites for this module
(none)
(none)
(none)
EC114

 

EC114, MA201, MA204, MA205, MA225, MA301, MA306, MA314, MA317

Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1G3 Economics with Mathematics (Including Placement Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

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 mathsug@essex.ac.uk before attempting to enrol. This module introduces students to the basics of linear algebra, emphasising vectors and matrices.

Module aims

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 R2 and R3;
- vector addition and scalar multiplication.

Matrices:
- matrix addition and multiplication, scalar 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.

Module learning outcomes

On completion of the course 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.

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 R2 and R3
- vector addition and scalar multiplication

Matrices:

- matrix addition and multiplication, scalar 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

Learning and teaching methods

This module consists of 1 lecture and 2 labs per week. There are three revision lectures in the Summer term.

Bibliography

This module does not appear to have a published bibliography.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework E-assessment 1 50%
Coursework E-assessment 2 50%
Exam 90 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%

Reassessment

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

 

Availability
Yes
Yes
No

External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 59 hours, 13 (22%) hours available to students:
46 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

 

Further information
Mathematical Sciences

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