## MA114-4-AU-CO:

Matrices and Complex Numbers

## Key module for

BSC N233DT Actuarial Science (Including Placement Year),

BSC N323 Actuarial Science,

BSC N323DF Actuarial Science,

BSC N323DT 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),

MMATG198 Mathematics,

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 G1F5 Mathematics with Physics (Including Foundation Year),

BSC GCF3 Mathematics with Physics (Including Year Abroad),

MSCIN399 Actuarial Science and Data Science,

MSCIG199 Mathematics and Data Science,

BSC N333 Actuarial Studies,

BSC N333DT Actuarial Studies,

BSC N334 Actuarial Studies (Including Placement Year),

BSC N334DT Actuarial Studies (Including Placement Year),

BSC N335 Actuarial Studies (Including Year Abroad)

## Module description

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.

## Module aims

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.

## Module learning outcomes

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.

## Module information

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

## Learning and teaching methods

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.

## Bibliography

## Assessment items, weightings and deadlines

Coursework / exam | Description | Deadline | Coursework weighting |
---|---|---|---|

Exam | Main exam: In-Person, Open Book (Restricted), 90 minutes during Summer (Main Period) | ||

Exam | Reassessment Main exam: In-Person, Open Book (Restricted), 90 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

Coursework | Exam |
---|---|

0% | 100% |

### Reassessment

Coursework | Exam |
---|---|

0% | 100% |

## External examiner

**35**hours,

**23 (65.7%)**hours available to students:

**12**hours not recorded due to service coverage or fault;

**0**hours not recorded due to opt-out by lecturer(s), module, or event type.

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