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## Course Overview

This course introduces the concepts of complex numbers, matrices and other basic notions of linear algebra over the real and complex numbers. This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.

### Course Details

Study Type Level Undergraduate 1 First Term 15 credits (7.5 ECTS credits) None. No This course has a diagnostic test which you must take before selecting this course. More information about the Diagnostic Tests Professor Vassili Gorbunov

### Qualification Prerequisites

• Not UoA Mathematics MABEG
• Either Programme Level 1 or Programme Level 2

### What courses & programmes must have been taken before this course?

• One of Mathematics (MA) (Studied) or MA Natural Philosophy (Studied) or MA Philosophy-Physics (Studied) or BSc Physics (Studied) or BSc Physics with Modern Languages (Studied) or BSc Physics with Philosophy (Studied) or Bachelor Of Science In Geophysics (Studied) or BSc Geology - Physics (Studied) or Master of Engineering in Computing Science (Studied) or BSc Computing Science and Physics (Studied) or Higher Grade (Sce/Sqa) Mathematics at Grade A1/A2/A/B3/B4/B/C5/C6/C or UoA Mathematics MAADV

None.

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### Course Description

The basic course includes a discussion of the following topics: complex numbers and the theory of polynomial equations, vector algebra in two and three dimensions, systems of linear equations and their solution, matrices and determinants.

Syllabus

• Solving equations.
• Polynomial equations and their roots, polynomial long division, the Rational root theorem.
• Introduction to complex numbers. The addition, subtraction, multiplication and division of
• Complex numbers. Modulus and Argument and the representation of such numbers on an Argand diagram. Loci and regions in the Argand diagram. De Moivre’s theorem and applications. Complex exponential, logarithm, sine and cosine.
• Systems of linear equations, Gaussian elimination.
• Matrix algebra. Determinants of square matrices (of any dimension). Matrix inversion (the cofactor method and Gaussian elimination).
• Vectors and linear maps. Special matrices (e.g rotation matrices). Matrix design. Eigenvalues and eigenvectors.
• Topics from: Diagonalizability. Subspaces, dimensions and linear independence. The rank and nullity of a matrix.

### Contact Teaching Time

Information on contact teaching time is available from the course guide.

### Teaching Breakdown

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

### Summative Assessments

1st Attempt: 1 two-hour written examination (70%) and in-course assessment (30%).

Resit: 1 two-hour written examination paper (maximum of (100%) resit and (70%) resit with (30%) in-course assessment).

### Formative Assessment

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

### Feedback

In-course assessment will be marked and feedback provided to the students.

Support tutorials to be arranged by the Course Coordinator, as need arises.

None.

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