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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 Sub Session 15 credits (7.5 ECTS credits) Aberdeen No This course has a diagnostic test which you must take before selecting this course. More information about the Diagnostic Tests Dr Simona Paoli

### Qualification Prerequisites

• Either Programme Level 1 or Programme Level 2

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

• Either Programme Level 1 or Programme Level 2
• One of Mathematics (MA) or Physics (PX) or Bachelor Of Science In Geophysics or Master of Engineering in Computing Science or Higher Grade (Sce/Sqa) Mathematics at Grade A1/A2/A/B3/B4/B/C5/C6/C or UoA Mathematics MAADV

None.

No

### 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 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

### Summative Assessments

#### Online Test

Assessment Type Weighting Summative 15
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Exam

Assessment Type Weighting Summative 70
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Class Test

Assessment Type Weighting Summative 15
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Formative Assessment

There are no assessments for this course.

### Resit Assessments

#### Best of written exam (100%) or written exam (70%) with carried forward in-course assessment (30%)

Assessment Type Summative
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
ProceduralApplyCarry out division of polynomials and solve polynomial equations up to degree three.
ConceptualUnderstandUnderstand matrix representation of systems of linear equations.
ConceptualRememberKnow the definition of complex numbers and their essential role in mathematics
ProceduralApplyPerform elementary manipulation of complex numbers and their geometrical representation.
ProceduralApplyPerform calculations, such as matrix inversion, finding eigenvalues and eigenvectors, and diagonalization.
FactualUnderstandHave an understanding of the need of precision in mathematics
ConceptualApplyHave a working knowledge of basic logical rules
ProceduralApplySolve systems of linear equations using Gaussian elimination.

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