# PMA Level 1 Modules

**MTH1002 - Numbers Vectors & Matrices (Full year)**

*Pre-Requisites:*

*Lecturers:* Dr P Siegl, Dr T Huettemann, Dr G De Chiara

**Introduction**

The module MTH1002 covers aspects of basic mathematics, in particular the main number systems, concepts of set theory, proof techniques, systems of linear equations, abstract linear algebra, vectors and geometry in three dimensions, matrices and determinants. Together with the module MTH1001, this builds a solid foundation for further mathematical studies.

**Content**

- Review of A-level mathematics: number systems, prime numbers, divisibility.
- Direct proofs, proofs by induction, proofs by contradiction.
- Bunded sets, suprema, infima.
- Complex numbers, conjugation, de Moivre's theorem.
- Basic set theory: union, intersection, product, and difference of sets, de Morgan's laws.
- Basic combinatorics, binomial theorem.
- Functions and their properties (injective, surjective, bijective), composition of functions, inverse functions, equivalence relations.
- Linear algebra: systems of linear equations, vector spaces, vectors, linear independence, span, basis, dimension.
- Applications of linear algebra in 3-dimensional space, cross products, scalar products and length of vectors.
- Matrices and linear maps, determinants, Cramer's rule, characteristic polynomial, Cayley-Hamilton theorem, eigenvectors and eigenvalues.

Assessment

2 class tests, each worth 15% of the total final mark; Exam, worth 70% of the total final mark** **

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**PMA1021 - Mathematical Reasoning (1st semester)**

*Pre-Requisites: None*

*Lecturer:* Dr T Huettemann

**Introduction**

In a nutshell, this module is about communicating mathematics. Using examples from A-level mathematics and the level-1 modules MTH1001 and MTH1002, students will discuss the use of language and logic, basic proof patterns, report writing and oral presentations. There are weekly small group meetings with various group discussion activities. The acquired skills will be put into practice with homework assignments, a written project and oral presentations.

**Course Content**

Problem solving; language in mathematics; the logic of negation; proofs by induction and contradiction; report writing; coomunication of mathematical ideas and content.

**Assessment**

The assessment for this module has several components: written homeworks, participation, written project report, oral presentations.

Homeworks (x4) 10% each

Participation 10%

Report 25%

Presentations 25% total