# PMA Level 1 Modules

• PMA1020 - Numbers Vectors & Matrices

Lecturers         Dr Thomas Heuttemann, Dr Gabriele De Chiara, Dr David Barnes

Course 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, basis, dimension theory, linear maps, dimension formula

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, finite fields

Assessment

2 one-hour class tests, each worth 15% of the total final mark

Compulsory computer-based test (worth 10%), pass mark 80%

3-hour written examination for 60%

• PMA1021 - Mathematical Reasoning

Lecturers:      Various

Introduction

Course Content:

The notion of mathematical statement, true and false statements and elementary logic. The language of sets. Beginnings of Analysis, Combinatorics and Algebra. The concept of mathematical proof. Examples of proofs by induction, contradiction, and direct proof. The role of notation in mathematics. Analogy and generalisation in mathematics. Communicating mathematics to others: basic principles.

Assessment

The assessment for this module has several components, typically attendance and participation, written homeworks, short class tests, oral presentations and a written project report.