Lecturers Dr Thomas Heuttemann, Dr Gabriele De Chiara, Dr David Barnes
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
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%
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.
The assessment for this module has several components, typically attendance and participation, written homeworks, short class tests, oral presentations and a written project report.
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