This unit introduces fundamental topics needed for later mathematical study. It also introduces students to
notion of proof and rigorous mathematical arguments.
Indicative Content: 1 Sets: Subsets, set operations, set algebra, Venn diagrams, power sets, Cartesian product, proof of simple
results including set equality from first principles.
2 Logic: Propositional algebra, truth tables, Boolean
algebra and application to switching circuits, logical arguments and methods of proof including proof by
induction. Predicate calculus and quantifiers.
3 Functions: Definition and general properties, injections,
surjections and bijections, odd and even functions, brief review of polynomials, rational functions (partial
fractions) and transcendental functions.
4 Complex Numbers: Argand diagrams, Cartesian, polar and
exponential representations, arithmetic of complex numbers, powers and roots, de Moivre's theorem.
5 Groups: Definitions and examples, permutation groups, cycle representation.
6 Convergence of
Sequences and Series: Introduction to convergence and limit using sequences, related notation. Rates of
convergence. Series, arithmetic and geometric progressions, simple tests for convergence, power series and
radius of convergence, absolute convergence.
7 Convergence of Functions: Limits and continuity.
8 Differentiation: Definition linked to the idea of convergence, proof of some simple standard
derivatives, revision of methods of differentiation, product, quotient, and chain rules. Applications to
stationary points and rates of change including kinematics. Curve sketching. Taylor series.
Integration: Introduction using the limit of a sum, outline proof of the fundamental theorem of calculus.
Standard integrals, integration by parts and by substitution. Applications including areas, volumes, mean
values, centroids and solutions of first order odes. Improper integrals of the first and second kind.
Linear Algebra and Programming Skills
This unit extends the work on matrices and vectors that students will have met previously and introduces
them to programming with MATLAB®.
Indicative Content: Linear Algebra [50%] Vectors in R2 and R3, notation, components, displacement diagrams, addition of
vectors and multiplication by a scalar. Dot and cross products. Vector form of a line and a plane.
Determinants, calculation of determinants, properties of determinants. Matrices, addition and multiplication of
matrices. Matrices as representations of linear transformations. Inverse matrices. Bases, orthonormal bases,
representation of a vector relative to a basis. Dimension of a space spanned by a set of vectors, linear
independence, spanning sets, row reduction of matrices, solution of systems of simultaneous linear
equations. <BR> <BR>MATLAB Programming [50%] The design and implementation of MATLAB programs.
The top down design process, basic arithmetic operators and precedence and use of in-built mathematical
functions. Input and detailed formatting of output. Use of input, disp and fprintf commands and graphical
output. Repetition and conditional statements. For and while, if and switch. 1D and 2D arrays and use of
linear algebra commands. User-defined functions in MATLAB
Mathematics Pedagogy 1
Through a variety of experiences, students explore current issues and develop understanding about
teaching and learning mathematics.
Indicative Content: Theories about mathematics learning; transformation of personal subject knowledge and understanding to
the knowledge and understanding needed for teaching; communicating mathematics; mathematics
curriculum; mathematics assessment; errors and misconceptions/partial conceptions; progression in areas of
mathematics: number and algebra, geometry, statistics and probability; mathematical reasoning; problem
solving and modelling; effective teaching strategies
The Nature of Schools
Students spend time in various educational contexts observing teaching and supporting learners. They are
introduced to a range of theory and research about education to inform their emerging understanding of
schools and educational practices.
Indicative Content: Theories of learning; history and philosophy of education and schooling; education policy; how to observe in
educational settings; reflection on personal experiences of education; teacher strategies for engaging
learners; the curriculum; assessment; purposes of education; evaluation of educational provision