Core Mathematics

• Credit value: 15 credits at Level 4
• Convenor: Dan McVeagh
• Assessment: a short-problem set (20%), online quiz (10%) and two-hour examination (70%)

In this module we provide you with a comprehensive overview of core mathematical concepts, including algebraic methods, coordinate geometry, real functions and sequences/series. You will develop skills in solving polynomial equations, working with complex numbers, analysing geometric properties, and manipulating functions and series.

Indicative syllabus

• Algebraic methods: polynomials, the Factor Theorem, polynomial equations, exact solutions to linear and quadratic equations, completing the squares, the Binomial Theorem, partial fractions, inequalities, arithmetic of complex numbers, complex numbers as the roots of polynomials
• Coordinate geometry: straight lines, finding the equation of a straight lines, perpendicular lines, circles, tangent to a point on a circle, equation of a circle, finding the centre and radius of a given circle
• Real functions: the properties and graphs of exponential, logarithmic and trigonometric functions, inverses, trigonometric identities
• Sequences and series: definitions, intuitive idea of a limit of a sequence, sigma notation, sum of i, i2 and i3 (i=1..n), arithmetic and geometric progressions

By the end of this module you will be able to:

• solve polynomial equations and simple inequalities
• express a rational function in partial fractions
• demonstrate knowledge of arithmetic and geometric progressions
• demonstrate knowledge of the Binomial Theorem
• demonstrate knowledge of the properties of standard functions of one variable.