Foundation course in Mathematics

Instruction is in the form of lectures, exercises, and laboratory sessions. Main course components: - Basic logic and set theory: symbols and concepts, basic principles of logical reasoning and proofs - Basic analytical geometry such as conic sections - Algebraic simplification, completing the square, factor theorem, equations such as trigonometric equations, inequalities, and absolute values - Complex numbers: Cartesian and polar form, de Moivres formula - Elementary functions: the concept of function, domain of definition, range of function, composition of functions, inverse functions - Basic functions: polynomial, power, logarithmic, exponential, trigonometric, and inverse trigonometric functions, their definitions, properties, graphs, and rules for calculation - Limits of sequences and functions, continuity, properties of continuous functions - Definition of the derivative and calculation laws, chain rule, derivatives of elementary functions, implicit differentiation, the mean value theorem - Basic applications of derivatives: tangents and normals, increasing and decreasing functions. - Function studies: graph construction, extreme points, asymptotes, concavity - Applications of derivatives: extreme value problems, linearisation, Taylor polynomial with error term using big-O notation and the Lagrange's form, l'Hopital's rules.