MAM2000W

MAM2000W is the course code for UCT’s Mathematics II course and includes:

ADVANCED CALCULUS
Multivariable calculus. Curves and surfaces in three dimensions, change of coordinates. Line
integrals, surface integrals. Stokes’. Green’s and divergence theorems.
DIFFERENTIAL EQUATIONS (for Actuarial and Business Science students)
First and second-order difference equations. Linear differential equations, constant coefficients. Laplace transforms. Nonlinear equations, phase plane analysis. Parabolic partial differential equations, separation of variables, boundary value problems. Black-Scholes equation.
Stochastic differential equations
INTRODUCTORY ALGEBRA
Introduction to abstract algebra and number theory. Topics include: induction, strong induction and Well-Ordering axiom. Divisibility and prime factorization. Modular arithmetic. Permutations.
Groups. Subgroups. Cyclic groups. Isomorphisms. Simple groups. Factor groups. Lagrange’s Theorem. The First Isomorphism Theorem.
LINEAR ALGEBRA
Vector spaces, linear independence, spans, bases, row space, column space, null space. Linear maps.
Eigenvectors and eigenvalues. Inner product spaces, orthogonality.
REAL ANALYSIS
Axioms of the real numbers, supremum and infimum. Countable sets. Sequences and series. Open and closed sets, compactness. Limits, continuity, differentiability. Sequences and series of functions,
uniform convergence, power series. Integration.