MAM2000W - Mathematics 2000

Course Outline:

This course aims to introduce students to the fundamentals of mathematics. 2AC: ADVANCED CALCULUS Multivariable calculus. Curves and surfaces in three dimensions, change of coordinates. Line integrals, surface integrals. Stokes'. Green's and divergence theorems. Topics from: 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 2IA: 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. 2LA: LINEAR ALGEBRA Vector spaces, linear independence, spans, bases, row space, column space, null space. Linear maps. Eigenvectors and eigenvalues. Inner product spaces, orthogonality. 2RA: 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.