Advanced Mathematics and Applications 1

This course begins an in-depth study of the fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas will allow students to develop analytical skills which will form a base for further study in fundamental mathematics, as well as providing a foundation for a wide range of quantitative areas such as actuarial studies, computer science, economics, engineering, physics and statistics. Topics to be covered include: Calculus/Analysis - suprema and infima of sets of real numbers, completeness, Riemann-Darboux definition of integration, introductory formal logic, axioms for the real numbers, convergence, limits, continuity, existence of extrema, differentiation, applications of derivatives, proof of the fundamental theorem of calculus, Taylor polynomials, l'Hospital's rules, inverse functions; Linear Algebra - solving linear equations, matrix equations, linear independence, matrix transformations, matrix operations, matrix inverses, abstract vector spaces, subspaces, dimension and rank, determinants, Cramer's rule, complex numbers, eigenvectors and eigenvalues. Note: This is an Honours Pathway Course (HPC). It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1013.