PREPARATORY · Postgraduate preparation

Preparatory Lessons for SPMS MSc Students

SPMS Mathematical Sciences MSc programmes

Course materials and assessment information for registered students are provided through NTULearn. External resource links may require NTU access.

Overview

This one-week module prepares MSc (by coursework) students to be ready for our intensive MSc programme before its start. This module covers the fundamental knowledge in linear algebra, calculus, and R programming. There is no assessment in this module but there are many worked-out examples done together with the students during the lessons.

Topics

[3.5hrs] Basics of Calculus and Linear Algebra (set theory, vector spaces, functions, limits and continuity)
[3.5hrs] Linear Algebra (matrix algebra, linear systems, eigenvalues and eigenvectors, diagonalization, SVD, quadratic form)
[3.5hrs] Calculus I (differentiation, approximation, optimization)
[3.5hrs] Calculus II (integration, ordinary differential equation)
[3.5hrs] R Programming

Reference books

H. S. Lee and G. H. L. Cheang. (2007) Introduction to Calculus and Matrix Algebra with Applications in Finance (2nd Edition). McGraw-Hill.
C. P. Simon and L. Blume. (1994) Mathematics for Economists. W. W. Norton & Co.
S. J. Leon. (2009) Linear Algebra with Applications (8th Edition). Pearson.
W. Briggs and L. Cochran. (2015) Multivariate Calculus (2nd Edition). Addison-Wesley.