Bachelor of Arts (BA) - The University of Hong Kong

• Matrices and linear transformations: matrices, addition and scalar multiplication of matrices,matrix multiplication, basic concepts of mappings (injective, surjective, bijective mapping,composition of mappings), matrix as a linear transformation, kernels and images (includingtheir relationship with system of linear equations), elementary row transformations, inverse of amatrix, solutions of system of linear equations.• Vector calculus (differentiation): derivatives and linear approximation in one dimension,partial differentiation, partial derivatives, gradient and directional derivatives, differentiability,derivative as a linear transformation, Jacobian matrix, chain rule, Taylor polynomials,classifying critical points of functions (local maxima/minima, saddle points), Lagrangemultipliers, inverse and implicit function theorems.• (Examples on applications in the physical sciences will be integrated into the course content.)Prerequisites: AS Mathematics and Statistics, or Mathematics at higher level.Duration: One semester (first semester)Assessment: One 2½-hour written examination (60%) together with coursework assessment (40%).259MATH1812.Mathematics II (6 credits)To provide students with the essential knowledge of linear algebra and vector calculus for furtherstudies in the physical sciences.Contents:• Linear algebra: linear combination, span, linear independence, basis, dimension, determinant,eigenvalue and eigenvector.• Vector calculus (integration): review on integral in one dimension, Fundamental Theorem ofCalculus, curve integrals and potential functions, double and triple integrals (includingdiscussions on polar, cylindrical and spherical coordinates), geometric interpretations ofdeterminants of 2 × 2 and 3 × 3 square matrices, the change of variables formula, surfaceintegrals, divergence and curl of a vector field, Green's Theorem, Stokes' Theorem, DivergenceTheorem (or Gauss-Ostrogradsky Theorem).• (Examples on applications in physical sciences will be integrated into the course content.)Prerequisites: (AS Mathematics and Statistics, or Mathematics at higher level) and having takenMATH1811.Duration: One semester (second semester)Assessment: One 2½-hour written examination (60%) together with coursework assessment (40%).Second and Third YearsStudents taking Mathematics must include in their choice the courses Calculus I, Calculus II, Linearalgebra I and Linear algebra II, unless they have already passed them, before considering othercourses. Apart from that, they may choose any of the listed courses, for which they satisfy the coursepre-requisites. For details of the pre-requisites, please refer to the listing under the Faculty of Science.MATH2001.Development of mathematical ideas (6 credits)Selected topics in the development of mathematics from ancient to modern times depending on interestof the students and the lecturer, with attention paid to the evolvement of mathematical ideas and theprocess of mathematical thinking and problem solving.Pre-requisite: MATH1101 and MATH1102 and MATH1201 and MATH1202.