Towards Modern AlgebraComplex Numbers and Analytic GeometryIntroduction to Discrete MathematicsNumbers Theory and CryptographyTowards Differential GeometryUnderstanding Non-Euclidean Geometry
Course CodeSAYT1014University Recognition1 credit of CUHKMedium of Instructionmainly in Cantonese with English course materialsExpected ApplicantsStudents who have high competence in abstract mathematical reasoning, and are promoting to Secondary 4 or Secondary 5.Introduction
Online ApplicationThe central themes of classical algebra includes the study of polynomials, finding roots of polynomials, solving system of equations, Compass-and-straightedge construction. In response to these problems, modern abstract algebra was introduced during 19th century.In this course, we start with classical algebra topics which include using radicals to solve cubic and biquadratic equations, bisection method, compass-and straightedge constructions, construction of regular-17-gon, relationship between roots and coefficients, symmetric polynomials, closed formula of sum of powers, among other things.We will then introduce abstract algebraic structures including groups, fields, vector spaces with emphasis on concrete examples. We will introduce concrete math objects, including complex numbers, quadratic fields, quaternions, polynomials, additive and multiplicative group mod n, permutation groups, elliptic curves, finite fields, among other things, to illustrate the concepts of the algebraic structures.
Conditions for Admission Screening Test ExemptionApplicants who have successfully completed any EPYMT course may be exempt from the Admission Screening Test and will be directly admitted to their chosen course(s).