Towards Modern AlgebraComplex Numbers and Analytic GeometryIntroduction to Discrete MathematicsNumbers Theory and CryptographyTowards Differential Geometry
Course CodeSAYT1114University Recognition2 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 ApplicationIn the first half, we will cover some basic knowledge in Number Theory, including modular arithmetic and Euler's theorem. Then, we will cover two topics in Number Theory: primality test and primitive root, which are indispensable in studying Cryptography. In the second half, we will explore some applications of Number Theory in Cryptography, including some classical systems such as Vigenere cipher and some modern systems such as DES, RSA, digital signature. We will also briefly discuss Shor's algorithm: a quantum-based algorithm and QKD: a quantum-based cryptosystem.
Conditions for Admission Screening Test ExemptionApplicants who satisfy either one of the following conditions may be exempted from Admission Screening Test and will be directly admitted into this course.*(Those who had taken "Enrichment Mentoring Mathematics I or II" still need to sit the Test, but will be considered with priority.)1. Passed in any of the following courses before: Geometric Perspectives of Complex Numbers, Complex Number and Analytical Geometry, and Towards Modern Algebra.2. Being admitted in one of the following courses before: Number Theory and Cryptography, Towards Differential Geometry, Mathematical Analysis, and Understanding Non-Euclidean Geometry.