Course Description:

This course is designed to introduce students to the fundamental concepts of mathematics such as sets, number systems, relations, functions and cardinality. It also serves as a bridge between computational and proof-based courses. By means of a wide variety of proof-writing and oral presentation practice, students will learn to communicate mathematics emphasizing precise logic and clear exposition. We hope that this course can invite students to explore mathematics more deeply and even entice some of them to become mathematics majors.

Course Contents:

1. Sets and Logic:
   Basic concepts of sets, Subsets, Venn diagrams, Power sets, Set operations, Statements, Conjunctions, Disjunctions and Negations, Conditional, Quantified Statements
2. Proof Strategies:
   Direct Proof, Proof by Contrapositive/Contradiction, Mathematical Induction, Counterexamples, Prove or Disprove
3. Equivalence Relations and Functions:
   Relations, Reflexive/Symmetric/Transitive Relations, Equivalence Relations, Equivalence Classes, Partitions, Functions, Injective, Surjective and Bijective Functions, Compositions, Inverses, Denumerable, Countable and Uncountable sets, Comparing Cardinalities
4. Other Topics:
   Introduction to Calculus: Sequences and Series; Introduction to Group Theory

Credit Bearing Programme: 6 credits

Assessment:

• Final exam (50%)
• Tests (32%)
• Assignments (8%)
• Tutorials (10%)

Date: July 4 - July 30, 2016 (Every Tuesday & Friday)

Time: 9:30 a.m. - 12:30 p.m. & 2:00 p.m. - 5:00 p.m.

Venue: The University of Hong Kong

Level-of-study: Secondary school students aged 16 or above

Pre-requisite: Pass the screening test

Details of the screening test:
Date: June 11, 2016 (Saturday)
Time: 10:00 am to 12:00 nn
Venue: KB 223, Knowles Building, HKU

Remark:

• Students with excellent performance will be granted scholarships. Local students in financial need are eligible to apply for partial or full subsidies (please upload application letter together with supporting documents such as a copy of documentary evidence of government subsidy schemes or a copy of salary slip/income proof within three months through "supporting documents--others").
• Students with non-Permanent HK Identity Cards may require visas to study in HKU. For student visa and accommodation, please see Visa and Accommodation.

Programme Webpage: Please visit http://www.aal.hku.hk/summerinstitute/hs-programmes/math2012-fundamental-concepts-of-mathematics-6-credits/ for "MATH2012 Fundamental Concepts of Mathematics".

Online Application: Please browse http://www.aal.hku.hk/summerinstitute/hs-programmes/math2012-fundamental-concepts-of-mathematics-6-credits/, and click "Apply Now".

Language of Instruction: English

Programme Fee: HK$4,260 and HK$350 Application Fee

Deadline for Application:

Enquiries: