Course Description:

This course is designed to introduce students to the fundamental concepts of mathematics such as sets, number systems, relations, functions, and cardinality. Such concepts are important for their subsequent studies in higher level mathematics courses including linear algebra and analysis.

This course also serves as a transition course to bridge the gap between computational and proof-based courses. Mathematics at university level introduces progressively more and more abstract ideas and structures, and demands an increasingly higher standard in the way of proof. By means of a wide variety of proof-writing and oral presentation in practice, students will begin to learn to communicate mathematics emphasizing precise logic and clear exposition. Students will also be given the chance to work on guided projects which are intended to let them discover more mathematics related to the course context themselves.

We hope that this course can invite students to explore mathematics more deeply and even entice some of them to become mathematics major.

Course Contents:

1. Sets and Logic:
   Basic concepts in the language of sets, subsets, Venn diagrams, Power sets, Set operations, Statements, Conjunctions, Disjunctions and Negations, Conditionals, Tautologies and Contradictions, Quantifiers, Quantified Statements
2. Proof Strategies:
   Direct Proof, Proof by Contrapositive, Proof by Cases, Proof by Contradiction, Proof by Mathematical Induction, Counterexamples, Prove or Disprove
3. Equivalence Relations and Functions:
   Relations, Reflexive, Symmetric and Transitive Relations, Equivalence Relations and Equivalence Classes, Partitions, Functions as Relations, Injective, Surjective and Bijective Functions Compositions, Inverse Functions, Denumerable, Countable and Uncountable sets, Comparing Cardinalities of Sets
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

Target Students: Non HKU Undergraduates

Pre-requisite: High score in NCEE (Gaokao) math or in AP Calculus, or Good grade in IB Math (DP) or in GCE A-level Further/Pure math, or Equivalent. Applicants should provide a list of current courses and past exam result sheets or transcripts

Remark: Students without 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/programme/math2012/ for "MATH2012 Fundamental Concepts of Mathematics".

Online Application: Please browse http://www.aal.hku.hk/summerinstitute/programme/math2012/, and click "Apply Now".

Language of Instruction: English

Programme Fee: HK$13,000 and HK$350 Application Fee

Additional Supporting Documents: List of current courses and Past exam result sheets or Transcript

Deadline for Application:

Enquiries: