Course Code: HS-MATH2012_2017
Level-of-study: Age: 16 or above
Course Period: July 3, 2017 to July 21, 2017
Programme Fee: HKD 4,260 and HKD 350 application fee
Deadline for Application:
- Non-local Applicants: March 15, 2017
- Local Applicants: May 31, 2017
Type of Programme: Credit-bearing course
Area of Interest: Mathematics
Managed by: Department of Mathematics, Faculty of Science
- Students: Local; Non-local
- Age: 16 or above
Pass the screening test. Remote screening test for non-local applicants would be held in March, 2017. The screening test for local applicants will be held on June 10, 2017 (Saturday).
Class Day: Tuesday, Thursday & Friday
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.
- 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
- Proof Strategies:
Direct Proof, Proof by Contrapositive, Proof by Cases, Proof by Contradiction, Proof by Mathematical Induction, Counterexamples, Prove or Disprove
- 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
- Other Topics:
Introduction to Calculus: Sequences and Series; Introduction to Group Theory
On successful completion of this course, students should be able to:
|Course Learning Outcomes (CLO)|
|CLO 1||understand the definition of a set and apply set theory in simple daily life problems|
|CLO 2||construct the truth table of a given statement|
|CLO 3||apply different proof strategies (e.g. proof by contradiction and mathematical induction) in proving a mathematical statement|
|CLO 4||demonstrate the basic properties of equivalence relations|
|CLO 5||understand the definition of the limit of a sequence of real numbers|
|CLO 6||demonstrate the operational properties of groups|
36 contact hours + 120 learning hours
- Final Exam: 50%
- Tests: 32%
- Assignments: 8%
- Tutorials: 10%
No supplementary examination will be offered.
#Important Note: You are required to settle the application fee of HKD 350 (non-refundable) when applying for admission to this credit-bearing summer course.
For more programme information, please visit http://hkumath.hku.hk/web/outreach/MATH2012-HKU-summer-institute-2017-HS.pdf.