Fundamental Concepts of Mathematics (6 credits)

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

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Type of Programme: Credit-bearing course

Area of Interest: Mathematics

Managed by: Department of Mathematics, Faculty of Science

Eligibility:

  • Students:       Local; Non-local
  • Age:                 16 or above

Admission requirements: 

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

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 Outline

  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

  1. Proof Strategies:

Direct Proof, Proof by Contrapositive, Proof by Cases, Proof by Contradiction, Proof by Mathematical Induction, Counterexamples, Prove or Disprove

  1. 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

  1. Other Topics:

Introduction to Calculus: Sequences and Series; Introduction to Group Theory

Learning Outcomes

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

Study Load

36 contact hours + 120 learning hours

Assessments

  1. Final Exam: 50%
  2. Tests: 32%
  3. Assignments: 8%
  4. 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.