The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Course outline Spring 2016
1. Instructor
Name: Professor Yue Kuen KWOK
Contact details: Office Room 3445, Tel: 23587418; Email: maykwok
2. Teaching assistant
Name: Dr Chi Man LEUNG
3. Meeting time
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999
Capstone Projects in Mathematics and Economics
First Test Fall 2015
Time allowed: 80 minutes
Course Instructor: Prof. Yue Kuen Kwok
[points]
1. Recall the following denitions for proportional division and envyfree division: Suppose X =
(x1 , . .
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Homework Two
Course instructor: Prof. Y.K. Kwok
1. Suppose there are four alternatives, named A, B, C and D. There are three voters who
have the following individual rankings:
B 1 C 1 D 1 A
C 2 D 2 A
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Homework Four
Course instructor: Prof. Y.K. Kwok
1. Suppose a velocity field is given by
dx
30x + 30L
= u(x, t) =
.
dt
15t + L
(a) Determine the motion of a car that starts at x = L/2 at t = 0. Notin
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Homework One
Course instructor: Prof. Y.K. Kwok
1. Six students Ann, Bob, Carl, Dora, Ed, and Fran are placed on an island for a contest.
This problem is related to the design of the rules of a game
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Topic Four Trac ow models
4.1 Characteristics of trac ows
Trac problems
Velocity and trac ows
Flux and conservation law
4.2 Method of characteristic line
Density wave velocity
4.3 Impact of a tra
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999
Capstone Projects in Mathematics and Economics
Second Test Fall 2015
Time allowed: 80 minutes
Course instructor: Prof. Y.K. Kwok
[points]
1. (a) Show that the Condorcet winner criterion fails for the Borda count method.
[2]
(b) Do both the Condor
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Topic 2 Voting methods and social choice theory
2.1 Social choice procedures
2.2 Analysis of voting methods
2.3 Arrows Impossibility Theorem
2.4 Singlepeaked preferences and the Median Voter Theorem
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Topic One: Fair allocations and matching schemes
1.1 Criteria for fair divisions
Proportionality, envyfreeness, equitability and eciency
1.2 Procedures for twoplayer and multiplayer cakecutting
The Hong Kong University of Science and Technology
Capstone Project for Mathematics and Economics
MATH 4999

Fall 2016
MATH4999 Capstone Projects in Mathematics and Economics
Topic 3 Proportional representation and Apportionment
Schemes
3.1 General issues of apportionment of legislature seats
3.2 Quota Method of the Greatest Remainder (Hamiltons method)
and paradoxes
3.3