Jointly offered by the
Departments of Mathematics and Economics
1
Agenda
•
•
•
Overview of the Program
-
who should choose this Program
-
career prospect
-
program requirements
-
admission requirements
Applications of mathematics in economics
-
Two-sided matching schemes
-
Powers in voting systems
-
US House seats apportionment
Views from leading economists
-
role of mathematics in economics
Academic Aspirations
 Students who are interested in learning to
apply mathematical ideas and techniques to
wide range of problems in economics.
- University admission schemes: 2-sided
matching
- Influenential power in various voting systems
- Proportional representation: apportionment of
legislature seats
- Financial economics: asset pricing theory and
portfolio selection
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 Provide a program of study for students who
seek the option of taking a quantitatively
oriented job in financial industry or intend to
pursue postgraduate study in applied
mathematics, economics, or in a related
area, like quantitative finance or
management science.
4
Stay competitive in the future job markets
 Provide students with solid training in
fundamental theories in both mathematics
and economics.
 Equip students with quantitative reasoning
skills, conceptual understanding, and the
a b i l i t y t o e ff e c t i v e l y c o m m u n i c a t e i n
m a t h e m a t i c s an d i n th e l a n g u a g e o f
economics and social science.
5
Why choose this degree program?
Liberal arts education versus professional
training
 The program is advantageous to students who
otherwise would take a single major in
mathematics or economics.
 Equip oneself with a strong quantitative
background in economics and related areas in
management and finance.
6
Career Prospects
 Ample career opportunities in the financial
sector and public sector for university
graduates that fully understand the use of
mathematical and economic tools and those
who are able to use the knowledge and
language of both disciplines.
 Equipped with the necessary background for
entry into postgraduate degree programs in
applied mathematics and economics.
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Preparation for postgraduate
studies
 Pursue
PhD study at Stanford University,
UCLA, Minnesota University, Boston
University, and others
 Enroll
in MSc degrees in Financial
Engineering / Mathematics at Columbia
University, University of California at
Berkeley, Imperial College, HKUST, etc.
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Key components in the curriculum
Subject area
No. of courses
Mathematics
8
Economics
8
Humanities and Social Science
4
Business
1
Computer Science
1
Language
2
Free electives
3
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Major Program Requirements
 Core Courses
MATH 101
Multivariate Calculus
[3-1-0:4]
MATH 111
Linear Algebra
[3-1-0:4]
MATH 201
Introduction to Analysis
[3-1-0:4]
ECON 198
Microeconomic Theory I
[3-1-0:4]
ECON 199
Macroeconomic Theory I
[3-1-0:4]
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 Required Courses
MATH 241
Probability
[3-1-0:4]
MATH 301
Real Analysis
[3-1-0:4]
ECON 200
Microeconomic Theory II
[3-1-0:4]
ECON 201
Macroeconomic Theory II
[3-1-0:4]
ECON 233
Introduction to Econometrics
[3-1-0:4]
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 Elective Courses
Three Mathematics electives are chosen at the 300-level
or above. Some recommended Mathematics electives
are
MATH310
Game Theory
[3-1-0:4]
MATH341
Stochastic Modeling
[3-1-0:4]
MATH362
Fundamentals of Mathematical Finance [3-1-0:4]
MATH392
Mathematics of Social Choice Theory
[3-1-0:4]
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 Elective Courses
Three Economics electives are chosen at the 300-level
or above. Some recommended Economics electives
are
ECON 329 Econometrics for Financial Data
ECON 330 Time Series Econometrics and
Business Forecasting
ECON 333 Money and Banking
ECON 335 International Trade and Finance
ECON 343 Economic Development and Growth
[3-1-0:4]
[3-1-0:4]
[3-1-0:4]
[3-1-0:4]
[3-1-0:4]
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 General Education Requirements
Electives must be selected from among those general
education courses that are listed under the section
“Designated General Education Courses”.
Minimum
Minimum
Elective Types
Number of Course Credits
________________________________________________________________
GEE (B&M)
Business and Management
General Education Elective
1
3
GEE (ENGG)
Engineering General Education Elective
1
3
GEE (H&SS)
Humanities and Social Science
General Education Elective
4
12
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ECON 150
[3-0-0:4]
Big Problems in Economics: Issues, Ideas, and Principles
_____________________________________________________________
The course introduces students to some of the economic principles that
never have proven to be powerful tools for analyzing real-world problems. A
wide range of the most pressing issues of our times will be identified and
discussed. The necessary framework for analyzing them ill be developed.
ECON 191
Honors Microeconomics
[3-1-0:4]
_____________________________________________________________
Application of economic theory to important real-world problems; reading of
selected excerpts from important books and articles; discussions of
methodology and current controversies. Exclusions: ECON 110, ECON 111,
ECON 113, SOSC 144, AL Business and Economics Prerequisite: B or above
in AL Economics
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COURSES IN LANGUAGE FOR BUSINESS
LABU 101
Business Case Analyses
[0-3-0:4]
______________________________________________________________
A one-year course for Business students and students in
Technology and Management. This course develops students'
critical thinking and communication skills as well as
interdisciplinary
awareness
through
a
process
of
comprehending, analyzing and presenting business cases in
various disciplines. Exclusion: LANG 107
LANG 201
Business Communication
[0-3-0:3]
______________________________________________________________
Restricted to students in the School of Business and
Management. Focuses on the processes and skills of effective
oral presentation, report and letter writing in business situations
where English is the medium of communication. Prerequisite:
LABU 101/LANG 107
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Overseas Exchange Programs
Students can choose either the list of exchange
partners from the School of Science or School of
Business and Administration.
• Take advantage of being a joint program offered by two
schools
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Admission channels and requirements
Interested applicants may apply via the JUPAS or
the Early Admission Scheme. In addition to the
General University entrance requirements, an
applicant must obtain
1. grade D or above in AS Use of English in HKALE
2. pass in AL Pure Mathematics
plus 1 AL / 2 AS subjects
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Views from leading economists
- Role of mathematics in economics
Paul Krugman - New York Times
(Sept. 11, 2009)

Mathematics in economics can be extremely
useful.
 The mathematical grinding serves an essential
function — that of clarifying thought.
 I started with some vague ideas; it was not until I
have managed to write down full models that the
ideas came clear.
 After the mathematics, I was able to express
most of those ideas in plain English, but it really
took the mathematics to get there, and you still
cannot quite get it all without the equations.
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Other views


The problem with mathematics in
economics is that most economists are
amateur mathematicians trying to fake it.
Their mathematics is sloppy and cuts
corners,
or
is
simply
applied
indiscriminately and inappropriately.
Reading general equilibrium theory makes
you want to study pure physics or
mathematics to see how it should be done.
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
Equations / models / methodologies are merely
tools to aid the financial / economic decision
making process.

A lot of Business schools teach models like
CAPM but do not teach their students to question
the underlying assumptions of the model.

Critical thinking is a must and no amount of
mathematics or econometrics methodology can
eliminate it.
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
It seems to me that it is hard to have a
substantive theory without mathematics,
but mathematics alone is not enough.

After all, mathematics is just a tool, one
which can be used well or badly, for the
right or wrong reasons.
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
Mathematics can and should be used in economics
to aid understanding. But this does not mean that
economist’s mathematical models are anywhere
close to being able to predict the future.

Mathematical models are merely “that models”.
The real life system of economic interactions, like
every other system in the natural world, is only
finitely divisible, that is not continuous and not
differentiable. The mathematical models are
generally assumed to be continuous and often
differentiable.
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Mathematics and its
applications in Economics
Two-sided matching schemes
 University admission schemes
− Each individual student has her preference list of
programs
− Each degree program has its own priority choices
of students
 Marriage: matching between pairs
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Program Optimal Approach
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Each admissions officer gives out all the K
offers to its chosen list of top K candidates
(represented by representatives).
If there are more than one offer given to the
candidate, then she returns the less preferred
offers to the admissions officers, who will then
give the offers to the next eligible candidate in
the queue.
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Student Optimal Approach
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A
soldier tries to break into the castle
through one of the gangways (in order of
his preference).
 When a compartment is full, the intruder
will fight with the weakest person admitted
in a tournament.
 If the intruder is victorious, then he kicks
out the weakest occupant.
 If the intruder is defeated, then he tries the
next preferred gangway (until having
exhausted all his choices).
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Characteristics of a stable solution
1.
For candidates who are not assigned to
any study programmes, they are inferior
to all the selected ones in all the
programmes they have applied for.
2.
For a candidate who is assigned to a
study programme which is not his first
choice, then in all his more preferred
choices, he is inferior to all the
candidates who have been accepted.
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In other words, a student cannot find a more
preferred curricula which is willing to accept
him, and an institution cannot get a more
eligible student willing to accept its offer to
replace the weakest one already accepted.

Stable solutions exist but they may not
be unique. However, in all the stable
solutions, it is always the same group of
applicants that are selected for
admission.
32
Measurement of political power
United Nations Security Council
Big “five” permanent members, each has veto power.
Ten “small” countries whose membership rotates.
Need 9 affirmative votes from the 15-member council to
pass a resolution.
What is the relative strength (political power) of the “big”
and “small” nations?
- Pivotal in turning a losing coalition into a winning one.
- How often can a member state play such a role?
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United States Federal System
 537 voters in the system: 435 Representatives, 100
Senators, the Vice President and the President.
 The President has veto power that can be overridden by a
two-thirds vote of both the House and the Senate.
 The Vice President plays the role of tie breaker in the
Senate.
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Apportionment of legislature seats based
on populations of districts
District
A
B
C
D
E
Population
9061
7179
5259
3319
1182
26000
25 seats
exact quota
8.713
[9]
6.903
[7]
5.057
[5]
3.191
[3]
1.137
[1]
25
26 seats
exact quota
9.061
[9]
7.179
[7]
5.259
[5]
3.319*
[4]
1.182
[1]
26
27 seats
exact quota
9.41
[9]
7.455*
[8]
5.461*
[6]
3.447
[3]
1.227
[1]
27
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 Method of the Greatest Remainders –
Favoring districts with larger population
Order the remainder qi - qi, and allocate,
one each, to the districts having the largest
fractional remainders.
 Integer programming problem – seek integer
solutions that minimize the discrepancies
between allocated seats and fair shares.
36
Alabama paradox – Loss of House Monotone Property
Increase in the total number of seats may force a state to lose
a seat.
− In 1880, Alabama would get 8 seats from total of 299, but
only 7 from total of 300.
It changes the priority order of assigning the surplus seats.
 Alabama had an exact quota of 7.646 at 299 seats and
7.671 at 300 seats.
Texas and Illinois increased their quotas from 9.040 and
18.640 to 9.682 and 18.702, respectively.
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Population paradox
State X could lose seats to State Y even though population of
X had grown faster than population of Y.
New States Paradox
Adding a new state and / or increasing number of seats may
cause another state to lose seats.
− In1907, Oklahoma was added as new state with 5 new
seats to the House (386 to 391). Maine’s apportionment
went up (3 to 4) while New York’s went down (38 to 37).
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Mathematics is …
 Advanced
language
 A tool of clarity, precision and correctness
 An aid to calculations – getting numbers
 Sources of concepts e.g. game theory,
equilibrium theory, optimization, statistics
 (quite often) difficult to use, to understand
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Insurance: Mathematics and Economics

The subject matter of the journal includes the
theory, models and computational methods of
life insurance (including pensions systems,
social insurance, and health insurance), of nonlife insurance, of reinsurance and other risksharing arrangements, as well as of risk
management.

It includes innovative insurance applications of
results from other fields, such as probability and
statistics, computer science and numerical
analysis, economics, operations research and
management science.
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For more details,
please visit the program web page
at
http://www.math.ust.hk/ug/programs/bsc.mathecon.shtml
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Thank you for your attention.
Questions!