1 Jointly offered by the Departments of Mathematics and Economics.

11

Jointly offered by theDepartments of Mathematics and Economics

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

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Academic AspirationsStudents who are interested in learning to

apply mathematical ideas and techniques to wide range of problems in economics.

- University admission schemes: 2-sdied 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 ormanagement science.

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Stay competitive in 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 ability to effectively communicate in mathematics and in the language ofeconomics and social science.

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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.

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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 Preparation for postgraduate studiesstudies

PhD study at Stanford University, PhD study at Stanford University, Washington University, and othersWashington University, and others

MSc degree in Financial Mathematics at MSc degree in Financial Mathematics at University of Chicago, HKUST, etc.University of Chicago, 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 [3-1-0:4]

ECON 330 Time Series Econometrics and Business Forecasting [3-1-

0:4]ECON 333 Money and Banking [3-1-

0:4]ECON 335 International Trade and Finance [3-1-

0:4]ECON 343 Economic Development and Growth [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 MinimumElective Types Number of Course Credits

________________________________________________________________

GEE (B&M) Business and Management 1 3 General Education Elective

GEE (ENGG) Engineering General Education Elective 1 3

GEE (H&SS) Humanities and Social Science 4 12General Education Elective

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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 191Honors 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

Mathematics and its applications in Economics

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Advanced languageAdvanced language A tool of clarity, precision and correctnessA tool of clarity, precision and correctness An aid to calculations – getting numbersAn aid to calculations – getting numbers Sources of concepts e.g. game theory, Sources of concepts e.g. game theory,

equilibrium theory, optimization, statisticsequilibrium theory, optimization, statistics (quite often) difficult to use, to understand(quite often) difficult to use, to understand

Mathematics is …

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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 A soldier tries to break into the castle through one of the gangways (in order of through one of the gangways (in order of his preference).his preference).

When a compartment is full, the intruder When a compartment is full, the intruder will fight with the weakest person admitted will fight with the weakest person admitted in a tournament.in a tournament.

If the intruder is victorious, then he kicks If the intruder is victorious, then he kicks out the weakest occupant.out the weakest occupant.

If the intruder is defeated, then he tries the If the intruder is defeated, then he tries the next preferred gangway (until having next preferred gangway (until having exhausted all his choices).exhausted all his choices).

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Characteristics of a stable solutionCharacteristics of a stable solution1.1. For candidates who are not assigned to For candidates who are not assigned to

any study programmes, they are any study programmes, they are inferiorinferior to all the selected ones in all the to all the selected ones in all the programmes they have applied for.programmes they have applied for.

2.2. For a candidate who is assigned to a For a candidate who is assigned to a study programme which is not his first study programme which is not his first choice, then in all his more preferred choice, then in all his more preferred choices, he is inferior to all the choices, he is inferior to all the candidates who have been accepted.candidates who have been accepted.

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In other words, a student cannot find a more In other words, a student cannot find a more preferred curricula which is willing to accept preferred curricula which is willing to accept him, and an institution cannot get a more him, and an institution cannot get a more eligible student willing to accept its offer to eligible student willing to accept its offer to replace the weakest one already accepted.replace the weakest one already accepted.

Stable solutions exist but they may not Stable solutions exist but they may not be unique. However, in all the stable be unique. However, in all the stable solutions, it is always the same group of solutions, it is always the same group of applicants that are selected for applicants that are selected for admission.admission.

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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 PopulationA 9061 8.713 [9] 9.061 [9] 9.41 [9]B 7179 6.903 [7] 7.179 [7] 7.455* [8]C 5259 5.057 [5] 5.259 [5] 5.461* [6]D 3319 3.191 [3] 3.319* [4] 3.447 [3]E 1182 1.137 [1] 1.182 [1] 1.227 [1]

26000 25 26 27

exact quota27 seats

exact quota25 seats 26 seats

exact quota

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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.

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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).

Views from leading economists

- Role of mathematics in economics

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Paul Krugman - New York Times Paul Krugman - New York Times (Sept. 11, 2009)(Sept. 11, 2009) Mathematics in economics can be extremely Mathematics in economics can be extremely

useful. useful. The mathematical grinding serves an essential The mathematical grinding serves an essential

function — that of clarifying thought. function — that of clarifying thought. I started with some vague ideas; it was not until I I started with some vague ideas; it was not until I

have managed to write down full models that the have managed to write down full models that the ideas came clear. ideas came clear.

AfterAfter the mathematics, I was able to express the mathematics, I was able to express most of those ideas in plain English, but it really most of those ideas in plain English, but it really took the mathematics to get there, and you still took the mathematics to get there, and you still cannot quite get it all without the equations.cannot quite get it all without the equations.

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The problem with mathematics in The problem with mathematics in economics is that most economists are economics is that most economists are amateur mathematicians trying to fake it. amateur mathematicians trying to fake it. Their mathematics is sloppy and cuts Their mathematics is sloppy and cuts corners, or is simply applied corners, or is simply applied indiscriminately and inappropriately. indiscriminately and inappropriately.

Reading general equilibrium theory makes Reading general equilibrium theory makes you want to study pure physics or you want to study pure physics or mathematics to see how it should be done.mathematics to see how it should be done.

Other views

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Equations / models / methodologies are merely Equations / models / methodologies are merely tools to aid the financial / economic decision tools to aid the financial / economic decision making process. making process.

A lot of Business schools teach models like A lot of Business schools teach models like CAPM but do not teach their students to question CAPM but do not teach their students to question the underlying assumptions of the model. the underlying assumptions of the model.

Critical thinking is a must and no amount of Critical thinking is a must and no amount of mathematics or econometrics methodology can mathematics or econometrics methodology can eliminate it.eliminate it.

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It seems to me that it is hard to have a It seems to me that it is hard to have a substantive theory without mathematics, substantive theory without mathematics, but mathematics alone is not enough.but mathematics alone is not enough.

After all, mathematics is just a tool, one After all, mathematics is just a tool, one which can be used well or badly, for the which can be used well or badly, for the right or wrong reasons.right or wrong reasons.

3939

Mathematics can and should be used in economics Mathematics can and should be used in economics to aid understanding. But this does not mean that to aid understanding. But this does not mean that economist’s mathematical models are anywhere economist’s mathematical models are anywhere close to being able to predict the future.close to being able to predict the future.

Mathematical models are merely “that models”. Mathematical models are merely “that models”. The real life system of economic interactions, like The real life system of economic interactions, like every other system in the natural world, is only every other system in the natural world, is only finitely divisible, that is not continuous and not finitely divisible, that is not continuous and not differentiable. The mathematical models are differentiable. The mathematical models are generally assumed to be continuous and often generally assumed to be continuous and often differentiable.differentiable.

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Insurance: Mathematics and EconomicsInsurance: Mathematics and Economics

The subject matter of the journal includes the The subject matter of the journal includes the theory, models and computational methods of life theory, models and computational methods of life insurance (including pensions systems, social insurance (including pensions systems, social insurance, and health insurance), of non-life insurance, and health insurance), of non-life insurance, of reinsurance and other risk-sharing insurance, of reinsurance and other risk-sharing arrangements, as well as of risk management. arrangements, as well as of risk management.

It includes innovative insurance applications of It includes innovative insurance applications of results from other fields, such as probability and results from other fields, such as probability and statistics, computer science and numerical statistics, computer science and numerical analysis, economics, operations research and analysis, economics, operations research and management science.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

Thank you for your attention.

Questions!