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Curriculum for the Financial Mathematics Stream
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The Professional Science Master's Degree is a two-year
program with a summer internship. There will be core and focus courses in
the Mathematics Department, as well as additional courses in Statistics,
Economics, and the Katz Graduate School of Business.
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Fall, Year 1
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Spring, Year 1
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Summer
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Mathematics of Finance I (Optional)
Scientific Computing I
Statistics elective
Optional elective
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Mathematics of Finance II
Scientific Computing II
Stochastic Processes (optional)
Projects Course
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Graduate Internship
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Fall, Year 2
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Spring, Year 2
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Mathematics of Finance III
Economics Elective I
MBA Essentials
Optional elective
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Mathematics of Finance IV
Economics Elective II
Projects Course
Optional elective
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Course Descriptions:
- Projects in Financial Mathematics (MATH 2980)
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Representatives from business or government will present real-world
problems and issues. Students will select and find solutions for one of
the problems, either independently or in teams. Oral and written reports
of the results will then be presented to both the posers of the problems
and to the faculty and students in the Professional Masters program.
All professional master's students must take this class each term.
In addition to working on projects, promaster's students will also focus
on career development issues such as preparing resumes, obtaining summer
internships and conducting job searches.
- Mathematics of Finance I (MATH 3225)
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This course covers the rudiments of the mathematical
subjects required for the mathematical finance program, and
assumes that the student has
an undergraduate degree with some technical component (e.g. Engineering,
Computer Science, Math, Statistics, Physics, etc.) Students are
expected to have knowledge of Multivariate Calculus and Linear Algebra,
and the sections on these topics
should be regarded as review. No financial background is needed, but
many of the examples and illustrations of the mathematics will be
drawn from the world of finance.
Prerequisites: Permission of instructor
- Mathematics of Finance II (MATH 3226)
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This is an introduction to modern mathematical finance. Topics include
pricing / hedging of derivative securities, the Black-Scholes
and Heath-Jarrow-Morton models (and extensions), risk management, and
portfolio optimization. Emphasis will be based on numerical techniques,
as well as the implementation of practical discrete-time models.
Prerequisites: Math Finance I or sufficient
background in Calculus, Linear Algebra, PDE, numerical methods and
Probability & Statistics
- Mathematics of Finance III (MATH 3227)
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This course focuses on techniques used to measure and manage financial
risk. Emphasis is placed on conceptual understanding and practial
implementation by numerical methods. Topics include an introduction to
risk management, hedging, Value-at-Risk, credit risk modelling, axiomatic
treatment of risk measures, and coherent measures of risk.
Prerequisites: Math Finance II
- Mathematics of Finance IV (MATH 3228)
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This course introduces the techniques of mathematical optimization to
financial problems, with a focus on optimal portfolio selection. Topics
include Markowitz mean-variance analysis, utility theory / maximization,
single- and multi-period models and stochastic programming, stochastic
control,and Merton's problems and extensions.
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Prerequisites: |
Math Finance II & III, Linear and Nonlinear Programming
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- Numerical Methods in Sci. Computing I & II (MATH 2070-71)
- MBA Essentials (offered by
Katz Graduate School of Business)
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- Possible statistics elective:
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Applied Statistical Methods I
(STAT 2131)
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Data Mining
(STAT 2270)
Theory of Statistics 1
(STAT 2631)
Applied Stochastic Processes 1
(STAT 2731)
- Stochastic Processes (STAT 1731)
- Possible economics elective sequences:
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1. Economics 2100
& 2110,
Advanced Microeconomic Theory I & II
2. Economics 2120
& 2130,
Advanced Macroeconomic Theory I & II
3. Economics 2020,
Introduction to Econometric Theory &
Economics 2150,
General Econometrics.
4. Game theory or Industrial organization courses when available.
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Prerequisites
Candidates should have taken the following Mathematics courses:
- Calculus I, II, & III
- Linear Algebra
- Ordinary Differential Equations
- Partial Differential Equations
- Probability & Statistics
- Numerical Methods (some Linear Programming)
The Department of Mathematics requires an overall 3.0 undergraduate QPA and a 3.25 QPA in undergraduate mathematics courses for full admission into its graduate programs.
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