Transcript Careers In Applied Mathematics -

CAREER OPPORTUNITIES IN
MATHEMATICAL SCIENCES
Dongming Wei
Professor of Mathematics
School of Science and Technology, Nazarbayev University
[email protected]
CAREERCAST.COM JOB SURVEYS
147 Stress pts: Quotas (5), Deadlines (9), Advocacy
(5), Win or lose situations (5), Working in public eye (5),
Competitiveness (15), Heavy lifting (5), Physical
demands (14), Environmental Conditions (13),
Machines and tools (5), Speed required (5), Hazards
(5), Own life at risk (8), Other lives at risk (10), Precision
required (5), Initiative required (5), Outdoor work (5),
Confinement (5), Detail (5), Public meetings (8)
CAREERCAST.COM 2014 BEST JOBS
http://www.careercast.com/jobs-rated/best-jobs-2014
Rank
Job
BLS Median Annual Salary Stress
Score
Hiring Outlook
1
Mathematician
$101,360
63
23%
2
Professor (Tenured)
$68,970
73
19%
3
Statistician
$75,560
96
27%
4
Actuary
$93,680
103
26%
5
Audiologist
$69,720
110
34%
6
Dental Hygienist
$70,210
112
33%
7
Software Engineer
$93,350
125
22%
8
Computer Systems Analyst
$79,680
126
25%
9
Occupational Therapist
$75,400
129
29%
10
Speech Pathologist
$69,870
128
19%
CAREERCAST.CO
HTTP://WWW.CAREERCAST.COM/SLIDE/BEST-JOBS-2013
M 2013 BEST JOBS
Ran
k
Job
Income
Stress
Hiring Outlook
1
Actuary
$87,650
123
27%
2
Biomedical Engineer
$81,540
133
62%
3
Software Engineer
$90,530
136
30%
4
Audiologist
$66,660
140
37%
5
Financial Planner
$64,750
159
32%
6
Dental Hygienist
$68,250
161
38%
7
Occupational
Therapist
$72,320
166
33%
8
Optometrist
$94,990
190
33%
9
Physical Therapist
$76,310
199
39%
10
Computer Systems
Analyst
$77,740
212
22%
CAREERCAST.COM 2012 BEST JOBS
Rank
Job
Income
Stress
Hiring Outlook
1
Software Engineer
$88,142
176
25%
2
Actuary
$88,202
266
27%
3
Human Resources Manager
$99,102
281
19%
4
Dental Hygienist
$68,109
289
36%
5
Financial Planner
$104,161
300
23%
6
Audiologist
$67,137
311
37%
7
Occupational
Therapist
$72,110
318
33%
8
Online Advertising
Manager
$87,255
343
26%
9
Computer Systems
Analyst
$78,148
370
23%
10
Mathematician
$99,191
392
17%
BIOSTATISTICS
HTTP://WWW.AMSTAT.ORG/CAREERS/BIOSTATISTICS.CFM
• Biostatisticians with advanced degrees can look forward to excellent career
opportunities in government, industry, and academia. The shortage of
biostatisticians is noted in Objectives for the Nation and the Seventh Report
to the President and Congress on the Status of Health Personnel in the
United States.
• Job prospects for new graduates with master's and PhD degrees in
biostatistics are excellent. Typical starting salaries range from $35,000 to
$65,000 for master's-level graduates and $55,000 to $85,000 for PhD-level
graduates.
• Recent graduates have found positions with employers as diverse as
pharmaceutical companies, university research groups, hospitals, and
health-related industries.
OPERATIONS RESEARCH ANALYST
HTTP://MONEY.USNEWS.COM/CAREERS/BEST-JOBS/OPERATIONS-RESEARCH-ANALYSTEARCH ANALYST
• Operations research analysts are high-level problemsolvers who use advanced techniques, such as
optimization, Queueing, data mining, statistical analysis
and mathematical modeling, to develop solutions that
help businesses and organizations operate more
efficiently and cost-effectively.
• UPS uses operations research to chart the flow of
packages, provide real-time route guidance to drivers
and help plan and manage distribution. In the health
care field, the Memorial Sloan-Kettering Cancer Center
in New York used operations research to design a
radiation treatment plan for prostate patients using
sophisticated modeling and computation techniques.
• Operations research originated with military planners in
World War II, according to INFORMS, but businesses and
other organizations soon began adopting the
techniques. Today, operations research analysts can be
found in virtually every industry, from manufacturing to
finance and throughout the spectrum of government
agencies. Demand for these professionals should remain
high for years to come, as companies and governments
seek greater efficiency and cost savings. The Bureau of
Labor Statistics projects employment growth of nearly 27
percent for operations research analysts between 2012
and 2022, much faster than average for all occupations.
During that time period, 19,500 new jobs will need to be
filled.
HTTP://MONEY.USNEWS.COM/CAREERS/BEST-JOBS/OPERATIONS-RESEARCHANALYST
• According to the BLS, the median annual salary for operations research
analysts was $74,630 in 2013. The highest-paid in the profession earned
more than $130,210, while the lowest-paid made less than $42,070. The
top-paying operations research analysts work in the securities and
commodity contracts sphere of the financial industry, and the highestpaying metropolitan areas are New York City; San Jose, California; and
San Diego.
• Salary Range
• 75th Percentile$99,210
• Median$74,630
• 25th Percentile$55,110
ACTUARY
HTTP://MONEY.USNEWS.COM/MONEY/CAREERS/ARTICLES/2008/12/11/JOB-UNIVERSE-ACTUARY
• Through their knowledge of statistics, finance, and
business, actuaries assess the risk of events occurring and
help create policies that minimize risk and its financial
impact on companies and clients. Most actuaries are
employed in the insurance industry, specializing in either
life and health insurance or property and casualty
insurance. Employment of actuaries is expected to
increase by about 24 percent over the 2006-16 period,
which is much faster than the average for all other
occupations. Employment growth in the insurance
industry—the largest employer of actuaries is expected
to continue at a stable pace, and more significant
growth in actuarial jobs is likely in other industries, such as
healthcare and consulting firms.
• Actuaries need a strong foundation in
mathematics, statistics, and general business. They
generally have a bachelor's degree and are
required to pass a series of exams in order to
become certified. Usually, actuaries earn an
undergraduate degree in mathematics, statistics, or
actuarial science, or in a business-related field such
as finance, economics, or business. Median annual
earnings of actuaries were $82,800 in May 2006. The
middle 50 percent earned between $58,710 and
$114,570. The lowest 10 percent had earnings of less
than $46,470, while the top 10 percent earned more
than $145,600.
HTTP://WWW.BEANACTUARY.ORG/
https://www.actuaryjobs.com/
Tracks:
Property & Casualty | Health | Life, Annuities &
Investments | Pension
QUANTS:QUANTITATIVE ANALYSTS
HTTP://WWW.INVESTOPEDIA.COM/ARTICLES/FINANCIALCAREERS/08/QUANTSQUANTITATIVE-ANALYST.ASP
• A blend of mathematics, finance and computer skills quants are in great demand and able to command
very high salaries.
• Demand for quants is high and driven by multiple trends:
• Rapid growth of hedge funds and automated trading
systems
• Increasing complexity of both liquid and illiquid securities
• Need to give traders, accountants and sales reps access
to pricing and risk models
• Ongoing search for market-neutral investment strategies.
• Compensation in the field of finance tends to be very high,
and quantitative analysis follows this trend. It is not uncommon
to find positions with posted salaries of $250,000 or more and
with bonuses, $500,000+ is achievable. As with most careers,
the key to landing the high-paying jobs is a resume filled with
experience, including well-known employers, and reliance on
both recruiting firms and professional networking for
opportunities.
• The highest-paid positions are with hedge funds or other
trading firms, and part of the compensation is dependent
upon the earnings of the firm, also known as the P&L (profit
and loss). At the other end of the pay scale, an entry-level
quant position may earn only $125,000 or $150,000, but this
type of position provides a fast learning curve and plenty of
room for future growth in both responsibilities and salary.
INTRODUCTION TO TRADING ALGORITHMS,
EDWARD A LESHIK AND JANE CRALLE, WILEY, 2010
“two major hedge funds such as J. Simons’
Renaissance and D.E. Shaw’s funds which generally
produce extraordinary returns on capital year in, year
out. It is rumored that each of these highly successful
operations employ a staff of something over 50 PhDlevel mathematicians, statisticians and physicists and
run some of the most powerful and advanced
computer hardware.”
HTTPS://WWW.QUANTSTART.COM
/ARTICLES/SELF-STUDY-PLAN-FOR-BECOMING-A-QUANTITATIVE-ANALYST
Quantitative analysts and financial engineers spend
their time determining fair prices for derivative
products. This involves some deep mathematical
theory including probability, measure theory,
stochastic calculus and partial differential
equations. Thus to become a quant analyst it is
necessary to have a strong mathematical
background in mathematics, usually through an
undergraduate degree in mathematics, physics or
engineering.
• Financial Knowledge
Many financial securities, such as options and convertibles,
are easy to understand conceptually, but are very difficult to
model precisely. Because of this hidden complexity, the skills
most valued in a quant are those related to mathematics and
computation rather than finance. It is a quant's ability to
structure a complex problem that makes them valuable, not
their specific knowledge of a company or market.
• A quant should understand the following mathematical
concepts:
• Calculus (including differential, integral and stochastic)
• Linear algebra and differential equations
• Probability and statistics
• Key financial topics include:
• Portfolio theory
• Equity and interest rate derivatives, including exotics
• Credit-risk products
• Some quants will specialize in specific products, such
as commodities, foreign exchange or asset-backed securities.
• Computer Competency
Software skills are also critical to job performance. C++ is typically
used for high-frequency trading applications, and offline statistical
analysis would be performed in Matlab, SAS, S-PLUS/R or a
similar package. Pricing knowledge may also be embedded in
trading tools created with Java, .NET or VBA, and are often
integrated with Excel. Monte Carlo techniques are essential.
• Education and Certifications
Most firms look for at least a Master's degree or preferably a PhD in
a "quantitative" subject, such as Mathematics, Economics, Finance
or Statistics. Master's degrees in Financial Engineering or
Computational Finance are also effective entry points for quant
careers. Generally, an MBA is not enough by itself to obtain a quant
position, unless the applicant also has a very strong mathematical or
computational skill set in addition to some solid experience in the
real world.
• Consulting firms such as Daniel H. Wagner Associates and McKinsey and
Company
• Aerospace and transportation equipment manufacturers such as Boeing;
Ford; General Motors; Lockheed Martin; and United Technologies
• Financial service and investment management firms such as Citibank;
Moody’s Corporation; Morgan Stanley; and Prudential
• Transportation service providers such as FedEx Corporation and United
Parcel Service
• Communications services providers such as Clear Channel
Communications; CenturyLink; and Verizon
• Chemical or pharmaceutical manufacturers such as DuPont;
GlaxoSmithKline; Merck & Co., Inc.; Pfizer
• Medical device companies such as Baxter Healthcare; Boston Scientific;
and Medtronic;
• Producers of petroleum and petroleum products such as Exxon Research
and Engineering; Petróleo Brasileiro S/A/ Petrobras; Shell; and Chevron
• Academic institutions such as the Institute for Advanced Study; the
Institute for Mathematics and Its Applications (IMA); and the
Mathematical Sciences Research Institute (MSRI)
• Consumer products companies such as Procter & Gamble and Mars
NYU MATHEMATICS OF FINANCE PROGRAM
HTTPS://WWW.QUANTNET.COM/RESOURCES/NYU-MATHEMATICS-OF-FINANCE-PROGRAM.2/
• 1. Derivative Securities
2. Risk & Potfolio Mgmt with
Econometrics
3. Stochastic Calculus
4. Computing in Finance
• 5. Credit Markets and Models
6. Scientific Computing
7. PDE for Finance
8. Interest Rates & FX Models
9. Scientific Computing
• 10. Advanced Risk Management
11. Continuous Time Finance 12.
Time Series Analysis And Statistical
Arbitrage
13. Case Studies in Financial
Modeling
14. Computational Methods in
Finance
15. Project & Presentation
16. Fin Eng Models for Corp Finance
THE MASTER OF SCIENCE IN OPERATIONS RESEARCH PROGRAM
COLUMBIA UNIVERSITY
• Operations Research: Deterministic
Models, Stochastic Models
• Simulation
• Introduction to Probability and Statistics
Logistics & Supply Chain Management Concentration
Management Courses (at least two):
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The Manufacturing Enterprise
Studies in Operations Research
Resource Allocation: Models, Algorithms,
and Applications
Quality Control and Management
Project Management
Applied Systems Engineering
Entrepreneurial Business Creation for
Engineers
Decision Models and Applications
Managing Technological Innovation and
Entrepreneurship
Technical Courses (at least three):
• Service Operations
• Supply Chain Management
• Demand and Supply Analytics
• Production and Operations Management
• Advanced Engineering and Corporate
Economics
• Production Scheduling
• Logistics and Transportation Management
• Operations Management: With Application to
Healthcare Management
• Machine Learning for OR & FE
• Applied Integer Programming
• Dynamic Pricing and Revenue Management
• Quantitative Risk Management
• Service Engineering
THE UNIVERSITY OF MINNESOTA, SCHOOL OF PUBLIC
HEALTH, DIVISION OF BIOSTATISTICS (MS CORE COURSES)
○ Biostatistics: Regression
○ Theory of Statistics I
○ Biostatistics : ANOVA and
Design
○ Analysis of Categorical Data
○ Theory of Statistics II
○ Survival Analysis
○ Two Biostatistics electives
○ Clinical Trials
o Statistical Learning and Data
Mining
o Latent Variable Models
○ Latent Variable Models
○ Statistical Methods for
Correlated Data
○ Statistics in Genetics and
Molecular Biology
○ Introduction to Bayesian Data
Analysis
○ Statistics for Translational and
Clinical Research
○ Modern Non-parametrics
○ Applied Multivariate Methods
○ Nonparametric Methods
BOSTON UNIVERSITY MASTER OF SCIENCE IN
ACTUARIAL SCIENCE
HTTP://WWW.BU.EDU/MET/COURSES/GRADUATE/ACTUARIAL-SCIENCE/
Probability and Statistics
•MET MA 581 PROBABILITY
•MET MA 582 MATHEMATICAL STATISTICS
•MET MA 603 SAS WITH STATISTICAL APPLICATIONS
•Mathematical Finance
•MET AT 721 MATHEMATICS OF COMPOUND
INTEREST
•MET AT 722 FINANCE FOR ACTUARIES
•MET AT 731 ACTUARIAL MATHEMATICS I
•MET AT 732 ACTUARIAL MATHEMATICS II
•MET AT 741 ACTUARIAL STATISTICS I
•MET AT 742 ACTUARIAL STATISTICS II
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MET AT 751 INDIVIDUAL INSURANCE
APPLICATIONS OF ACTUARIAL PRINCIPLES
MET AT 752 GROUP INSURANCE APPLICATIONS
OF ACTUARIAL PRINCIPLES
MET AT 754 CASUALTY INSURANCE PRINCIPLES
MET AT 761 MATHEMATICS FOR INVESTMENT
AND PORTFOLIO THEORY
MET AT 762 MATHEMATICAL FINANCE FOR
ACTUARIAL SCIENCE
MET AT 782 PENSION MATHEMATICS AND
MORTALITY TABLES
ORGANIZATIONS THAT HIRE APPLIED
MATHEMATICIANS
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Government labs and research offices such as Air Force Office of Scientific Research; Lawrence
Berkeley National Laboratory; Los Alamos National Laboratory; Oak Ridge National Laboratory;
Pacific Northwest National Laboratory; and Sandia National Laboratories
U.S. government agencies such as Institute for Defense Analyses Center for Communications
Research, National Center for Computing Sciences; National Institute of Standards and
Technology (NIST); National Security Agency (NSA); Naval Surface Warfare Center, Dahlgren
Division; and the U.S. Department of Energy
International government agencies such as the Defence Science and Technology Organisation,
DSTO (Australia); French Alternative Energies and Atomic Energy Commission (changed name);
and National Research Council Canada
Federally funded contractors such as the Mitre Corporation; RAND Corporation; and the
Aerospace Corporation
Engineering research organizations such as AT&T Laboratories – Research; Exxon Research and
Engineering; NEC Laboratories America, Inc.; Schlumberger-Doll Research; and IBM Research
Computer information and software firms such as Adobe; Google; Kuberre Systems; The
MathWorks, Inc.; Mentor Graphics; Microsoft; Mosek; MSC.Software Corporation; Palo Alto
Research Center; Thomson West; and Yahoo Research
Energy systems firms such as Lockheed-Martin Energy Research Corporation and the Schatz
Energy Research Center (SERC)
Electronics and computer manufacturers such as Alcatel-Lucent; Hewlett-Packard; Honeywell;
IBM Corporation; Motorola Mobility and Motorola Solutions; Philips Research; and SGI
INTERNSHIP AND CAREER INFORMATION IN INDUSTRY, RESEARCH INSTITUTIONS,
AND GOVERNMENT LABS
HTTP://WWW.SIAM.ORG/CAREERS/
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Corporate Organizations
AT&T Laboratories – Research
Bell Labs, Alcatel-Lucent
The Boeing Company
Birkhäuser
Booz Allen and Hamilton
General Motors Corporation
Hewlett-Packard
IBM Corporation
Kuberre Systems
Lockheed Martin
Mentor Graphics
Merck & Co
Mining Plazza
NEC Laboratories America, Inc.
Palo Alto Research Center
Philips Research
Schlumberger-Doll Research
SAIC
Springer
Government and Non-Profit Institutions
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The Aerospace Corporation
Air Force Office of Scientific Research
American Institute of Mathematics
Argonne National Laboratory
Defence Science and Technology Organization
Institute for Computational Engineering and Sciences
Institute for Defense Analyses
Johns Hopkins Applied Physics Laboratory
Lawrence Berkeley National Laboratory
Lawrence Livermore National Laboratory
Los Alamos National Laboratory
Mathematical Sciences Research Institute
National Aeronautics and Space Administration
National Institute of Standards and Technology
National Research Council Canada
National Security Agency
Naval Surface Warfare Center
Oak Ridge National Laboratory
Sandia National Laboratories
United States Department of Energy
U.S. Army Corps of Engineers, Engineer Research
and Development Center
HARRY MARKOWITZ
HTTPS://EN.WIKIPEDIA.ORG/WIKI/HARRY_MARKOWITZ
• Harry Max Markowitz (born August 24, 1927) is an American economist, and a
recipient of the 1989 John von Neumann Theory Prize and the 1990 Nobel
Memorial Prize in Economic Sciences.
Markowitz is a professor of finance at the Rady School of Management at the
University of California, San Diego (UCSD).
• During high school, Markowitz developed an interest in physics and philosophy, in particular
the ideas of David Hume, an interest he continued to follow during his undergraduate years at
the University of Chicago. After receiving his B.A., Markowitz decided to continue his
studies at the University of Chicago, choosing to specialize in economicsWhile still a student,
he was invited to become a member of the Cowles Commission for Research in Economics,
which was in Chicago at the time. Markowitz chose to apply mathematics to the analysis of
the stock market as the topic for his dissertation.
JAMES HARRIS SIMONS
HTTP://EN.WIKIPEDIA.ORG/WIKI/JAMES_HARRIS_SIMONS
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James Harris Simons was born
to a Jewish family, the only child
of Marcia (née Kantor)and
Matthew Simons, and raised in
Brookline, Massachusetts. His
father owned a shoe factory.
He received a Bachelor of
Science in mathematics from
the Massachusetts Institute of
Technology in 1958 and a
Ph.D., also in mathematics,
from the University of California,
Berkeley, under supervision of
Bertram Kostant in 1961, at the
age of 23.
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In 1964, Simons worked with
the National Security
Agency to break
codes.[20] Between 1964
and 1968, he was on the
research staff of the
Communications Research
Division of the Institute for
Defense Analyses (IDA) and
taught mathematics at the
Massachusetts Institute of
Technology and Harvard
University, ultimately joining
the faculty at Stony Brook
University. In 1968, he was
appointed chairman of the
math department at Stony
Brook University.
Simons was asked by IBM in
1973 to attack the block
cipher Lucifer, an early but
direct precursor to the Data
Encryption Standard
(DES).[21]
Simons founded Math for
America. He funds a variety
of research projects.
For more than two decades, Simons' Renaissance
Technologies' hedge funds, which trade in markets
around the world, have employed mathematical models
to analyze and execute trades, many automated.
Renaissance uses computer-based models to predict price
changes in financial instruments. These models are based
on analyzing as much data as can be gathered, then
looking for non-random movements to make predictions.
Renaissance employs specialists with non-financial
backgrounds, including mathematicians, physicists,
signal processing experts and statisticians. The firm's
latest fund is the Renaissance Institutional Equities Fund
(RIEF). RIEF has historically trailed the firm's betterknown Medallion fund, a separate fund that only contains
the personal money of the firm's executives.
"It's startling to see such a highly successful
mathematician achieve success in another field," says
Edward Witten, professor of physics at the Institute for
Advanced Study in Princeton, NJ, and considered by
many of his peers to be the most accomplished theoretical
physicist alive... (Gregory Zuckerman, "Heard on the
Street", Wall Street Journal, July 1, 2005).
In 2006, Simons was named Financial Engineer of the
Year by the International Association of Financial
Engineers. In 2007, he was estimated to have personally
earned $2.8 billion, $1.7 billion in 2006,[17] $1.5 billion
in 2005,(the largest compensation among hedge fund
managers that year) and $670 million in 2004.
Ivo Babuška
He studied civil engineering at the Czech Technical
University in Prague, where he received the Dipl.
Ing in 1949. In 1951 he received the degree Dr.
Tech.; his doctoral dissertation was supervised by
Eduard Čech and Vladimir Knichal. From 1949 he
studied at Mathematical Institute of the
Czechoslovak Academy of Sciences and then was
the head of the Department of Partial Differential
Equations. In 1955, he received a Ph.D. in
mathematics and in 1960 D.Sc. in mathematics.
Babuška works in the field of mathematics, applied
mathematics, numerical methods, finite element methods, and
computational mechanics. In 1968, he became a professor at
University of Maryland, College Park, where he retired in
1996 as a Distinguished University Professor. In 1989 he cofounded the company ESRD, Inc. (http://www.esrd.com/)
which developed the StressCheck finite element software,
putting into practice much of Dr. Babuška's research and
contributions to the finite element method.[
PROFILE OF AN APPLIED
MATHEMATICIAN
J. Tinsley Oden
The University of Texas at Austin
Associate Vice President for Research
Director, Institute for Computational Engineering and
Sciences
Cockrell Family Regents' Chair in Engineering no. 2
Peter O'Donnell Jr. Centennial Chair in Computing
Systems
Professor of Aerospace Engineering and Engineering
Mechanics
Professor of Mathematics
EDUCATION AND HONORS
• Dr. Oden finished secondary school in Alexandria in 1955
and entered Louisiana State University in the fall of that
year. He earned a B.S. degree in civil engineering from
LSU in 1959. Dr. Oden earned a Ph.D. in engineering
mechanics from Oklahoma State University in 1962
• He is a Fellow and past President of both the American
Academy of Mechanics and the Society of Engineering
Science. He was awarded the A. C. Eringen Medal, the
Worcester Reed Warner Medal, the Lohmann Medal, the
Theodore von Karman Medal, the John von Neumann
medal, the Newton/Gauss Congress Medal, and the
Stephan P. Timoshenko Medal. He was also knighted as
“Chevalier des Palmes Academiques” by the French
government
FELLOWSHIP AND SUMMER PROGRAMS
• The Langley Aerospace Research Summer Scholars program
(http://www.nianet.org/larss/) offers opportunities for both
undergraduate and graduate students to spend a summer at
NASA Langley working with a researcher. The NASA Graduate
Student Researchers Program
(http://fellowships.hq.nasa.gov/gsrp/nav/) is an agency-wide
fellowship program for graduate study in science,
mathematics, and engineering related to NASA research and
development. The award recipients are encouraged to spend
part of the year at NASA. Once you are looking for a job, you
can place your CV at www.usajobs.gov, which advertises jobs
in government labs. You can sign up for announcements of
NASA Research Opportunities
(http://nspires.nasaprs.com/external/)