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Science and Industry Advance with Mathematics CAREERS in MA TH and Applied Mathematics 2 “There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.” — Nikolai Lobachevsky From N. Rose, Mathematical Maxims and Minims, Raleigh NC, Rome Press Inc., 1988. A surprising variety of career opportunities are open to people with mathematical talent and training — What kind of problems mathematics and computational science are utilized in almost every discipline of science, engineering, industry, and technology. New can I solve? application areas are discovered constantly and older techniques aThe careers may differ, but one thing remains constant—problem applied in new ways and in emerging fields. Industry relies on solving. Listed below are some examples of problems that someone applied mathematics and computational science for the design and with mathematical training might be asked to solve. It may be optimization of products such as aircraft, automobiles, textiles, useful to note which problems you find most intriguing, and why. computers, communication systems, and prescription drugs; Examples of organizations doing each type of work are also given. processes such as supply chains, logistics, and scheduling; and a How can an airline use smarter scheduling to reduce wide range of other products and services. Applied mathematics and computational science have become costs of aircraft parking and engine maintenance? essential tools in the development of advances in science and American Airlines; IBM Research technology. Innovative mathematical and computational techniques have become prevalent in areas such as the biological sciences, How can a detailed plan for a clinical trial be designed? Boston Scientific; Medtronic; Wyeth; Pfizer information technology, climatology, combustion and emission control, and finance and investment. Is the replacement Mathematical careers outside of academia rarely carry a simple title of gasoline with of “mathematician.” The very idea of a career in mathematics has ethanol a viable evolved and diversified and is often coupled with a specialty or area of research interest. Applied mathematicians and computational solution to the world’s dependence scientists working in industry, business, and government often hold on fossil fuels? Can jobs with titles such as statistician, scientific programmer, electrical engineer, computer scientist, operations researcher, systems biofuel production be engineer, analyst, research associate, or technical consultant. optimized to combat Mathematics is involved in more fields than you may have thought negative implications possible and there are many options to consider when choosing a career. Applied mathematicians and computational scientists work on the worlds’ economy and for federal and state governments, the military, financial services, environment? scientific research and development services, and consulting U.S. government agencies and labs; Amoco Exxon Research and services specializing in management, science, and technology. Engineering; Petrobras Software publishers, insurance companies, aerospace, pharmaceutical, and other manufacturing companies also employ How might the U.S. Social Security system be changed applied mathematicians and computational scientists. Many also work in academia, teaching the next generation and developing to guarantee the integrity of the system’s future? innovations through their own research. U.S. Social Security Administration In this guide, you will find answers to many of your questions How can automotive about careers in applied mathematics and computational science, systems become such as: What’s out there for someone with my interests and more efficient and background? Where can I work? Where are the up-and-coming job reduce emissions as opportunities? How should I pursue my studies? Who are the people working in industry today? mandated by U.S. public policy? Ford Motor Company; General Motors How can the current uncertainty of nuclear stockpile stewardship and management be estimated for optimum efficiency and safety? U.S. government agencies and labs; Lockheed-Martin Energy Research Corporation; Schatz Energy Research Center (SERC) 3 How can climate modeling at the global, regional, and How can you mathematically model the spread of a local levels reduce uncertainties regarding long-term forest fire depending on weather, ground cover, and climate change, provide input for the formulation of types of trees? energy and environmental policy, and abate the Fire departments; U.S. government agencies such as the National impact of violent storms? Oceanic and Atmospheric Administration (NOAA) U.S. government agencies and labs such as the National Oceanic How can you allocate an investment among various and Atmospheric Administration (NOAA) financial instruments to meet a risk/reward tradeoff? How can automotive and aircraft companies test Citibank; Moody’s Corporation; Prudential performance, safety, and ergonomics, while at the Computer chips are “printed,” much like photographs, same time lowering the cost of construction and from a negative, but manufacturing the “negative” prototype testing? is too expensive to permit cut-and-dry testing of The Aerospace Corporation; Lockheed Martin; Boeing; General proposed layouts and the corresponding “print.” Motors; Ford Motor Co. Are there accurate A pharmaceutical company wants to search a very mathematical models large database of proteins to find one that is similar in of the exposure process? shape or activity to one they have discovered. What’s Can they be coupled with the most efficient way to do this? efficient computational GlasoSmithKline; Merck & Co., Inc implementations to obtain How might disease practical, low-cost spread in populated areas simulations to guide chip in the event of a design and manufacture? bioterrorism incident? Bell Laboratories, Alcatel-Lucent; Hewlett-Packard; Honeywell; U.S. government agencies and IBM Corp.; Motorola; Philips Research; SGI labs; U.S. Department of A chemical manufacturer must shift one of its product Homeland Security lines to a new family of compounds that will not How do you cram enough data through a high- harm the ozone layer. Can computational simulations bandwidth communications network to deliver large show sufficient detail to capture the effects of the data sets reliably? chemicals, but still be fast enough to permit studies Clear Channel Communications; Qwest Communications; Verizon of many different chemicals? U.S. government agencies and labs; DuPont; Kodak When we pick up a quarter our brain sends complicated signals to our nerves and These are just a small sample of the types of problems mathematicians and computational scientists might work on. muscles. How do you design As you consider your career options, think how you might parlay a mechanical hand to grip a coin and drop it in a slot? your talent into a field that interests you. Shadow Robot Company; iRobot Corporation Remember: Mathematical and computational talent is a huge career asset that sets you apart and opens doors. 4 Part of the preparation for your future is obtaining a solid Producers of petroleum and petroleum products such as Amoco; foundation in mathematical and computational knowledge — Exxon Research and Engineering; and Petróleo Brasileiro S/A, tools like differential equations, probability, combinatorics, applied Petrobras. algebra, and matrices, as well as central skills like the art of Publishers such as Birkhauser and Springer. abstraction, communicating, and being able to do advanced computing and programming. Preparation for a career in applied University-based research organizations such as the Institute for Advanced Study; the Institute for Mathematics and Its mathematics and computational science also involves being able to Applications (IMA); and the Mathematical Sciences Research apply this knowledge to real-life problems. With preparation in Institute (MSRI). mathematics or computational science and a background in another U.S. government agencies such as the Institute for Defense field, you can enjoy the dual reward of utilizing your skills and Analyses (IDA); NASA’s Institute for Computer Applications in achieving practical results. The next question is: Science and Engineering; National Institute of Standards and Technology (NIST); National Security Agency (DIRSNA); Naval Surface Warfare Center, Dahlgren Division; Supercomputing Research Center; and the U.S. Department of Energy. Where can I work? U.S. government labs and research offices such as the Air Force Many different types of organizations, from governmental research Office of Scientific Research; Lawrence Berkeley National organizations to independent consultants, hire mathematicians and computational scientists. Experience gained through internships and Laboratory; Los Alamos National Laboratory; Oak Ridge National work-study opportunities can help you determine your personal Laboratory; Pacific Northwest National Laboratory; and Sandia National Laboratories. preferences in a workplace, such as an organization’s size, whether you prefer working for a non-profit or for-profit company, whether you prefer to work independently or on a team, and how much customer contact you prefer to have. You can easily search the websites of organizations and corporations that interest you to learn more about their locations, mission statements, objectives, history, and job requirements. Here are some examples of organizations, corporations, and research institutions that hire mathematicians and computational scientists: Aerospace and transportation equipment manufacturers such as The Aerospace Corporation; Boeing; Ford Motor Co.; General Motors; Lockheed Martin; and United Technologies. Chemical and pharmaceutical manufacturers such as DuPont; What’s out there for GlaxoSmithKline; Kodak; Merck & Co., Inc.; Pfizer; and Wyeth. someone with my talent, Communications service providers such as Clear Channel Communications; Qwest Communications; and Verizon. Computer service and software firms such as Adobe; Google, interests, and background? Inc.; Kuberre Systems; The MathWorks, Inc.; Mentor Graphics; Microsoft Research; Mosek; MSC Software Corporation; Palo Alto …Emerging fields to consider Research Center; ThomsonWest; and Yahoo Research. Consulting firms such as Daniel H. Wagner Associates and Bioinformatics McKinsey & Company. Electronics and computer manufacturers such as Bell A career in bioinformatics (computational biology) can include a Laboratories, Alcatel-Lucent; Hewlett-Packard; Honeywell; wide range of biological fields from genomics to neuroscience and IBM Corporation; Motorola; Philips Research; and SGI. anywhere in between. For example, mapping and understanding the human genome relies on the use of sophisticated mathematical and Energy systems firms such as Lockheed-Martin Energy Research computational tools. Although human and other genome projects Corporation and the Schatz Energy Research Center (SERC). are essentially complete, there are numerous others still left to Engineering research organizations such as AT&T Laboratories – sequence. Other research challenges include understanding how Research; Exxon Research and Engineering; NEC Laboratories America, Inc.; Schlumberger-Doll Research; and Telcordia genes interact, how they are switched on or off, and how they differ Technologies. from one individual to another. Research in neuroscience ranges from the operation of single Federally funded contractors such as the Mitre Corporation and neurons to the dynamics of small circuits and the cooperative action RAND. of whole populations of cells. Current and future work will involve Financial service and investment management firms such as Citibank; Moody’s Corporation; Morgan Stanley; and Prudential. mathematics and computational research in neurological processes International government agencies such as the Defence such as vision, learning, and decision-making, as well as in emerging treatments for neurological disorders such as Parkinson’s disease. Science and Technology Organisation, DSTO (Australia); French There is a great need for newer and better mathematical and Atomic Energy Commission, CEA/DAM; and National Research Council Canada. computational tools to make research quicker and cheaper, resulting Medical device companies such as Baxter Healthcare; Boston in the creation of new career opportunities in technology, medicine, Scientific; and Medtronic. and drug development and design. Nonprofit organizations such as the American Institute of Mathematics (AIM) and SIAM. 5 Data Mining Ecology, Epidemiology, and Environmental Issues Data mining is a broad mathematical area with many applications. Professionals in these fields might look at populations and their It involves the discovery of patterns and previously unknown interactions and use systems of differential equations to model information in large data sets. Emerging career opportunities can diseases in human populations (i.e. the spread of infection under be found in applications of data mining in fields such as security, various immunization protocols). Other applications in these fields forensics, e-commerce, bioinformatics and genomics, astrophysics, include the management of ocean fisheries and the study of insect medicine, and chemical and electric power engineering. population growth, spread, and reaction to insecticides (ex: flea beetles in a collard patch). Materials Science Climatology Materials science is the study of the properties, processing, and production of a broad range of existing and new materials, Climatology depends on simulating the component forces that drive including metallic alloys, composites, liquid crystals, biological the climate, for example, ocean circulation and heat exchange materials, and thin films. The rational design and analysis of between land, air, and ocean. It requires very sophisticated models materials depends on mathematical models and computational based on physical principles, expressed as complex partial tools. Career opportunities abound in science, manufacturing, and differential equations. These are implemented in very large-scale materials design for applications in fields such as aerospace, numerical codes on high-performance computers, and use data engineering, electronics, biology, and nanotechnology. from observations of satellites, ocean buoys, and other monitoring equipment to drive the solutions. Typically, these rely on input from researchers in academia. Teams of workers at institutions such as Computer Animation and Digital Imaging the Department of Energy National Laboratories, NASA, and the National Oceanic and Atmospheric Administration (NOAA) develop To get an idea of what this field entails, consider the following description from the Fields Institute in Toronto: “Computer the computational codes. animation is an eclectic science that uniquely combines mathematics, computer science, fine art, classical animation, physics, biomechanics, and anatomy, to name but a few fields. Algorithms for computer animation rely heavily on techniques from scientific computation, statistics, signal processing, linear algebra, control theory, and computational geometry.” With a diverse and exciting set of applications in areas such as medical diagnostics, entertainment (film, television, and video games), and fine arts (dancing, sculpture, painting), there are many avenues and career opportunities to explore. Finance and Economics Financial mathematics is the development of mathematical tools and computational models used in the financial industry. As new quantitative techniques have transformed the financial industry, How do I get there? banks, insurance companies, investment and securities firms, energy companies and utilities, multinationals, government regulatory A wide range of possibilities are available to individuals studying institutions, and other industries have come to rely on applied applied mathematics or computational science. But how do you mathematics and computational science. Sophisticated math find them? To start, here is a sampling of degree programs in the models and the computational methods and skills needed to mathematical sciences and academic disciplines requiring implement them are used to support investment decisions, to mathematical and computational skills: develop and price new securities, to manage risk, and for portfolio Mathematical/Computational Science Disciplines selection, management, and optimization. For example, modern hedge funds depend on these sophisticated techniques as do Applied and Experimental Statistics pricing of bonds and commodity futures. Applied, Natural, and Mathematical Sciences Bioinformatics/Computational Biology Computational Mathematics/Science Computer and Information Sciences Computer Science Financial Mathematics Operations Research Mathematics and Applied Mathematics Statistical and Actuarial Sciences 6 Other Academic Disciplines Universities make up a small portion of the potential co-op and Aerospace Engineering and Engineering Mechanics post-grad employers in the applied sciences. “Recently, we’ve seen Atmospherics, Space, and Planetary Science increased recruiting efforts by government agencies and a variety of scientific positions available from pharmaceutical companies and Bioengineering, Biomedical Engineering, and Biotechnologies larger national and multi-national employers,” Kohen said. Biostatistics Business and Management Sciences “Remember, your university’s career center is there to make sure its students are well-equipped when making the transition from school Cell Biology, Biophysics, Microbiology, Molecular Biology, to career, and to make that transition as smooth as possible.” Biochemistry, and Genetics Chemistry and Chemical Engineering Civil and Environmental Engineering Earth and Environmental Sciences “Whatever you decide to do, Experiment with internships, summer Ecology and Evolutionary Biology make sure it is something you jobs, and work-study Electrical Engineering like! Also, a friend says he always What better way to determine the range Epidemiology and Public Health tries to work with people who are of opportunities and explore possible areas of Financial Engineering smarter than him so that he will interest than to actually be in the workplace? Geosciences/Geology get smarter in turn. Look into Internships and work-study opportunities are Industrial Engineering how to network with people in a great way to start on your career path by Materials Science allowing you to get a realistic feel for the field your field or interest area, in which you are interested. Most importantly, Mechanical Engineering especially through professional internships provide opportunities to network Neuroscience societies.” and forge connections for future job Nuclear Science and Engineering — Barbara Hamilton, Manager, possibilities. Many internships turn into Petroleum Engineering Information Support Services, permanent positions, and even if they don’t, Physics and Mathematical Physics Institute for Defense Analyses, the experience will broaden your perspective Software Engineering and help narrow your career search. Check Center for Communications with your university’s career center and online Systems Engineering Research Division, Princeton Theoretical and Applied Mechanics job portals for internships in your area(s) of interest. The National Science Foundation and other groups offer programs How do I find career such as Research Experiences for Undergraduates (REUs) that support active research participation by undergraduate students in many areas. According to the NSF, these projects involve students in opportunities? meaningful ways in ongoing research programs or in research Your school’s career center can help you find a job in your area of projects specifically designed for the REU program. A directory of interest. At the very least, services such as career assessments can active NSF REU sites and contact information can be found at help you narrow your search to suit your personality and interests. www.nsf.gov/crssprgm/reu/reu_search.cfm. There are many resources available through a career services venue such as résumé help, interview preparation, and job opening announcements. Arnie Kohen is a career counselor at Drexel University’s Steinbright Career Development Center, which provides an interesting set of services for students — services that are not always utilized. “I help students with a career assessment through the administration of personality and interest inventories,” said Kohen. “Interpretations are individualized and are gratis to the student. These assessments and subsequent interpretation with a career counselor will enable a student to identify and clarify their career motivators and satisfiers, and compare them to the elements of an academic program, major, or potential employer. Students can also learn about other available career center and university services, which will help them determine their field of interest.” James Osse, a University “The career center has several events throughout the year where of Washington field students can make contacts and network with employers: they can engineer, skims ice from the surface of a hole used receive résumé critiques; go to job and career fairs; participate in on-campus recruiting; and attend various networking functions and to retrieve a deep-sea information sessions,” Kohen added. “If a student doesn’t take mooring at the National advantage of these services, they are probably missing out on Science Foundation's understanding the current job market.” North Pole Environmental Observatory. Photo courtesy of Peter West National Science Foundation 7 Do your research Books There is an incredible amount of information available on the 101 Careers in Mathematics, Second Edition Internet, in libraries, and in bookstores. This may sound like simple Andrew Sterrett, Editor; Mathematical Association of America, 2003 advice, but while you are obtaining your degree, be aware of the A Mathematician’s Survival Guide: Graduate School and Early career options that correspond to your studies. Too often, students Career Development emerge from college without a point of reference or direction. Steven G. Krantz; American Mathematical Society, 2003 Check out the career and job resources on the SIAM website at www.siam.org/careers, especially the SIAM Job Board, internship Careers for Number Crunchers & Other Quantitative Types, opportunities, and career websites of SIAM corporate members and Second Edition sponsors. Search for career opportunities, explore job descriptions Rebecca Burnett; McGraw-Hill, 2002 for keywords to do more extensive searches, and get acquainted Great Jobs for Math Majors, Second Edition with the many types of opportunities available. Stephen Lambert & Ruth DeCotis; McGraw-Hill, 2005 Secrets to Success in Industry Careers: Essential Skills for Science Network and Business L. Borbye; Academic Press, 2007 Join a professional organization (see suggestions below). Attend conferences, symposia, lectures, and meetings to connect with She Does Math: Real-Life Problems from Women on the Job other individuals in your field. Marla Parker, Editor; Mathematical Association of America, 1995 SIAM conferences provide venues for networking with mathematicians and computational scientists working in industry, Websites and hearing about their work. Published research articles are also Art of Problem Solving a window to the research and activities that take place within an www.artofproblemsolving.com industrial organization. Includes forums, free online classes, games, and resources for the young mathematician. Careers in Mathematics Where can I find more www.msri.org/ext/CareersInMathematics.html Explore the career paths of people with degrees in mathematics working in industry, business, and government. information? Check out the information listed below for sample resources, The Math Forum @ Drexel opportunities, and career options in the mathematical sciences. http://mathforum.org A leading online resource for improving math learning, teaching, Professional Societies and communication, includes forums, problems, puzzles, and other resources for mathematicians, teachers, researchers, students, and American Chemical Society..........................................www.parents. American Geophysical Union......................................www.agu.org MentorNet American Institute of Aeronautics and Astronautics ..www.aiaa.org www.mentornet.net A mentoring network, particularly for women and minorities in American Mathematical Society ................................www.ams.org American Physical Society ..........................................www.aps.organd engineering. PhDs.org American Society for Microbiology ............................www.asm.owww.PhDs.org American Society of Civil Engineers ..........................www.asce.A website created to help students prepare for the challenging American Society of Mechanical Engineers ..............www.asme.org demands of today’s job market and provide a voice for early career scientists. Includes career resources for mathematicians, engineers, American Statistical Association ............................www.amstatand scientists at all levels, from undergraduates to Ph.D.s and beyond. Association for Computing Machinery ......................www.acm.org Sloan Career Cornerstone Series Association for Women in Mathematics ..........www.awm-math.org www.careercornerstone.org/math/math.htm SIAM, MAA, and AMS contributed Institute for Operations Research and the resources to the Alfred P. Sloan Management Sciences..........................................www.informs.org Foundation to develop the pages Institute of Electrical and Electronics Engineers..........www.ieee.orgof this site on how business, industry, Mathematical Association of America........................www.maa.org and government use mathematical expertise. Materials Research Society..........................................www.mrs.org Young Mathematician’s Network Society of Automotive Engineers ................................www.saewww.youngmath.net Society for Industrial and Applied Mathematics ........www.siam.org Includes numerous forums to serve the community of young Society for Mathematical Biology ..............................www.smb.org Society for Neuroscience..............................................www.sfn.orgians including discussions on paths to math, SPIE, The International Society for Optical job searches, careers, undergrad life, Engineering ..............................................................http://spie.orgk and family life, research, and teaching. Image courtesy of Sloan Career Cornerstone Center 8 Profiles of Professional Mathematicians Dimitris Agrafiotis Kimberly J. Drake Vice President of Informatics Mathematician Johnson & Johnson Pharmaceutical Research & Development Naval Surface Warfare Center, Carderock Division Exton, PA Machinery Research and Silencing Division Philadelphia, PA Adjunct Professor of Informatics Indiana University School of Informatics, Bloomington B.S. mathematics and computer science (double major with a teaching certificate), Montclair State University, NJ B.S. chemistry, University of Patras, Greece M.S. mathematics, North Carolina State University Ph.D. theoretical organic chemistry, Imperial College, Ph.D. applied mathematics, concentration in computational science, University of London North Carolina State University Background I pursued computational chemistry as a graduate topic based on my Background undergraduate advisor’s recommendation, but the turning point was During college, I participated in a semester-long internship at the Lawrence Livermore National Laboratory (LLNL) sponsored by the my postdoctoral tenure at Harvard, where I was introduced to the Department of Energy. The intern program was extremely well-run beauty of expert systems, computer programming, and algorithm and students were exposed to all kinds of science and technology in and software development. I converged on informatics and software development because I found them extremely fulfilling. It was the the northern California area. I was exposed to world-class scientists practical use of computers and modeling that ultimately defined my who were using their scientific skills to solve problems that could career; I pursued an industrial career because several opportunities really impact people’s lives. By the time I left LLNL, my career plans had changed: I’d planned on studying pure math as a graduate presented themselves. student and then teaching, but after my time there, To get to where I am today, I developed many I decided to pursue a career in applied math innovative algorithmic methods and published “There are so many extensively. Most importantly, I embedded these learning opportunities for instead. students in engineering, algorithms into software that appealed to end users, who were not computationally inclined. science, and mathematics. Job Characteristics I would recommend that I develop algorithms and technologies to solve students seek out those problems related to diagnostics and prognostics on Job Characteristics machinery systems typically used by the Navy. Much In my position, I develop algorithms and opportunities and apply for of the work that I do on a daily basis relates to visualization techniques for analyzing and mining every one. For example, using computers to solve problems. Once we large data sets, with special emphasis on summer internship develop or find an interesting algorithm for solving chemo- and bio-informatics. During a typical day, programs. The Navy has problems, we have to actually implement and test there are a lot of management duties and an internship program that the algorithm. This usually involves running relentless email. The best parts of my job are experiments and analyzing the results. I also have algorithm development, software engineering, and generally gets few a small test project, where we are implementing working on projects that have real impact. My least applicants who are math algorithms that have already been developed on real favorite parts are the administrative duties that majors.” come with a managerial position. My work machinery systems to evaluate their usefulness to — Kimberly Drake, Naval the Navy. Finally, I’m building a video and image schedule consists of 40 hours per week in theory, Surface Warfare Center, processing laboratory, which will have the 12 70 in practice; I never leave my job. Carderock Division different varieties of video cameras used by the I believe the future of math in the pharmaceutical Navy. We will have state of the art computing power and will be working on the development and industry will involve mining of large data and heterogeneous sets implementation of video and image processing technologies of and information integration. Someone looking to get involved in this field should expect to do algorithm and software development as it interest to the Navy. applies to drug discovery projects. People working in these areas should expect to work in interdisciplinary groups. While my work is mathematical, I work with I am very happy with my career. I have managed to do the things I enjoy and make an impact within my organization and the broader engineers, chemists, and physicists to solve problems. There are scientific community. Balancing utility with innovation has been the key.ny opportunities for mathematicians in our area. Mathematical modeling is an area that the Navy invests more time, energy, and money in every year. Salary Range Salaries vary greatly. For Ph.D.-level positions, it could range from $80,000 to over $200,000 for managerial positions. Salary Range Salaries range from $70,000 to $150,000 or more for starting, mid-level, and senior positions. It really depends on education level, length of service, and location. 9 Anshul Gupta Bill Mawby Research Staff Member Manager of Statistical and Mathematical Support Services Mathematical Sciences Department Michelin America Research and Development Corporation IBM T. J. Watson Research Center Greenville, SC Yorktown Heights, NY B.S. natural systems, The Defiance College, Defiance, OH Bachelor of Technology (B.Tech), computer science, Ph.D. biomathematics, North Carolina State University, Raleigh Indian Institute of Technology, New Delhi Ph.D. computer science, University of Minnesota Background I arrived at my career path Background through a mixture of chance and I did not start out with a major in mathematics; instead, my necessity. My undergraduate background is in computer science. During my undergraduate years, training and interest was in parallel computing (using several processors simultaneously to run a biology, but I soon concluded large computer program faster) was an emerging and exciting new that this field would require area of computer science. In graduate school, I learned that some of mathematics if any progress the most challenging problems requiring parallel computing are in understanding biological numerical in nature. I therefore focused my attention on applying processes and systems was ever parallel computing to numerical problems. going to be made, and so I went to graduate school for biomathematics in order to Job Characteristics pursue this dream. There were two professors, Dr. Bernie Mikula at I do basic research and develop algorithms and software to solve Defiance and Dr. Harvey Gold at NCSU, who nurtured my interest, problems in science, engineering, and optimization. Many of these problems involve simulating a physical system using a computer but it was the book series on “Towards a Theoretical Biology” that probably did the most to convert me. Work-study experiences at program, where real-world experiments might be too costly or Argonne National Laboratory and Roswell Park Memorial Institute impractical. For example, with the help of software, an automobile also largely influenced my choices. company can simulate a large number of crash scenarios to improve the safety of a vehicle. Real crash tests may be expensive and not After graduate school I tried being an independent consultant, accurate enough. These problems are usually so complex that they but, mostly due to my distaste for the business end of the endeavor, I chose a more mainstream job as a statistician at Michelin Tire are often solved either on clusters of several computers or on Corporation. I found that mathematics, like quickness in sports, can supercomputers containing several processors. The algorithms and find profitable application in any field. Over the last 25 years, I have software that I develop help solve some of the underlying mathematical equations involved in these simulations efficiently held positions as Principal Statistician for Research and Development, on a large number of processors. Corporate Statistician, and Manager of STATMATH (statistical and mathematical support services). The stress level and the number of hours worked fluctuate a lot; however, a typical research career affords a lot of flex time, which helps keep stress levels down even during long days. Job Characteristics In my role as manager of statistical and mathematical support, I believe the future of math in the computer industry lies in computer chip technology. Interestingly, just like a lot of other I help create proposals, lead projects, guide technical personnel, things, computer chips and the circuits laid out on them are also contribute technically to projects, and evaluate results. simulated to detect possible defects before a chip goes into My position has two features that really motivate me to do better manufacturing. In order to build faster processor chips, one needs to work: a constant variety of problems and a direct impact on business create larger and more complex simulations, which in turn, requires results. Workload and schedule are dictated entirely by project faster processors. needs, but this does not typically involve a lot of overtime. Daily work is split rather evenly between administrative work, project meetings, creating documents, and doing mathematical research. Salary Range Starting: around $80,000 to $100,000; mid-level: $150,000 to Employees without the managerial role spend most of their time doing mathematical research, with perhaps 25% of the remaining $200,000; senior positions $250,000 or more. time spent on meetings and documentation. The applications of mathematics, including quality control statistics, design of experiments, sampling plans, finite element work, physical modeling via differential and partial differential equations, reliability, forecasting, data mining, optimization, and stochastic processes can be seen in all manner of research, industry, and commercial and administrative processes. Salary Range Salaries range from about $75,000 to about $150,000. 10 Ed Moylan other departments, including finance, human resources, purchasing, and engineering. I needed to better understand their viewpoints, Research Engineer, Methods & Systems Analyst, Project Leader, tenets, needs, and constraints. I felt that a formal education in these Supervisor, and Manager (retired) areas would be a good complement to my on-the-job education. I Ford Motor Company, Dearborn, MI therefore went to night school, and earned an MBA in 1989; I B.S. mathematics, University of Detroit retired in 2000. M.S. mathematics, University of Detroit The most satisfying aspects of my experiences were interacting with M.B.A. University of Michigan research mathematicians, working with people in other fields, contributing to joint solutions, seeing those solutions implemented worldwide, and teaching others what I learned. Background I earned my B.S. in mathematics in 1962 and M.A. in 1964, taught full-time for three years, and joined Ford Motor Company in 1967 as Job Characteristics a member of the team that developed Computer Aided Design I was not a researcher, but rather a “productionizer”; that is, I was (CAD). CAD was being developed simultaneously at Ford, General able to read and comprehend published mathematical articles and Motors, Boeing, and other large companies; computer graphics adapt the results to an industrial environment. By adapting the technology was in its infancy. My initial contributions at Ford were totheory and applying new methods to improve an existing production analyze what earlier developers had achieved, to evaluate what process, the impact can be significant, such as reducing costs by methods and technologies were available, to learn the theory of hundreds of millions of dollars. automotive design, to create additional methods, and to implement software that teamed the skill of the designer with the speed of the Most important industrial problems initially are ill-defined and are rarely posed in mathematical terms. The critical first steps are to computer. My knowledge of calculus, differential geometry, linear employ one’s “mathematical mindset” by defining terms, algebra, and numerical analysis, was critical in doing this work. distinguishing between independent variables and dependent Computer aided design, computer aided manufacturing, and variables, and understanding the relationships among those computer aided engineering simulation systems began to be used variables. The next steps are to employ one’s “mathematical toolset” worldwide throughout Ford for developing vehicle exteriors, interiors, by testing assumptions against data and, if possible, using classical structures, electrical circuitry, and powertrains. Data exchange solution techniques. However, if new tools are needed, a literature standards and software for communication with suppliers had to be search may be appropriate. Once sources are found, their established. Plans had to be coordinated with counterparts in Europe assumptions need to be adapted to the problem at hand, and other international locations. My title evolved along with my applied, and validated. They then become part of one’s expanded career: Research Engineer, Methods & Systems Analyst, Project “mathematical toolset.” Leader, Supervisor, and Manager. Having management responsibility involves not only being able to Salary Range oversee technology development, but also being able to build Salary range: $75,000 to $150,000. business cases for technology investments or process changes. It was essential to communicate effectively with business partners in What is important to industry? “Mathematical training enables one to identify and analyze intricate relationships among various aspects of complex problems. This capability is marketable if it is documented and communicated in language that is understood outside of the mathematics classroom. Mathematics majors can augment their communications skills if they develop the ability to listen and continually ask deeper questions in order to define the structure of a problem or a process, to identify the most highly leveraged variables, to develop pragmatic solutions, and to carry them through to implementation. One must be willing to continue learning and taking on additional diverse tasks. Mathematical methods and thought processes are universally applicable. For the future, much groundbreaking mathematics can be done in life sciences, data mining, supply chain management, agent-based modeling, network analysis, and many other areas and fields.” — Ed Moylan, Ford Motor Company, retired 11 Nancy Heinschel Edmond Chow Applied Research Mathematician Computational Scientist National Security Agency (NSA) D. E. Shaw Research Fort Meade, MD New York, NY B.S. mathematics, University of California, Davis Bachelor of Applied Science (B.A.Sc.), systems design engineering, M.A and PhD. mathematics, University of California, Santa Barbara University of Waterloo, Ontario Ph.D. computer science, University of Minnesota Background The National Security Agency (NSA) is the agency of the Defense Background Department responsible for solving cryptographic problems for the I’ve always liked math, but it was computers in junior high school federal government, and is the largest employer of mathematicians that triggered the math questions I would pursue for a long time in the U.S. The NSA sponsors several paid summer internship afterward. Questions like “how do computers know how to programs for undergraduate and graduate students. I first became compute sin(x)?” were the beginnings of applied math for me. I was aware of the NSA through one such program that allowed me to lucky to have encouraging teachers, particularly one in high school spend two summers as an intern during graduate school working who arranged a number of meetings for me with Professor Tom Hull on real problems with intelligent and enthusiastic Agency mentors. at the University of Toronto, with whom I did a small project on Summer internships are a great way to learn firsthand what the NSA computing elementary functions. Later, I participated in Lawrence does and what it is like to be an Agency employee. Livermore National Laboratory’s high school program and got a Like nearly all NSA mathematicians, I spent my first three years at chance to try programming on Cray supercomputers. By then, I was NSA in a training program, during which I worked in five different hooked. offices. I also took courses in cryptography, statistics, and math, andIn addition to math, I was also interested in science, and I decided attended a variety of talks and conferences to improve my technical very early on that I wanted to apply numerical methods to science skills. The training program allowed me to gain experience in a wide by doing computer simulations. Unfortunately, as an engineering variety of project areas, to develop a network of valuable contacts, undergraduate at that time, I didn’t find anyone doing this until my and to find an office that best fit my interests and strengths. senior year, when I took three courses in numerical analysis and did My graduate research was in pure mathematics, but the idea of a project in the computer science and applied math department. applying mathematics to important real-world problems always Professor Wei-Pai Tang was my project advisor. He took me under appealed to me and working at the NSA has given me the his wing and introduced me to numerical linear algebra. He also introduced me to Yousef Saad, who later became my Ph.D. advisor. opportunity to do just that. NSA mathematicians use tools from diverse areas including number theory, Fourier analysis, and statis- tics, but being an expert in these areas is not a requirement to Job Characteristics become an NSA mathematician, nor is having a Ph.D. Working at the NSA, I have utilized essential problem-solving skills gained by In my current position, I work on the algorithms and software used working on problems involving diverse math disciplines. I have also in molecular dynamics simulations. It is a highly varied and interdisciplinary role. Almost daily, I talk to chemists about their seen potential to apply these abilities to new challenges. The scientific problems, as well as hardware and software engineers who complex problems we work on generally require computers to solve, want to find accurate and efficient ways to implement chemistry and because of this, some computer programming experience can algorithms. In computational science, math and algorithm problems be helpful. However, I have learned most of my programming skills on the job. pop up everywhere. Often these are very specific problems that require specialized solutions. There may be a complicated potential energy function we want to minimize, and we may want a minimizer tailored for a specific computer architecture. Sometimes Job Characteristics the problems seem easy, but they’re made difficult because of Much of my day is spent working on a computer, but it is far from solitary work. With such challenging problems to solve, I work on constraints, even if the constraint is that the solution is robust yet project teams with mathematicians, computer scientists, engineers, easy to implement. and many other colleagues. Some of my projects have tight deadlines, but others are longer range. In addition to computer Salary Range work, I do a fair amount of writing and speaking in order to Starting about $100,000, depending on location and company communicate my results to coworkers. Due to the classified nature (urban areas of California and New York are higher). of what I work on, I’m not allowed to take any work home, so I have evenings and weekends to recharge, pursue other interests, and return to work refreshed and prepared for new challenges. Salary Range In 2008, math and statistics positions at the NSA had starting salaries of $49,685 for those with bachelor’s degrees, $59,811 for master’s, and $83,720 for Ph.D.’s. The best place to find out more about careers at NSA is on the website, www.nsa.gov. 12 Barbara Hamilton Mark Zandi Manager, Information Support Services Chief Economist Institute for Defense Analyses (IDA) Moody’s Economy.com Center for Communications Research Division, Princeton, NJ West Chester, PA B.S. mathematics (computer science), Central Michigan University B.S. economics, Wharton School M.A. mathematics, Central Michigan University at the University of Pennsylvania M.L.S. library science, Rutgers University, NJ Ph.D. economics, University of Pennsylvania Background I was always good in math and enjoyed it. I had excellent math Background teachers in both the sixth and seventh grade who made math fun I knew I wanted to be an economist just a couple of weeks int

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