Careers in the Mathematical Sciences ... -...
Transcript of Careers in the Mathematical Sciences ... -...
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Careers in the Mathematical Sciences
Pietro PaparellaVisiting Assistant Professor, Department of Mathematics
Email: [email protected]
Web: http://ppaparella.people.wm.edu
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My Background
• Visiting Assistant Professor, W&M, Aug. 2013-pres.– Ph.D., Mathematics, Washington State University, July
2013
• Operations Research Analyst, Avista Corp., May 2012-May 2013
• Mathematics Instructor, Spokane Falls CC, 2006-2007
• Mathematics Instructor, North Idaho College, 2004-2006
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Overview
• Mathematical Association of America: http://www.maa.org/careers/– Teaching
– Actuarial Science
– Computer Science (CS)
– Operations Research
– Biomathematics
– Cryptography (subset of CS)
– Finance
• Mathematics
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Teaching
• K-12 (BS/BA w/ teaching cred.)– Public, Private– High-demand
• Collegiate– Community College (MS/MA)
• strictly teaching
– Teaching-university (Ph.D.)• less research
– Tier I research-university (Ph.D.)• less teaching
• More info: http://www.nctm.org/
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Actuarial Science
• Apply mathematical and statistical methods to assess risk in insurance, finance, and other industries
• Employers: insurance companies, corporations, government, credit evaluators (Experian, Trans-Union, Equifax), etc.
• Being an actuary is consistently ranked as one of the best jobs (Jobs Rated Almanac, US News & World Report, CNN Money, etc.)– Perhaps the most lucrative field in mathematics
• More info: http://www.beanactuary.org/
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Computer Science
• “[T]he study of the theoretical foundations of information and computation and their implementation and application in computer systems”.
• Theoretical & Applied• Areas:
– Big Data– Data science
• Signal processing; machine learning; pattern recognition
– Cloud computing – Quantum computing– Cryptography
• Very Lucrative
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Operations Research
• Apply mathematical modeling, statistics, and optimization to assist in decision-making– Minimize cost/maximize profit, etc.
• Very lucrative• Employers
– Shipping (e.g., Amazon, Fedex, UPS, USPS, etc.)– Scheduling (e.g., major airlines)– Banking– Government (e.g., Departments of Defense, Energy, & Treasury;
IRS; Army, Air Force, Navy) – Energy
• Public/private • optimize energy portfolios
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Mathematics
• Statistician
• (Applied) Mathematician
– Industry: Amazon, Boeing
– Labs: MIT Lincoln Laboratory, Argonne National Laboratory, Pacific Northwest Laboratory
– Government: Treasury, National Security Agency
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Mathematics II
• University Professor– Teach undergraduate/graduate courses in
mathematics
– Conduct Mathematical Research in designated field• Biomathematics
• Biostatistics
• Statistics
• Financial mathematics
• Computational mathematics
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Mathematics III
• J. C. F. Gauss: “Mathematics is the queen of sciences and number theory is the queen of mathematics”.
• A prime number is any positive integer that is divisible by 1 and itself
– E.g., 2, 3, 5, 7, 11, 13,…
– Euclid proved that there are infinitely primes
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Mathematics IV
• A twin prime 𝑝 is any prime such that 𝑝 + 2 is prime– E.g., (3,5), (5,7), (11,13),…,(137,139),…
• Q: How many twin primes are there?
• Twin Primes Conjecture (TPC): There are infinitely many primes 𝑝 such that 𝑝 + 2 is also prime.
• Recent progress has been made, but the TPC is far from being completely solved
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Mathematics V
• Select positive integer 𝑛0– If 𝑛0 is even, set 𝑛1 = 𝑛0/2.– If 𝑛0 is odd, set 𝑛1 = 3𝑛0 + 1. – Let
𝑛𝑘 =
𝑛𝑘−12
, 𝑛𝑘−1is even
3𝑛𝑘−1 + 1, 𝑛𝑘−1is odd
– E.g. • 6, 3, 10, 5, 16, 8, 4, 2, 1• 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
– Collatz Conjecture: Every Collatz sequence ends with 1. – Paul Erdős: “Mathematics may not be ready for such
problems”.
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Questions?