Careers in the Mathematical Sciences

Pietro PaparellaVisiting Assistant Professor, Department of Mathematics

Email: ppaparella@wm.edu

Web: http://ppaparella.people.wm.edu

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

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

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/

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/

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

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

Mathematics

• Statistician

• (Applied) Mathematician

– Industry: Amazon, Boeing

– Labs: MIT Lincoln Laboratory, Argonne National Laboratory, Pacific Northwest Laboratory

– Government: Treasury, National Security Agency

Mathematics II

• University Professor– Teach undergraduate/graduate courses in

mathematics

– Conduct Mathematical Research in designated field• Biomathematics

• Biostatistics

• Statistics

• Financial mathematics

• Computational mathematics

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

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

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”.

Questions?