2017 K-State Undergraduate Lecture Series in Mathematics

Presentations by five mathematics alumni, a business representatives, two of our faculty, a professor emeritus in mathematics from KU, and a staff member were the highlights of the 2017 Undergraduate Lecture Series in Mathematics at Kansas State University.

Andy Brownback presented Behavioral Economics and the Role of Mathematical Models. Andy asked the questions: how do people respond to incentives to save for retirement, or to changes in tax laws? We tend to respond predictably to regular changes in income, but may respond in unpredictable ways to an unexpected bonus or to lotterey winnings. Although many economists study utility assuming that preferences are independent of irrelevant alternatives, the 2017 Nobel prize winner in economics Richard Thaler studied those supposedly irrelevant factors, showing that people can act irrationally in ways that do not increase their utility. Also marginal analysis may not be valid; the utility function may not be differentiable. Dr. Andy Brownback received a B.A. in mathematics and economics from Kansas State University in 2010, and his PhD in economics from the University of California, San Diego, in 2015. He is now in his 3rd year as an assistant professor of economics at the University of Arkansas.

Michael Higgins gave a talk titled The Large Problem of Big Data: Finding Solutions to Practical Problems by Combining Mathematics, Statistics, and Computer Science. He gave a wide variety of massive data examples and practical problems in retail sales, legislation, online searches, and social networking structures where traditional statistical methods are inadequate. He said that to handle these big data problems statistical researchers have developed data mining and computational complexity techniques and found new applications for optimization and numerical approximation techniques and ideas from computer science. He said that the analysis of big data requires knowledge of applications, computational skills, and mathematical and statistical intuition and that there are many career opportunities for individuals with these skills. He recommended that students take courses in mathematical statistics, linear algebra, mathematical analysis, high dimensional data methods, and machine learning. Dr. Michael Higgins is an Assistant Professor of Statistics at Kansas State University. He has a B.S. in Mathematics and Statistics 2006, Kansas State University and a Ph.D. in Statistics 2013, University of California, Berkeley.

Doug Howe gave a talk on Digital Cryptography - An Introduction to Number Theoretic Methods in Secure Communications. Doug discussed the number theory used in digital encryption, such as exponentiation modulo a large prime number. A symmetric encryption key uses the same key for decrypting as for encrypting, and must be kept secret. These symmetric keys are then shared with others by sending them via a public key algorithm (which are too inefficient and require too much computation to send long messages). The discrete logarithm problem, or finding logarithms in modular arithmetic, is a very difficult computational task. Dr. Doug Howe received a B.S. in mathematics from Kansas State University in 1972 and a Ph.D. in mathematics from the University of Pennsylvania in 1977. He has taught at Haverford College in Pennsylvania, and has spent the majority of his career working in the information technology sector and the energy sector. He is currently the Chairman of the Western Energy Imbalance Market and lives in Santa Fe, New Mexico.

Marianne Korten gave a presentation entitled How To Be the Best Math Student You Can Be. She described the new challenges and environment students face in studying mathematics at the University level. She explained to our new students: how to manage their time, use a syllabus, and allot their energy; how to get the best from their professors, advisors, classmates, and friends; and what to expect and how to handle the work. Marianne also hosted panel discussions on Graduate Studies in Mathematics and Research Experiences (Off Campus) and NSF Fellowships. Dr. Marianne Korten is a Professor of Mathematics at K-State.

John Maginnis gave a presentation entitled Planning Your Career to help students develop a career plan that works. He said the key to successful job placement is to increase your experiences each year so you can make better career decisions. He outlined steps to take each semester relating to course planning, internships, and career fairs to develop and achieve a desired career goal. He talked about how the undergraduate lectures and the career information on the math department home page will reveal the many career paths K-State math graduates have taken. He described how to use career portfolios to track progress and gave insight into job placement in today's competitive and rapidly changing world. John Maginnis is the Director of Undergraduate Studies in the Department of Mathematics at Kansas State University.

Eric Mann talked about Finding an Actuarial Internship. He explained how to: pass an actuarial exam; do well at college; look for companies to apply to; prepare a resume and cover letter; and interview. He focused on the resources available at K-State to make oneself a great internship candidate. Eric Mann, FCAS, is a Vice President and Senior Pricing Actuary at Swiss Re in Overland Park, Kansas. He has a B.S. in Mathematics and Statistics 2006 and an M.S. in Statistics 2011, Kansas State University.

Ashley Motley gave a presentation on Career Readiness for Math Majors. She described the Career Center resources available to math majors and discussed upcoming events such as the All-University Career Fair. She showed math majors how to activate their Career Center account and how to use the account to find jobs and internships. She showed how to learn what you can do with a major in math. Ashley Motley is an Assistant Director and Liaison to the College of Arts and Sciences in the Career Center at Kansas State University.

Roger Offermann spoke on What's an Actuary? He described how actuaries use strong analytical skills, business knowledge, and an understanding of human behavior to manage risk. He said that actuaries have job security as they are always in demand. He explained that actuaries have low stress in their work and a good work/life balance. He said that actuaries make an impact by managing today's complex risks facing our society. He outlined in detail the actuarial exam structure of the Casualty Actuarial Society and the Society of Actuaries. He talked about company exam and study programs. Roger Offermann, FSA, is Senior Vice President and Chief Actuary at Security Benefit in Topeka, Kansas. He has worked at Security Benefit since 1995 and previously worked at Nationwide Life Insurance in Columbus, Ohio prior to coming to Security Benefit. He has a B.S. in Secondary Education (Math and Music), Concordia University, Seward, Nebraska; and an M.S. in Applied Mathematics, University of Missouri Columbia.

Mike Reppert talked about A Few Good Problems: Finding Some Good Math in Physics and Chemistry. Mike discussed experiments in quantum theory, such as the double-slit experiment and the "thought experiment" of Schrodinger's cat. He said that to study quantum mechanics, you need to know the linear algebra of infinite dimensional vector spaces, but you may also need to know about topology, group theory, real analysis, and partial differential equations. Mike discussed his progress as a student starting with undergraduate research in both chemistry and mathematics, completing his first publication after two years of work. While earning his PhD in chemistry, he used ultrafast spectroscopy to study proteins, and he is now interested in features of photosynthesis that have been predicted using quantum mechanics but for which there are now explanations using classical mechanics. After graduating in 2009 with a BS in Chemistry, Biochemistry, and Mathematics, Dr. Mike Reppert spent a year abroad as a Fulbright student researcher in Warsaw, Poland, and entered the PhD program at MIT in 2010, graduating in 2016. Having completed a short-term research visit at the University of Stuttgart (Germany) in the fall of 2016, Mike is currently a Banting Postdoctoral Fellow at the University of Toronto.

Saul Stahl spoke on The Evolution of the Normal Distribution. Before the concept of probabilities had developed, scientists like Galileo or Huygens spoke of advantages, expectations, or dividing gambling stakes. Gauss used the method of least squares to predict the region in the sky where the asteroid Ceres would reappear after vanishing behind the sun. The normal distribution was first used to describe the errors made in making many different observations of a single phenomenon; small errors are more likely than large ones, and observations tend to be symmetrically distributed around the mean average. Only later did it become apparent that the normal distribution also applied to collections of measurements, such as the chest size of various soldiers. Bernoulli tried to use semicircular and parabolic error curves, but the Cental Limit Theorem of Laplace was the culmination of the evolution of the normal distribution. Dr. Saul Stahl is an emeritus professor of mathematics at the University of Kansas. He has authored several books on upper division mathematics whose development of their subject is historically motivated.