Student panel: What did you do last summer? Thursday October 1 @ 4pm in Olin 268

Title:  What did you do last summer?

Abstract:   There are many exciting summer opportunities for students in the mathematical sciences! These range from internships in financial companies to research experiences at other universities to leadership development programs. In this week’s colloquium, a panel of your peers will tell you their experiences. What did they enjoy about their experiences? When did they apply? There will also be ample time for questions and answers. These varied opportunities, as well as being terrific fun, are also immensely valuable as you begin to think about your careers after Bucknell.

DVP Talk: Takunari Miyazakie, October 1 @ 4 pm in Olin 372


Title: Computing canonical forms of graphs

Abstract: Determining the computational complexity of the problem of finding canonical representatives of graphs is a long-standing unresolved question.  This question is of fundamental interest in the theory of computing because of its close relationship with graph-isomorphism testing.

While the problem may be difficult in general, group-theoretic methods have enabled polynomial-time solutions for important classes of graphs, including graphs of bounded valence.  In practice, however, variants of backtrack search to find lexicographic leaders have long been accepted as quite effective; for example, the system nauty is the leader in this category.

In this talk, I will discuss theoretical limitations of the lexicographic-leader approach to finding canonical forms.  It turns out that this approach leads to NP-complete problems, even for very restricted classes of graphs for which there are simple polynomial-time solutions by group-theoretic methods.

DVP talk: James Wilson, September 29th 4pm in Olin 372


Title: Tying different knots: problems with isomorphism in algebra

Abstract: In 1905 Max Dehn proved if you tie a knot by “over-under” you never end up with the same knot as when you tie it “under-over”.  His proof — still the only proof — hinged on a very delicate and typically difficult problem of computing isomorphisms in algebra.  By the 1950’s Adian and Rabin had proved the approach in general is undecidable — no computer can do it.

Yet, the uses for isomorphism are too profound to give up after undecidability. The decades that followed saw the founders of computational algebra – Cannon, Neubuser, and Sims – make substantial inroads on the problem.  Theoretical Computer Scientists Miller, Lipton-Zalcstein, and Tarjan framed the problem in the emerging complexity zoo with the curious realization that group isomorphism is in one form easier than graph isomorphism and in another form harder.

Today isomorphism in algebra is experiencing a renaissance.  Long-standing “hard cases” are crumbling with the discovery of new linear perspectives.  Old practical algorithms are being combined with new data structures to result in exponential improvements.  And the approaches grow by the month.  The vanguard of this exciting new wave are researchers at  Aachen, Auckland, Bucknell, Chicago, Colorado State, London, Santa Fe, and Sydney.

We will report on what we know, what we want to know, and give the reasons for all the recent attention. The talk will not assume a technical proficiency in mathematics or computation.

Allyssa Ward ’12: Case studies in actuarial science Tuesday, September 22nd @ 5pm in Olin 266


If you like the concept of applying mathematics in a business setting, actuarial science may be the perfect career path for you. To learn more, please join Cigna on Tuesday, September 22 at 5 PM in Olin 266 for an actuarial case study to see a preview of what healthcare actuaries do on a daily basis. Snacks will be provided and you can enter to win a gift card to the bookstore just by attending!

Internship, externship and full-time opportunities in Cigna’s Actuarial Executive Development Program will also be discussed. Please visit our website​ or contact Allyssa Ward (Bucknell 2012) at to learn more.

Student Information Session: Dr. John MacCarthy, Systems Engineering Education Program University of Maryland, College Park, Thursday, September 17th in Olin 372 @ 4 pm

  • Learn about the career field of systems engineering.
  • Learn why a technical liberal arts degree (e.g., in engineering, science, mathematics, or computer science) provides an excellent foundation for a career in systems engineering.
  • Learn how the University of Maryland’s Master of Science in Systems Engineering (MSSE) can prepare you for such a career.
  • Development of large, complex systems requires the integration of a broad range of engineering disciplines.
  • Systems Engineering provides tools, techniques, and processes for managing the development of such systems.
  • Systems Engineers guide and coordinate the work of teams of engineers from a variety of disciplines to develop such systems.
  • Systems Engineers are in demand, well-compensated, and have opportunities for advancement.
  • In 2009, Money magazine rated Systems Engineer as the best job in America because of its high salaries, opportunities for advancement, and inherently interesting and creative work.

Student Talk Series: Dr. John MacCarthy, Systems Engineering Education Program University of Maryland, College Park, Thursday, September 17th in Olin 268 @ noon


Title: The Use of Markov State Models in Reliability, Availability, and Maintainability (RAM) Analysis

Abstract: Three of the most important attributes of a system are its availability, reliability, and maintainability. A large portion of a typical system’s life cycle cost is driven by its reliability and maintainability. Reliability, Availability, and Maintainability (RAM) analyses are performed as a part of the development of almost all large-scale systems. Conceptually, there is a simple algebraic relationship between these three parameters that may be derived from a simple Markov state model. For complex systems, the models can become quite challenging. This seminar will provide 1) a discussion of why availability, reliability, and maintainability are important characteristics of a system; 2) definitions for each characteristic and their associated metrics; 3) an example of a simple system and how a simple Markov state model may be developed and used to derive the algebraic expression for the relationship between the three metrics; 4) an example of how the expression may be used to perform trade studies and sensitivity studies; and 5) a discussion of the simple analytical framework may be extended to address more complex systems.