| Date | Speaker | Title and Abstract |
| Thursday June 15 | Art Benjamin Harvey Mudd College
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Title: Counting on Determinants Abstract: We demonstrate how determinants solve many interesting combinatorial problems, and how many interesting theorems about determinants can be viewed combinatorially. Applications to Pascal's Triangle, Fibonacci numbers and Catalan numbers will also be given. |
| Thursday June 22 | John Milton Joint Science Department Claremont Colleges
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Title: Pupil light reflex: Delays and oscillations Abstract: The pupil light reflex has long been regarded to be the paradigm of a neural delayed feedback control mechanism. Experimental access is facilitated by the fact that this reflex can be ÒclampedÓ using non-invasive techniques. The reflex-feedback loop is first ÒopenedÓ by focusing a small-diameter light beam onto the center of the pupil. This circumvents the shading effects of the iris on the retina. The feedback loop is then reclosed with a clamping box which relates measured changes in pupil area to changes in retinal illuminance. By careful design of the clamping box a variety of feedbacks can be inserted into the pupil light reflex. Although the mathematical models take the form of nonlinear delay differential equations, analytical insight using elementary techniques can be obtained by approximating the feedback with piecewise constant functions. Thus direct comparisons between theory and observation become possible. |
| Thursday June 29 | L.G. de Pillis Harvey Mudd College |
Title : Mathematics and Medicine: Modeling Cancer and the Immune
System Abstract: The mathematical modeling of cancer growth and treatment is one that does not admit only narrow knowledge, but requires skills from multiple disciplines. This field of study lies at the intersection of biology and medicine, with mathematics at the core. Cancer development and the dynamics of the immune system have been a significant focus of mathematical modeling in recent decades. Immunotherapy, a treatment approach that enhances the body's natural ability to fight cancers, is becoming increasingly prevalent in many multi-stage treatment programs that also include chemotherapy, radiation, and surgery. The critical importance of the immune system in combating cancer has been verified both clinically and through mathematical models. In this talk we will discuss both the biological and mathematical sides of the question of how cancer grows, how the cancer interacts with the immune system, and new treatment approaches that harness the power of the immune system. |
| Thursday July 6 |
Judith Grabiner Pitzer College) |
Title: The Changing Concept of Change: The Derivative from Fermat to Weierstrass Abstract: First the derivative was used; then it was discovered; then it was explored and developed; and, only after all this, it was defined. We'll follow this history from the 17th to the 19th century, and reflect on what it tells us about the way mathematics is actually done. |
| Thursday July 13 | Art Lee Claremont McKenna College |
Title: Sorting and Searching Abstract: The goal of this talk is to give mathematics students a flavor of computer science. Sorting and searching are important tasks for companies like Google. Donald Knuth, a mathematician-turned-computer-scientist states in his book on "Sorting and Searching" that: "... the area of sorting and searching provides an ideal framework for discussing a wide variety of important general issues like - How are good algorithms discovered? - How can given algorithms and programs be improved? - How can the efficiency of algorithms be analyzed mathematically? - How can a person choose rationally between different algorithms for the same application? - In what senses can algorithms be proved "best possible"? - How does the theory of computing interact with practical considerations? Indeed, I believe that virtually every important aspect of programming arises somewhere in the context of sorting and searching!" In this talk I will show several sorting algorithms: some slow and some fast, and compare them. I will also show why sorting is closely related to searching. Those sorting algorithms will be demonstrated with a graphical animation to show their inner workings during execution. The intended audience are math students who are not familiar with computer science at all, or had only an introductory level course. |
| Thursday July 20 | Tamas Kalman USC | Title: Constructions of Legendrian Knots Abstract: What makes a knot (a simple closed curve in R^3) Legendrian is that at each of its points, its tangent direction is constrained to a certain plane. (The planes change from point to point.) I will give an elementary introduction to the theory of these knots. In particular, I will discuss ways of producing useful diagrams for them. |