**September 15**,

*Student Colloquium Series**,*12:00-1:00 p.m., 372 Olin, Rich Weida: Bucknell University, Department of Mathematics.

*"How Do I Love Combinatorics: Let me Count the Ways"*

Absract: Many counting problems can be modeled by putting objects into boxes. There are several variations of this model, only some of which have been completely solved. This talk will discuss one of the partially solved versions.

**September 29**

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**11:00-12:00 p.m., 383 Olin, Robert Rhoades, University of Wisconsin, Madison and 2005Graduate of Bucknell University**

*Putnam Club Guest Speaker,***"**

*All the Tricks that I Know"*

Abstract: The Putnam exam is hard. Often it is hard to even start thinking about the problems on the exam. The goal of this talk is to give you some tools that will help to make many of the problems on the Putnam easier. We will assume a basic knowledge of Taylor series.

**September 29**

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**, 12:00-1:00 p.m., 372 Olin, Robert Rhoades, University of Wisconsin, Madison and 2005Graduate of Bucknell University.**

*Student Colloquium Series*

*"Reducing Complicated Objects to Simple Ones: Coefficients of Modular Forms"*

Abstract:Mathematics is filled with complicated objects. Even worse there are often complicated relationships between the complicated objects in mathematics. One ''complicated'' object is a modular form. In this talk we will relate modular forms to simple combinatorial objects, the binomial coefficients. We will discuss a few major results from the study of modular forms and show how these complicated results boil down to an elegant and simple expression.

**October 13**

October 13

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**, 12:00-1:00 p.m., 372 Olin, Charles Morgan, Lockhaven University Pennsylvannia.**

*Student Colloquium Series***Title**:

**"**

*How bad can a homomorphism be?"*

Target Audience: Anyone who has taken Calculus I

Abstract:A function f which satisfies the equation f(x+y) = f(x) + f(y) for all x and y in some space is called a homomorphism. If we consider functions from the real line to itself, it is easy to see that any function of the form f(x)=mx is a homomorphism. We address the question of whether all homomorphisms must be of this form. Using a controversial (yes, controversial) idea from 1905 by Georg Hamel, we show that there exist homomorphisms which are not of this form, and we show that these homomorphisms (in fact, all homomorphisms not of the form f(x)=mx) have the surprising property that their graphs are dense in the plane.

**October 14-19**

**r, William Kantor: Dept. of Mathematics, University of Oregon**

*Distinguished Visiting Professo***Colloquium - Monday - October 174:00 - OLIN 372**

"The Probability of Generating"Abstract. Suppose you write down a couple of square matrices with entries mod 2. If you repeatedly add and multiply like mad, you'll get lots of matrices. What is the set of matrices you'llprobablyget?

Suppose you write down a couple of permutations of {1,2,....n}. If you repeatedly multiply like mad, you'll get lots of permutations. What is the set of permutations you'llprobably get?

I'll describe the answers, with hints of proofs, starting with elementary tools and working up to the use of properties of all finite simple groups.

**An Undergraduate Talk - Tuesday - October 1812:00 - OLIN 372 **

t: What integers are sums of two square integers?"SUMS OF SQUARES"Abstrac

Three square integers? Four? Which integers can be written as x12+2 x22+5x32+5x42 for some integers x1, x2, x3, x4? I’ll discuss these and related questions, for example by expanding the notion of using both number theory and algebra.

**October 27,**

**, 4:00 p.m.,**

*Student Colloquim Series***ROOKE 116 Auditorium**

**The ****Physics Department and the Mathematics Department Present a Joint Student Series Colloquium**Arthur Shapiro, Department of Psychology, Bucknell University

"

The visual response to color is often thought to be slow (typically, chromatic modulation thresholds at 10 Hz are about eight times higher than at 1 Hz). Recent studies, however, have shown that the visual system can adapt perfectly well to fast chromatic contrast (>10 Hz) and that cells in the primary visual area of the brain respond to fast chromatic contrast modulation. To investigate this apparent discrepancy, my laboratory has developed a class of stimuli based on shifting the temporal phase of multiple sources of contrast information. In this talk, I will show how this class of stimuli can be used to generate a wide variety of compelling visual illusions, and how these illusions lead to new insights into lightness/brightness, color, and motion perception. I will also discuss some simple mathematical models of the phenomena. Examples of the illusions can be seen at www.shapirolab.net.Perception and Illusion"Abstract:

Visual illusions based on the asynchronous modulation of contrast

**November 10**,

**, 12:00-1:00 p.m., 372 Olin, Reza Noubary, Department of Mathematics, Computer Science and Statistics, Bloomsburg University.**

*Student Colloquium Series***For Teachers (K-6), Librarians, and Caregivers**

&

Children Are Welcome

&

Children Are Welcome

*Bucknell Mathematics*

*BOOK BLAST*

**Bucknell University will be hosting a non-profit mathematics book fair called "Bucknell Math Book Blast" in conjunction with National Book Week on Thursday, November 17, 2005 from 6:00-7:00 PM in the Bertrand Library Traditional Reading Room. Bucknell students will be selling and promoting mathematically related children's books to elementary school teachers, librarians, caregivers and elementary students in addition to presenting related math activities. The book fair is free and open to the public; books will be available for browsing or purchase (cash or check only) and copies of extenstion activities will be provided.**

**Thursday, November 17, 2005**

**6:00-8:00pm**

**Location: **

**Bucknell University Bertrand Library, Traditional Reading Room**

***********Books to browse or buy and suggested extension activities***********

For Bucknell University parking information, visit Documents/PublicSafety/ParkingBrochure.pdf

For more information contact Mathematics Department (570) 577-1343 or math@bucknell.edu

**December 1**

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**, 12:00-1:00 p.m., 372 Olin, Linda Scalici, Mathematics Major, 2006 Graduate, Bucknell University:**

*Student Colloquium Series*

*Title: The Structure of Digroups*

Abstract:A digroup is an algebra defined on a set having two associative binary operations. Digroups play an important role in an open problem from the theory of Leibniz algebras. I will present a brief overview of this problem. I will also discuss some fundamental properties of digroups, including a new axiomatization scheme that I developed as part of an REU research project last summer.