Wednesday, September 24, 2008, 3-4pm
130 ECC

Utilities of Proofs and Characteristics of Mathematical Reasoning in China—Case Study of Suanli (Mathematical Principles)

Dr. Jeff Chen
Dept. of Mathematics
St. Cloud State University

Traditional Chinese mathematics treatises did not have western-style proofs. Even after proof-writing was introduced to China in the translation of Euclid’s Elements (Jihe yuanben) in 1607, writing proofs and citing axioms and/or proved properties never became a standard practice in mathematical treatises in China. Instead, the discussion or explanation of suanli (mathematical principles) replaced the proof under the heading, lun (discussion), where the proof should have been. Scholars well-versed in mathematics sometimes evoked suanli to support the correctness of their claims, especially facing common mistakes made by others. It seems that in understanding mathematics reasoning in late imperial China, examining the the concept of suanli might be more appropriate than trying to determine whether the discussions qualified as proofs.

In this case study, I will examine a case of suanli in the mathematical reasoning. This case study suggests a re-examination of the utilities of proofs. In this talk, I will also discuss the characteristics of suanli. This presentation is just a preliminary finding of a project, which will hopefully, through case studies, illuminate the philosophy of reasoning in mathematics as Chinese scholars/mathematicians viewed it in Late Imperial China.

Wednesday, October 8, 2008, 3-4pm
ECC 130

Commercial Mathematics of the Middle Ages

Dr. William Branson
Dept. of Mathematics
St. Cloud State University

The rising commercial city-states of 14th and 15th century Italy needed a mathematically literate business class, and so the `abbaco schools' were born. In these schools, students around ten years old were taught the basic mathematics they would need in their careers as merchants. The teachers of these schools wrote textbooks (as teachers often do), and in this talk we'll look at two of them: Fibonacci's Liber Abaci of 1202 and Jacopo da Firenze's Tractatus Algorismi of 1307. This talk will focus on two aspects of these texts: the mathematics involved, and the picture these texts paint of the life and concerns of a merchant of the Middle Ages. The mathematics is largely simple algebra and proportions, with some geometry; interestingly, some of the problems in these texts are very close to problems in our Math 196 and Math 112 texts. Merchants of the Middle Ages shared many concerns with modern businessmen, such as how to divide the profits of a venture between investors, but they also had difficulties that we don't, such as a coinage that varied wildly in value. By looking at these texts, we can uncover a little bit of what it was like to be a merchant of the Middle Ages.

Wednesday, November 5, 2008, 3-4pm
ECC 130

Election Post-Game Coverage III

Dr. David Robinson
Dept. of Statistics and Computer Networking
St. Cloud State University

By Wednesday, Nov. 5, the upcoming presidential election will be over (well, sort of). We need to meet as a group, to help bring this campus together – no more red professors and blue professors, no more red students and blue students! Come together and follow an analysis of the results and the polls taken shortly before the election. Hear a bit about how polls are weighted to adjust for non-representative samples. How did it work in the recent SCSU Statewide Poll? Also you may be able to hear the inside scoop about what exit polling is all about. And of course we’ll find out winners of this year’s election prediction contest! All within about 50 minutes! What a deal!

Wednesday, November 19, 2008, 3-4pm
ECC 130

Fractional Calculus

Dr. Ravi Kalia
Dept. of Mathematics
St. Cloud State University

French nobleman Marquis de l’ Hospital (1661-1704), in the spirit of inquisitiveness, asked Gottfried Wilhelm Leibniz (1648-1716) the natural question: “What if n be ˝ (in dⁿy/dxⁿ)?” The reply by the latter, in 1695, served as a catalyst to the investigations by S. F. Lacroix, N. H. Abel, J. Liouville, A. V. Letnikov, A. K. Grünwald, G. H. Hardy, W. C. Brenke, H. T. Davis, H. Weyl, and E. Post. The first conference on Fractional Calculus and its applications was held in 1974 (Ross, 1974). Thereafter, several books or edited volumes were published. Noteworthy among the 1990s are : (Samko, 1993), (Kalia, 1993), (Kiryakova, 1994). Of special interest to the present proposals are the ones involving applications to Physics such as (Hilfer, 2000), (West, 2003), and to Bioengineering, (Magin, 2006). These days numerous researchers are investigating applications of Fractional Calculus to problems in the following areas very avidly:

1. Fractional order differential equations
2. Fractional Order Partial Differential Equations and Problems in Physics and Engineering
3. Interaction of Fractional order Physical and Biological Phenomena with Fractional Derivatives
4. Numerical verification of the results obtained by closed form techniques
5. New results in Special Functions involving student research
6. Applications to Biology

Wednesday, December 3, 2008, 3-4pm
ECC 130

U Can't Prove This

Dr. Steve Walk
Dept. of Mathematics
St. Cloud State University

We will encounter two famous theorems. One is very natural and intuitive. The other is so counterintuitive as to command utter disbelief from anyone who’s paying attention. Despite their differences in shock value and subject matter, we will see that these two theorems have an important connection in math history and the foundations of mathematics. We will also explore the world of infinite ordinals, because we cannot really understand why the latter theorem works unless we have infinite ordinals to help us. The prerequisites for attendance are curiosity about large numbers and infinity, a tolerance for mathematical abstraction, and an open mind. This talk is appropriate for students—and in fact is geared toward them—as well as for faculty who either haven’t heard these things before or don’t mind hearing them again if free cookies are involved.

Wednesday, February 4, 2009, 3-4pm
ECC 130

A Genetic Algorithm for the Unconstrained Facility Location Problem

Bryant Julstron
Dept. of Computer Science
St. Cloud State University

Given a collection of warehouse locations, each with a fixed cost, and customers to be served from those warehouses, each with a cost associated with both the customer and the one warehouse from which the customer is served, the unconstrained facility location problem seeks to identify a subset of the warehouse locations that minimizes the total cost. A genetic algorithm for this NP-hard problem encodes candidate subsets as permutations of the available locations; a greedy decoder identifies the subset that such a chromosome represents. Three heuristic extensions reorder chromosomes so that they list included locations before excluded; mutate chromosomes by always swapping an included location with an arbitrary one; and rescan the included locations to exclude any whose exclusion reduces the total cost. Four versions of the GA implement none, one, two, or all of these extensions. In tests on 235 publicly available problem instances whose optimum solutions are known, all the versions perform reasonably well, but the heuristic extensions enable the version that uses them all to find optimum solutions very quickly on almost every trial on the test instances. The heuristic techniques should be effective in permutation-coded evolutionary algorithms for other problems that seek subsets of initially unknown sizes.

Wednesday, February 18, 2009, 3-4pm
ECC 130

Exploring Decision Tree/Decision Analysis with the case study method

Dr. Bruce Busta
Dept. of Accounting
St. Cloud State University

Dr. Bruce (Harv) Busta from the accounting department will demonstrate how the concept of decision trees could be taught with the use of the case method. The strengths of the case method is that it is interactive and can highlight assumptions used in the decision making process.

Wednesday, March 4, 2009, 4-5pm
ECC 130

SCSU: Supporting K-12 Teachers in Increasing Student Achievement in Mathematics

Drs. Sonja Goerdt, Sue Haller, Sandy Johnson
Dept. of Mathematics
St. Cloud State University

In 2008-2009, a team of St Cloud State University (SCSU) mathematics faculty facilitated professional development experiences to help teachers support students in attaining Minnesota’s rigorous K-12 Academic Standards for Mathematics.

A series of 3-full day professional development institutes was designed to provide teachers with increased facility using research-based instructional strategies to engage ALL students in a study of algebra. The series was developed for and delivered to more than 100 teachers of grades 5-8 and 9-12 from 14 school districts by Janis Cimperman, Sonja Goerdt, Sue Haller, Sandra Johnson, and Cathy Wick.

The team of mathematics faculty will provide an overview of the professional development experiences they provided to these teachers, discuss the participating teachers’ evaluations of this series, and outline their plans for maintaining these collaborative relations with K-12 schools.

Wednesday, March 18, 2009, 3-4pm
ECC 130

Tropical Geometry

Dr. Kris Nairn
Dept. of Mathematics
St. John's University/College of St. Benedict

Algebraic geometry studies polynomials, polynomial equations and looks at polyhedral geometry. Tropical geometry is algebraic geometry over the tropical semi-ring, where the sum of two numbers is their minimum and their product is their sum. From a topological point of view, algebraic varieties become piecewise-linear polyhedral complexes with nice combinatorial structure. Although tropical geometry has only been around since 2002, it has many useful applications to distinct areas of mathematics ranging from algebraic and symplectic geometry, and geometric combinatorics to integrable systems and string theory. I will give an introduction to tropical geometry and briefly discuss a few of its applications.

Thursday, April 15, 2009, 3-4pm
ECC 130

Groundwater Seepage Past An Obstacle: An Asymptotic Solution

Sean Lynch
Dept. of Mathematics
University of Illinois Chicago

A 2D model representing steady state groundwater seepage past a circular, impenetrable obstacle is presented. The water particles diffuse in the plane and are subject to a uniform drift field (gravity). The concentration of groundwater is modeled by a linear, elliptic PDE. Using two independent methods, asymptotic representations of the concentration profile are obtained under the assumption that the drift field is stronger than the diffusion.

Thursday, April 29, 2009, 3-4pm
ECC 130

Dr. Tina Garrett
Dept. of Mathematics
St. Olaf College

TBA

TBA