Dealing with Math Test Anxiety

Jayne Lokken
Counseling and Psychological Services
St Cloud State University

Do you have an hour to spare? Taking one hour to look at better ways of coping with anxiety related to taking math tests could be a good investment with big payoffs.

Wednesday, October 3, 2007, 4-5pm
Atwood Glacier Room

Dealing with Math Test Anxiety

Jayne Lokken
Counseling and Psychological Services
St Cloud State University

Do you have an hour to spare? Taking one hour to look at better ways of coping with anxiety related to taking math tests could be a good investment with big payoffs.

Wednesday, October 17, 2007, 3-4pm
ECC 130

Why are there Math Professors?

William Branson
Dept. of Mathematics, St Cloud State University

The first universities were established by 1200; the title "Professor of Mathematics" doesn't appear until 1500. Why this gap?
The answer lies largely with the social views of mathematics as a practical art. Some math was necessary for astronomy and astrology, for commerce, art and architecture, but math itself was not a field of inquiry. The humanists of 15th century Italy challenged medieval views; their emphasis on classical Greek and Roman knowledge changed how society viewed mathematics. In particular, the recovery of Plato's philosophy and the role of mathematics within it was of primary importance. Finally, the advent of new technologies in the late 15th century (especially cannons) led to mathematical explanations of natural behaviour. All these, together, led to a rise in the status of mathematics and the new professors of mathematics.

Wednesday, October 31, 2007, 3-4pm
ECC 130

Making a Case for Supplemental Instruction: Study-sessions closely aligned with regular class instruction can result in better study habits and improved performance

Roozbeh Vakil and Bishnu Naraine,
Dept. of Mathematics, St Cloud State University

In Spring 2007, an IPESL grant provided funding for us to plan supplementary activities and conduct supplemental instruction in mathematics for a group of elementary education students.
The primary goal of this initiative was to help students develop an effective approach to studying mathematics. Our method to achieve this goal had two components: (1) a highly structured cooperative learning environment and (2) specially designed activities. In study sessions the instructor had the role of a facilitator rather than a teacher. The initiative was in the form of a study-session which supported a regular session of this course. We will describe the project, share the results, and discuss implications.

Wednesday, November 14, 2007, 3-4pm
ECC 130

Evolution of Spherical Trigonometry--From 17th-century Europe to 18th-century China

Jeff Chen
Dept. of Mathematics, St Cloud State University

In 17th- and 18th- century China, problems in spherical trigonometry arising from astronomy were often reduced to problems in plane trigonometry and then solved with Pythagorean theorem and proportionality of corresponding sides of similar right triangles. In the literature of the history of Chinese mathematics, however, it lacks systematic discussions on how these problems were reduced from the sphere to the plane, and how the reduction process evolved. This presentation will address these issues and reassess the mathematical achievements of an influential Chinese scholars.

Wednesday, November 28, 2007, 3-4pm
ECC 130

Math and Descartes' Brain: The Place of Analytic Geometry in Descartes' Philosophy and the Role of "Determination" in Descartes' Philosophy of Mind

Andrew Platt,
Dept. of Philosophy, St Cloud State University

Mathematicians know Descartes as the discoverer of analytic geometry – including the Cartesian coordinate system that bears his name. Philosophers remember Descartes as the author of Meditations, a work that marked a revolutionary change in the focus of Western philosophy. The identity of these two Descartes is more than coincidental. Descartes saw his work in mathematics as both an example of his broader philosophical method, and as a model for human knowledge (or “science”) in general. In this talk I examine the interrelationship between Descartes’ work as a mathematician and his work as a philosopher. I will focus on a particular mathematical concept – the idea of “determination” – and discuss its role in Descartes’ views about the relationship between the human mind and the world of material objects that is described by physics.

Wednesday, February 6, 2008, 3-4pm
ECC 130

Get Fuzzy

Justin Braith and Steve Walk,
Department of Philosophy and Dept. of Mathematics (respectively), St Cloud State University

Aristotle taught that every statement is TRUE or FALSE. But some statements—
“Cornelius is a tall man.”
“This is a cramped room.”
“Cloverfield is a good movie.”
—have no respect for Aristotle. These statements can be considered TRUE to some degree; perhaps the first statement is 70% TRUE if Cornelius is 5-foot-9. If we refuse to be limited to two truth values, and we allow ourselves to consider a continuum of truth values between TRUE and FALSE, then we are entering the realm of fuzzy logic.

Far from being just an esoteric subject of curiosity to logicians, fuzzy logic has found industrial applications in products ranging from hair dryers to trains. But we will focus on a classic puzzle of logic, the Liar Paradox, and consider how embracing the fuzzy logic viewpoint leads to some very specific approaches to that paradox.

Wednesday, February 20, 2008, 3-4pm
ECC 130

Finding All Homomorphisms from Z_m to Z_n

Hallie Elich and Danrun Huang,
Dept. of Mathematics, St Cloud State University

Finite cyclic groups, Z_n's, are the building blocks of finite Abelian groups. They are also simple examples of finite rings. In introductory abstract algebra, students often encounter specific questions on group and ring homomorphisms from Z_m into Z_n. For example, “Is `x->4x' from Z₈ to Z₁₂ a group (ring) homomorphism?” “How many group (ring) homomorphisms are there from Z₂₄ onto Z₆? How many to Z₆?” etc. A general solution to questions like these would enable students to efficiently and systematically answer a variety of related questions. Surprisingly, no textbooks, to our knowledge, include generalizations to these questions. Gallian and Buskirk helped bridge the concrete-abstract gap by proving that the number of group homomorphisms from Z_m to Z_n is gcd(m,n) and also by counting the number of ring homomorphisms from Z_m to Z_n. However, their proofs provide little insight on the actual forms of these homomorphisms. In this discussion, we give new, elementary proofs of Gallian and Buskirk’s theorems as well as methods to explicitly find all group and ring homomorphisms from Z_m to Z_n. Furthermore, these useful methods can be used to solve numerous exercises throughout Gallian’s text in a uniform and transparent way

Wednesday, March 12, 2008, 3-4pm
ECC 130

The Current State of the State K-12 Math Standards: Collaborating with K-12 Educators

Sonja Goerdt,
Dept. of Mathematic, St Cloud State University

The 2007 MN Mathematics Standards describe the expectations in mathematics that all K-12 students must satisfy to meet the state requirements for graduation. The standards specify that all students must satisfactorily complete an Algebra I credit by the end of 8th grade, and all students must satisfactorily complete an Algebra II credit by graduation. These requirements raise the expectations for mathematics teaching and learning in all grades, K-12. Hence the question: How can St Cloud State University support local school districts as they work to implement the new math standards?

Dr. Sonja Goerdt is working to develop collaborations between SCSU and local K-12 schools. She is providing professional development specifically designed to assist the school districts in their understanding and implementation of the new mathematics standards. She will identify some of the specific challenges facing school districts, outline the professional development she is providing, and discuss the districts’ responses to the developing collaborations.

Wednesday, April 2, 2008, 4-5pm
ECC 130

An Introductory Bioinformatics Course

Jennifer Galovich,
Dept. of Mathematics, College of St Benedict's/St John's University

I spent my 05-06 sabbatical developing and (I hoped) learning enough to teach an introductory course in bioinformatics. Last fall I actually got to teach the course I had developed, and I will report on what I did, plus the challenges and opportunities involved in teaching such a course. For those unfamiliar with bioinformatics, my report will include a (necessarily) small introduction to the field and its intersection with mathematics.

Wednesday, April 9, 2008, 3-4pm
ECC 130

Fixed Points and Fractals

Keith Agre,
Dept. of Mathematics, St Cloud State University

If g is a real-valued function, then the number p is a fixed point for g if g(p) = p. Suppose we begin with a real number a₁ and we define a_n=g(a_n-1) for n=2,3,…. Then under certain circumstances, we will have lim_{n →  ∞} a_n = p This technique is called fixed-point iteration or functional iteration. This simple technique turns out to be incredibly useful and can be generalized to much more complicated settings. Consider each of the following situations:

• Solving the equation f(x) = 0 via Newton’s Method.
• Proving that the initial-value problem dy/dx=f(x,y), y(x₀ )= y₀ has a unique solution on some interval.
• Writing a computer program to generate an approximation to a fractal such as the Sierpinski Triangle shown below. In this talk I will briefly discuss how to approach each situation above using fixed-point iteration in an appropriate setting. In particular, I will emphasize the use of fractal generation as a fun setting in which to reinforce the important concept of convergence of a sequence.

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  Thursday, April 24, 2008, 4-5pm
  ECC 130

  Fractals and Algebras

  Sam Schmidt,
  Dept. of Mathematics, University of Iowa

  Beautiful and interesting things happen when studying rational functions dened on subsets of the complex numbers. This talk will explore some of the visualy stimulating fractal sets and also investigate the correspinding dynamical systems that arise. By attaching certain algebraic structures to the sets, one can better understand these dynamics.