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What Are Seniors Doing For IS? · Jun 21, 01:40 AM
posted by Dr. Jon Breitenbucher
Another year is in the books (well not really) but for Seniors it sure feels that way. Monday March 28th was IS Monday and most Seniors managed to beat the 5 pm deadline. This year marked the first time that Seniors were required to turn in an electronic copy of their IS. I must say the Math and CS majors were the envy of the other Seniors.
What follows are self-submissions from some of the 26 Math and CS majors:
Zach Carter (Mathematics) looked at non-Euclidean geometry. Zach also wrote a unit for an enriched high school geometry class in non-Euclidean geometry.
Ali Nau (Mathematics and Economics) studied the conceptualization and measurement of state power in the international system. She hoped to construct a model of power which would incorporate traditional power elements (such as military might, economic strengths and resources) as well as ``soft power,’’ which would include cultural influence and the spread of a state’s values.
Nancy Djumovic (Computer Science and Mathematics) studied the P=NP question. In her IS, ``This Is Hard’’, she looked at a number of NP Complete graph theory problems, heuristics for finding approximate solutions, and implemented a number of the approximation algorithms.
Jacob Frank (Mathematics) investigated Chaos Theory, and studied the dynamics of one-dimensional dynamical systems that lead to chaos.
``Bootstrap is a computationally demanding, non-parametric approach for making inference about a population characteristic, θ, based on an estimator θ^. Bootstrap samples are created by randomly selecting elements from the original sample with replacement. The bootstrap samples are utilized to estimate the bias of θ^ and calculate confidence intervals around θ. Bootstrap is most useful in situations where the distribution of the population is unknown or intractable,’’ says Becky Young (Mathematics).
Brian Goche’s (Mathematics) IS entitled ``M’’ looked at the history and development of fractals, with special attention on the Mandelbrot set (M). Brian investigated many of the topological properties of the Mandelbrot set and the connections between the Mandelbrot and Julia sets.
Karen Pearson’s (Mathematics) IS is a study of the dynammic programming model. She tried to develop a logical, theoretical explanation for the model and explain it in a clear manner, as well as demonstrate the applications of this model in the real world.
Jesse Smith (Computer Science) decided to make a virtual copy of Taylor Hall. Jesse was often seen measuring tables and chairs so that his virtual copy accurately reflected the real thing. Jesse was also asked to present his IS to members of the Board of Trustees, a very nice honor.
The Math Center Story · Jun 21, 01:19 AM
posted by Dr. Jon Breitenbucher
Peer tutoring was the norm for beginning level math students at The College prior to the early 1980s. When tutoring expenses repeatedly exceeded the budget, the math department decided to centralize tutoring by providing group tutoring. Math majors provided the assistance although there was not an actual room designated for tutoring. Some years, a recent graduate provided the bulk of the tutoring while majors assisted.
With the renovation of Taylor Hall in 1985, a room was designated to be the tutoring location and the Math Center was born. A recent college graduate who wished to remain at Wooster for a time staffed it. In the spring of 1986, there wasn’t a graduate available so the department advertised in local newspapers for a ``math center coordinator’’. The responsibilities included staffing the math center afternoons, arranging for knowledgeable peer tutoring in the evenings, and teaching a non-credit class 3 days a week for students with weak algebra skills. Linda Barbu, a local resident and graduate of the College of Wooster with 14 years teaching experience, became the math center coordinator and remains so.
In 1988, the department discontinued the non-credit class due to declining enrollment and the math center hours increased instead. However, the center has continued to offer assistance for those wishing to hone algebra skills. First the department purchased several copies of a text loaned to those who needed help along with guidelines for usage with tutoring in the center. With the continued development of computer technology, the center next provided ``programmed learning’’ software. Currently we offer a connection to an online site that provides algebra review.
We determined that peer tutors are more helpful and efficient when they have seen the materials in calculus more than once, and can keep up with the progression of the course each semester. Thus, in hiring new student tutors, we pick students (if possible) who have done some grading for the department. We try to arrange the schedule so that each tutor works at least two different times during the week so tutors can more easily keep up with the course content.
As years progressed, we eliminated Sunday afternoon hours since few students used the center at that time. The current hours are Sunday through Thursday evenings 7 – 10 pm and weekday afternoons from 1 – 5 pm. The center also moved from Taylor 211 to Taylor 301 two years ago in a space trade with User Services. In addition to more room, the center is on the same floor as the math department’s offices; thus the center feels more like a part of the department.
In general, students in beginning level math classes find excellent assistance that enhances understanding and alleviates a lot of stress. For example, a student who used the math center last spring wrote ``Thank you so much for all the help in calculus this semester! I never would have made it through the class and done as well as I did without your help.’’ In the last few years, we’ve begun tutoring multivariate calculus students, also. As well, we endeavor to assist students with math questions from courses offered outside the department like chemistry or economics or statistics for social scientists.
Thus the Math Center continues to be a place where current math students receive help and math majors have a chance to review calculus concepts.
What Should Every Undergraduate Mathematics Major Know? · Jun 21, 01:07 AM
posted by Dr. Jon Breitenbucher
Last spring I taught a course in complex analysis. Near the beginning of that course it is common to extend the ideas from the calculus of real valued functions of a real variable to complex valued functions of a complex variable. One extension involves the idea of exponentiation. Upon beginning to talk about the definition of zw where z and w are complex numbers, I asked the question of what was meant by 2π. Students were, in general, not able to answer that question. I was somewhat dismayed and began to ask myself if students were learning anything in our courses.
This event also made me think back to the differential equations course, which I taught in the spring of 2003. In that course, I wanted to use the concept of eigenvalues and eigenvectors, which are introduced in linear algebra. To my dismay again, students seemed to not even know the definitions for these concepts. I was actually more distressed in this situation because I knew that many students in that course had taken linear algebra the previous semester. Moreover, I had taught that course!
These experiences, along with the impetus to assess student learning in mathematics, have caused me to wonder just what every ``good’’ undergraduate mathematics major should know. Are there definitions and theorems that every major should be able to recite from memory upon graduation? Are there particular skills that they should exhibit? Are there particular experiences they should have had?
We would appreciate your feedback on this issue as students or former students. If there is some particular thing that you think every mathematics major should know or be able to do, e-mail me with that at hartman@wooster.edu.
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