Letter to Prospective Students

I understand that you are interested in mathematics, so I thought you might want to know a bit more about what it is like to study mathematics at Kenyon. We are a small department, six faculty members and seven to ten graduating seniors per year. Thus our classes are very small. Our introductory courses have an upper limit of 25 students, and our advanced courses typically have eight students or fewer. Studying mathematics at Kenyon means a lot of personal attention from faculty and close working relationships with other students.

We've built our mathematics curriculum around a couple of beliefs about learning and doing mathematics:

• Mathematical thinking is a combination of rigorous logical analysis and highly trained intuition.
• Communication---speaking, listening, reading, and writing about mathematical ideas---is also essential. It is not an extra; clear communication is an integral part of clear thinking, and vice versa.

These principles influence the way we teach our courses. Some of our students find it surprising at first that we frequently ask them to write and speak about mathematics. They soon realize that one way to sharpen their understanding of mathematics is to try to explain it to others! In many of our courses students work on term projects leading to papers and in-class presentations. They also often work together in small groups. Doing mathematics is a collaborative business; we find that bright students who work together can often tackle more challenging material and gain a deeper understanding than they can manage individually.

Of course, there is nothing wrong with a little friendly competition. In our calculus classes this year, student groups competed in the design of wine goblets. The goblet designs were solids of revolution that had to meet mathematical requirements of size, stability, and so forth. Kenyon President Robert Oden judged among the qualified goblets to choose the most beautiful and functional entry, and the winning team won a cash prize. In our upper-level math modeling course, the students took on the problem of designing an efficient algorithm for searching the ocean floor for a shipwreck, a situation inspired by the real-life problem of hunting for the wreck of the Titanic. They divided into two teams that developed competing strategies and raced their computer "subs" against each other. Twenty visitors (including me) came to the class that day to watch the competition.

The computer is a common tool in mathematics, and we use it in many of our courses. In fact, our introductory calculus and statistics courses are held in a specially equipped classroom in which each student has a computer on the desk. Computer software helps us explore mathematical ideas that would have been completely out of reach for undergraduates a decade ago. It allows us to use graphical and numerical approaches to mathematics in a more complete and helpful way. By using the computer, we are able to form conjectures and build our intuition through exploration.

Computers help, but mathematics is still something that we do with our brains. Throughout our curriculum we emphasize the conceptual threads that tie together mathematical ideas.

Kenyon students also find many opportunities to do mathematics beyond the classroom.

• We participate in several math competitions, including the regional Five College Contest (where this year we are defending our first-place finish from last spring), a national mathematical modeling contest, and the (very challenging) William Lowell Putnam Exam. Our Putnam team this year was in the top 15% of teams nationally, and junior math-physics double major Lei Yu scored in the top 5%.
• We invite several interesting speakers each year to give talks of mathematical interest. Last year we heard fascinating talks ranging from models of blood flow during surgery to the application of linear algebra to archaeology.
• Each summer, students work with mathematics faculty members on research problems in the Kenyon Summer Science Scholar program. In January of last year Eric Newman (Kenyon '96) tied for first place at the national meeting of the Mathematical Association of America for a poster presentation of statistics research done the previous summer with Professor Brad Hartlaub. This summer three more students will be working on dynamical systems and Gödel's theorems. (Other Kenyon math students have had the opportunity to do summer research at institutions around the country.
• Our honors students focus on projects tailored to their specific interests. Two years ago, the honors statistics work of Greg Stark and Brian Vannoni (both Kenyon '95) with Professor Hartlaub won the three of them a $25,000 grant from the Mellon Foundation to support a detailed statistical study of Kenyon admissions data.

Even more impressive than their achievements at Kenyon, our graduates in recent years have gone on to top graduate programs in physics, economics, and law, not to mention mathematics and statistics. One of this year's seniors, Lora Ballinger, has been awarded an impressive fellowship from the National Physical Sciences Consortium, giving her six years of support in the graduate program of her choice supplemented by two summers of research work at Lawrence Livermore National Laboratory. She plans to study mathematical biology. The success of our students has not been limited to graduate study; other students have found excellent jobs right out of Kenyon with prestigious consulting firms and insurance companies, Wall Street banks, Compuserve, the Mayo Clinic, Proctor and Gamble, and other employers.

For myself, I find that one of the best things about teaching at Kenyon is the opportunity that I have here to form close relationships with my students. Math faculty and students eat lunch together every Tuesday, and we join the physics department for a picnic each semester. Professor Brian Jones and the students of the Kenyon juggling club meet once a week to toss things around. Professor Hartlaub has been known to play a round of golf with his students. I sing in a small choir with a couple of junior math majors. I have fond memories of students around my dining room table eating cookies and drinking tea or playing cards late into the night, singing songs around my piano, or chopping vegetables for a shared stir-fry dinner. Last fall a few of our students invited my husband and me to a lovely dinner that they prepared in their campus apartment. We are brought together by a common love of mathematics, but we share many interests and many good times that go beyond that. Basically, we have a roaring good time, filled with intellectual challenges and personal satisfactions. I hope that you will decide to come and join in the fun.

Sincerely, Carol S. Schumacher Associate Prof. and Chair Department of Mathematics

Course of Study Advice

For those students who want only an introduction to mathematics, or perhaps to satisfy a distribution requirement, selection from MATH 5, 6, 10, 11, and 18 is appropriate. Students who think they might want to continue the study of mathematics beyond one year, either by pursuing a major or minor in mathematics or as a foundation for courses in other disciplines, usually begin with the calculus sequence (MATH 11, 12, and 21). Students who have already had calculus or who want to take more than one math course may choose to begin with the Elements of Statistics (MATH 6) and Data Analysis (MATH 26) or Introduction to Computer Science (MATH 18). A few especially wellprepared students take Linear Algebra (MATH 24) or Foundations of Analysis (MATH 22) in their first year. (Please see a member of the math faculty if you think you may wish to do this.)

Pre-calculus (MATH 10) is a course for students with a weak background in mathematics whowish to prepare for calculus. MATH 11 is an introductory course in calculus. Students who have completed a substantial course in calculus might qualify for one of the successor courses, MATH 12 or 21. MATH 6 is an introduction to statistics, which focuses on quantitative reasoning skills. Surprises at Infinity (MATH 5) is a course on the mathematics of the infinite. It is designed especially for students who want a very different view of mathematics than they have seen previously. MATH 18 is an introduces students to computer programming in the C language.

Please read the course descriptions (located in the "Academic Program" section of this website) for further information concerning these courses, and look for the * symbol, which designates those courses particularly appropriate for first-year or upperclass students new to the mathematics curriculum. To facilitate proper placement of entering students, the department administers a calculus readiness exam and a calculus placement exam during Orientation. This and other entrance information is used during the orientation period to give students advice about course selection in mathematics.