# Mathematic Research Opportunities

The department strongly encourages interested students to undertake independent research under the supervision of a faculty member. This ranges from participating in Diving into Research with a small group of students, to individual projects submitted as honors projects for graduation. For more advanced students, participation in the honors program is one traditional way to do this.

We especially wish to draw your attention to our Diving into Research Groups which provide opportunities to both first-year and upper class students to participate in research in small groups.

## Diving Into Research: First and Second Year Research Groups

Every year, via Diving into Research (MATH110, MATH 111), the department provides opportunities for first-year and upper class students to work in groups with faculty members on research projects.

MATH110 Diving into Research is a year long opportunity for first-year students to work in groups with faculty members on research projects.

Recent topics have included modeling re-entry communication blackout on the space shuttle caused by plasma, and the connection between rigidity of engineering structures (such as the Eiffel Tower) and elementary mathematics

Groups are limited to at most 8 students. Students earn 0.5 credits each semester, and the full year is necessary to obtain credit. May be repeated as MATH111.

Note: Neither MATH 110 nor MATH 111 count as credit towards the Math major.

Below is a description of some recent first-year Research Groups in Mathematics. You can enter similar groups next Fall, and start doing real research. We invite you to participate which gives you an opportunity to actively do research side by side with a faculty member. There will be no more than 8 students in one research group.

### Diving into Research: Mathematics behind Plasmas

Plasma televisions, plasma lights, the heat around the space shuttle and communication blackout caused by plasma, laser treatments in medicine, and production of microchips for computers are just a few applications of plasmas that became a big part of our lives. Students will learn about plasmas by developing and studying mathematical models that explain the experiments and help to obtain plasmas with certain properties. There are no prerequisites. This is a l credit course with 0.5 credit each semester. Math 110 is intended for freshmen and Math 111 is for upperclassmen. Many people take Math 110 along with another first-year Seminar. MATH110 does not satisfy any requirement of the Math major.

(Instructor: N.Sternberg)

### Diving into Research: Rigidity and Geometry

In elementary geometry you have learned the SSS Theorem: Given two triangles in the plane, if the three corresponding sides of the triangles have the same length, then the two triangles are congruent. This simple theorem has the practical consequence that triangles caannot be distorted, and for that reason triangles are a fundamental unit in many rigid structures. Just check out the Eifel Tower.

While engineers have been building such rigid structures successfully for centuries, the mathematical theory underlying them is not yet complete. In our Diving into Research class we will examine the connection between rigidity of engineering structures and elementary mathematics. We will use the example of rigidity to introduce new mathematical ideas from geometry, algebra, and combinatorics. We will survey the state of current research and identify where new questions are waiting to be answered.

This is not a course in engineering, but the mathematics behind engineering. The object of the course is to both see mathematics you already knew in a new context, as well as to introduce new mathematics in a practical,intuitive, and geometrically pleasing setting. There are no prerequisites. This is a 1 credit course with 0.5 credit each semester. Math 110 is intended for freshmen and Math 111 is for upperclassmen. Many people take Math 110 along with another first-year Seminar.

(Instructor: H. Servatius)

### Diving into Research: Knots and Mathematics

Physicists tie knots in cooked spaghetti to study how materials break down when subjected to stress. Chemists synthesize knotted polymers. To decipher the details of cellular reproduction, biologists watch long strands of DNA tie and untie themselves. All these applications of knots to the sciences - and more - depend on mathematics. Knot theory started to develop in the early 20th century and is now one of the most vibrant areas of on-going mathematical research. Using computers, students will draw and manipulate mathematical knots, study the geometry and algebra of knots, and learn how knots are being applied by scientists.

(Instructor: L. Rudolph)