An Investigative Report By the SFC Math/ACM Committee Math and ACM at Caltech An Investigative Report By the SFC Math/ACM Committee

Student Members Bud Coulson - Math Co-Chair Waley Chun - ACM Co-Chair Roger Lee – ARC Liason Sherwin Dorundi Evan Dummit Abhi Gulati Christine Parry Will Shao

Faculty Members Michael Aschbacher - Shaler Arthur Hanisch Professor of Mathematics Eric Wambach – Ogla Taussky-John Todd Instructor of Mathematics Oscar Bruno - Professor of Applied and Computational Mathematics Dan Meiron - Fletcher Jones Professor of Applied and Computational Mathematics and Computer Science Niles Pierce - Associate Professor of Applied and Computational Mathematics and Bioengineering

Math & ACM Difficult options which attract only the brightest and most talented students We are happy to have had a chance to meet with professors and learn more about the way these subjects are taught at Caltech

Introductory Courses Two purposes: They are: Teach material necessary for further study in the major Introduce students to the method of rigorous proofs in mathematics They are: Math 5 for the math option ACM 95 for the ACM option

Math 5 Introduction to Abstract Algebra About 50% of math majors take this class as freshmen Suggestion: hold midterm and final reviews to help new students adjust to the difficulty of the class

ACM 95 Introduction to the Methods of Complex Analysis Students feel this class is very useful and like the real-world applications presented in class Midterms and finals very hard 95c has no exams, and allows referencing past homework sets - students don’t learn as much and grade distribution skewed

Other Courses Cannot survey all the courses in the options, and feel no need to try Not every student takes the same courses Present a collection of classes for which we felt we could propose some improvements

Math 6a Introduction to Discrete Math Partial requirement for Math, CS, and ACM majors Instructor and material taught have changed from year to year Noted for various problems with homework: typos and distribution errors

Math 6a Propose that the material and textbook be kept the same from year to year More standardized teaching would fit in with the core nature of the class while making the overall experience much more enjoyable

ACM 106 Introduction to the Methods of Applied Mathematics Not a requirement, but commonly taken sophomore/junior year Assumes intensive prior knowledge of a math programming language,which not all students have learned yet

ACM 118 Introduction to Applied Statistics Very useful for further study of statistics However, the lack of textbook and/or course notes posted makes it hard to make up missed classes

Other Proposals This committee has one major proposal, for a new course in the ACM option Other than that, we offer some general comments about the options

CS course In the CS major, there is a three-unit class CS 11 which teaches the basics of a programming language This course is useful for students who may need to know some language, but have not had prior exposure to it A similar situation arises for ACM students who need to use a computer algebra system such as Matlab or Maple

Math Programming A new 3-unit ACM/CS course teaching Matlab/Mathematica/Maple would be easy to implement, but invaluable to ACM students It could be taught by a graduate student or postdoc with relatively minimal effort and low cost

Student Opinion A survey of all undergraduate ACM majors found that a large majority were in favor of such a new course An editorial in a recent issue of the California Tech made a similar proposal

Departments In addition to the classes themselves, we have some comments on the administrative departments and general structure of each option These include suggestions for tweaking the major requirements as well as minor improvements that could be made to the administration

Math In some classes (notably Math 6a and 108, two requirements for the major) homework sets are collected and returned very late Also, in some classes, there is not enough emphasis on the office hours for the grader and professor of the course

ACM ACM at Caltech leans towards the abstract To cater to students who want a more computational approach, we propose that the 27 Math unit requirements for ACM be made into Math/ACM Another suggestion is to allow ACM 216 and 217 to fulfill the 27 units ACM requirement, to allow probability-minded students to take the ACM 116/216/217 sequence more easily

Good Aspects There are some aspects of the two options which we felt are particularly exemplary and deserve praise Other options could well learn from these special areas

Math Omsbudsmeetings always planned out in advance, allow valuable feedback from each class The speaking and writing courses (Math 10 and 11) do a very good job in preparing students for conducting mathematical research Website very well designed and maintained

Website

ACM Major is very flexible, allowing students to plan out their courses according to their interests Small major ensures personal connection with professors and TAs, as well more opportunities for research projects

Final Comments In general, ACM and Math at Caltech are very flexible and well-designed options We have made suggestions to deal with the few minor problematic areas, which can only add to the high level of excellence already enjoyed We hope you have learned from our presentation

Thanks To all of the professors who attended our meetings and helped us learn To the committee members for their time and dedication towards improving the their options To the SFC for having this conference and allowing us to express our opinions