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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Website

23. 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

24. 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

25. 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