Transcript Math and ACM at Caltech

Math and ACM at Caltech
An Investigative Report
By the SFC Math/ACM Committee
Student Members
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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:
 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