I began teaching Calculus and Linear Algebra back in China when I was 18 years old. After teaching for two years, I resumed my studies at Shanghai Teachers’ University, but then I paid special attention to how the best teachers taught their classes. When I went back to the college to continue teaching, I received the Outstanding Teaching Award each year for the next two years. At that time, I taught Calculus, Linear Algebra, Abstract Algebra, Ordinary Differential Equations, and Statistics.

It was a challenge when I started as a Teaching Assistant at the University of Pennsylvania. I was worried. However, it turned out that I really enjoyed it, and I was pleased with the students reactions and comments. At Penn, I taught all levels of Calculus as a Teaching Assistant, and had full responsibility for summer courses in Calculus, Fourier Series & Boundary Value Problems, and Linear Algebra. A videotape of the summer course on Linear Algebra that I taught at Penn has been a “model” for the three years from 1993 to 1996 in the Department’s Instructional Program for new Teaching Assistants.

Since I have been at Harvey Mudd, I have taught Advanced Differential Geometry, Linear Algebra, Elementary Differential Geometry, Multi-variable Calculus and Advanced Linear Algebra. Usually, I teach three courses or sections in the fall semester and two courses in the spring semester. The teaching evaluation of my courses is around 6 points out of a total 7 points. (The highest one was 6.87 out of 7.) I held weekly evening problem sessions on Sunday nights in addition to my regular office hours, held review sessions on weekends, and held extra office hours to help students with weak backgrounds. My students greatly appreciated my hard work.

Here are some examples of course evaluations:

Prof. Gu is very enthusiastic about teaching and put a lot of effort and work: into helping the students understand the material. She makes linear algebra a very enjoyable and understandable course. Gu often holds homework sessions ,for us and gives us a lot of extra material to help us study. She is very nice and approachable professor and one of my favorite teachers.

Professor Gu was interested in the course and taught the material well. I liked how she did not go in the order of the book. The organization was very good. She cares about her students a lot.

Professor Gu was energetic and motivating which made everyone want to do their best work. She also explained material very clearly.

A lot of challenging material was covered. It was fun to learn so much… Very dedicated and well-prepared …whenever there were gaps in our knowledge, Prof. Gu would quickly and effectively review …Kept a good pace going through material: when it was simple it was covered quickly, but more difficult subjects were given more time and useful examples.

Professor Gu is an excellent teacher with a clear mastery of advanced mathematics. I liked that the class was able to cover some advanced material in depth… The “big picture” guides were very helpful for the organizing the rnate rial in my mind… The material was extremely challenging, but Prof. Gu did an excellent job of making it interesting and understandable.

In order to improve my teaching constantly, I have been observing how some of the best professors at Harvey Mudd teach their classes. I learned a lot from their teaching techniques. Still there is much more for me to learn. Throughout these years, I have thoroughly enjoyed my teaching, and intend to keep doing it for the rest of my life.

## Course Information

### Development

- Developed a multi-media course on the Geometry of Curves and Surfaces with Applications to Computer Aided Geometric Design. (As the principal investigator on this three-summer Mellon funded project), supervised 7 summer working students and collaborated with Professor Michael Moody and Professor Ran Libeskind-Hadas in the summer of 97.
- Modified Math 73 (Linear Algebra) and its successors in the new core math curriculum and Math 173 (Advanced Linear Algebra) so that they fit better into the college curriculum.
- Reestablished a course, Math 142 (Elementary Differential Geometry) which had not been taught at HMC for many years.
- Created a new course, Math 143 (Topics in Geometry), to provide a strong background for our advanced mathematics and physics students in their future graduate study.
- Created a Geometric Modeling Course, Math 460. Currently being taught at CGU.
- I am currently writing a book on “Differential Geometry for Advanced Undergraduate Students” following an invitation from the AMS. (Please see the included draft in my submitted folder).
- Currently updating Math 12 and Math 63.

### Materials

I have prepared course materials for the following classes.

- Math 12 – Linear Algebra & Discrete Dynamical Systems I
- Math 14 – Multivariable Calculus I
- Math 61 – Multivariable Calculus II
- Math 63 – Linear Algebra II
- Math 73 – Linear Algebra
- Math 142 – Differential Geometry of Curves and Surfaces
- Math 143 – Topics in Differential Geometry
- Math 173 – Advanced Linear Algebra
- Math 198 – Undergraduate Mathematics Forum

### Courses Taught

#### Fall, 2005

- Math 12-3, Linear Algebra/Discrete Dynamic Systems (meet 4 times per week).
- Math 12-5, Linear Algebra/Discrete Dynamic Systems (meet 4 times per week).
- Math 142, Elementary Differential Geometry.
- Math 193, Math Clinic.
- CGU-Math 460, Geometric Modeling.

#### Summer, 2005

- Math 63, Section 1, Linear Algebra II (summer math).
- Math 63, Section 2, Linear Algebra II (summer math).

#### Spring, 2005

- Math 173, Advanced Linear Algebra.
- Math 193, Math Clinic.
- Math 196, Independent Study supervising.

#### Fall, 2004

- Math 142, Elementary Differential Geometry.
- Math 193, Math Clinic, Faculty Adviser.
- Math 196, Independent Study supervising.

#### Summer, 2004

- Math 61, Section 1, Multi-variable Calculus II (summer math).
- Math 61, Section 2, Multi-variable Calculus II (summer math).

#### Spring, 2004

- Math 143, Topics in Geometry.
- Math 193, Math Clinic.
- Math 196, Independent Study supervising.(In order for me to attend workshops in geometry at MSRI, Art arranged my teaching so that I had a heavier load in 2003 instead.)

#### Fall, 2003

- Math 12-1, Linear Algebra/Discrete Dynamic Systems, meet 4 times per week.
- Math 12-2, Linear Algebra/Discrete Dynamic Systems, meet 4 times per week.
- Math 142, Elementary Differential Geometry.
- Math 193, Math Clinic, Faculty Adviser. 5. Math 196, Independent Study.

#### Summer, 2003

- Math 61, Section 1, Multi-variable Calculus II (summer math).
- Math 61, Section 2, Multi-variable Calculus II (summer math).

#### Spring, 2003

- Math 14, Section 1, Multi-variable Calculus I.
- Math 14, Section 2, Multi-variable Calculus I.
- Math 173, Advanced Linear Algebra.
- Math 196, Independent Study.
- Math 198, Math Forum, taking care for both Monday and Wednesday sections.

#### Fall, 2002

- Math 142, Elementary Differential Geometry.
- Math 12-4, Linear Algebra/Discrete Dynamic Systems, meet 4 times per week.
- Math 12-6, Linear Algebra/Discrete Dynamic Systems, meet 4 times per week.
- Math 198, Math Forum, taking care for both Monday and Wednesday sections.
- Math 196, Independent Study, supervising three students.

#### Spring, 2002

- Math 14, Multivariable Calculus I, Section 3.
- Math 14, Multivariable Calculus I, Section 4.
- Math 143, Advanced Geometry.
- Math 193, Mathematics Clinic.
- Math 196, Independent Study.
- Math 197, Senior Thesis coordinator.

#### Fall, 2001

- Math 142, Elementary Differential Geometry.
- Math 198 and 198c, Undergraduate Math Forum.
- Math 198, Mathematics Clinic.

#### Spring, 2001

- Math 14, Multivariable Calculus I, Section 1.
- Math 14, Multivariable Calculus I, Section 5.
- Math 14, Multivariable Calculus I, Section 6.
- Math 196, Algebraic Topology.

#### Fall, 2000

- Math 142, Elementary Differential Geometry of Curves and Surfaces.
- Math 173, Advanced Linear algebra.
- Math 196, Lie groups and Lie algebra.

#### Spring, 2000

- Math 73, Linear Algebra, Section 1.
- Math 73, Linear Algebra, Section 2.
- Math 143, Topics in Differential Geometry.

#### Spring, 1999

- Math 73, Linear Algebra, Section 2.
- Math 173, Advanced Linear algebra.

#### Fall, 1998

- Math 73, Linear Algebra, Section 1.
- Math 73, Linear Algebra, Section 2.
- Math 142, Elementary Differential Geometry of Curves and Surfaces.

#### Spring, 1998

- Math 73, Linear Algebra, Section 1.
- Math 143, Topics in Differential Geometry with Applications to Einstein’s Relativity.

#### Fall, 1997

- Math 73, Linear Algebra, Section l.
- Math 73, Linear Algebra, Section 2.
- Math 142, Elementary Differential Geometry of Curves and Surfaces.

#### Spring, 1997

- Math 73, Linear Algebra, Section l.
- Math 143, Seminars in Advanced Differential Geometry.

#### Fall, 1996

- Math 73, Linear Algebra, Section 1.
- Math 73, Linear Algebra, Section 2.