MATH 165, Fall Quarter, course information

Meetings: MWF 12:10pm-1:00pm, PHYSICS 140.

Instructor: Jesús A. De Loera.


Phone: (530)-554 9702

Office hours: Monday and Wednesday 1:10pm-2:00pm or by appointment. My office is 3228 Mathematical Science Building (MSB). The TA for this class is Mr. Mohamed Omar. His office hours are Thursdays 10am-11am at room 2125 MSB. We will be glad to help you with any questions, concerns, or problems.

Prerequisites and expectations: This class is intended for Math and CS majors in their junior or senior year. It is necessary that you have a solid idea of how to write proofs and true familiarity with computer programming (say as in ECS 30). In particular you will have to learn MAPLE. If in doubt please ask me about it.

You are expected to work outside the classroom programming, thinking about the theorems and exercises, etc. I estimate a minimum of 3 hours work at home per lecture. The most important thing is what YOU learn by doing. Math and CS are not spectator sports!

Text: The only mandatory text for this course is

Other (more advanced, not required) references:

Software: This class will use MAPLE as the software for class discussion, tests, homeworks, projects, etc. Due to logistic reasons, no other software will be allowed. A very useful resource, an e-book about MAPLE, is accessible to all UC Davis students for free in the electronic book (you do not need to buy this book!):

Maple and Mathematica :a problem solving approach for mathematics by Inna Shingareva and Carlos Lizarraga-Celaya, Springer, 2009, online resource (xviii, 483 p.).

To access the book there is a SpringerLink free to all UC campuses e-book about MAPLE

If you wish to access the book from outside campus internet, then you can do this using the VPN link of the library (go to the UCD library link).

Finally (NOT required) but a great text for all about MAPLE is

``An introduction to MAPLE'', by A. Heck, Springer, 2006.

Description of this Course: : This course has two goals:

1) To introduce undergraduate students to Algebraic/Symbolic Computation. This is the part of mathematics dedicated to algorithms where the answer is to be computed exactly. This is complementary to the area of numerical analysis (MATH 128ABC) where answers are computed with limited precision and error.

2) It is now undeniable that computers are useful tools for finding counterexamples, discover patterns, and even proof theorems! For example, the proof of the four color theorem, investigation of fractals, etc. Thus, the second goal of the course is to learn how computers are useful tools for mathematical research, experimentation and can even help to generate formal proofs automatically. In fact, knowing how to use computers can go a long way toward solving a math problem (e.g. see the wonderful site of Project Euler ).

Course outline: In general what I will try to do is to cover the first four chapters of the text book, plus some scientific applications.

(weeks 1-2) Motivation, Introduction to MAPLE and Symbolic Computation. The algebra of univariate polynomials,
Euclid's algorithm and GCD of polynomials. Real and rational roots of univariate polynomials (Sturm sequences and Descartes's rule of signs).


(week 3-4) Ideals and Varieties, Multivariate systems of polynomial equations, monomial ideals, term orders and Multivariate Division Algorithm.


(week 5-6) Groebner bases and Buchberger's algorithm


(week 7-8) Solving systems of multivariate polynomial equations. Elimination theory, Hilbert's Nullstellensatz and unsolvable systems.


(week 9-10) Applications. Engineering problems (e.g. Robotics), Automatic Theorem proving.

THIRD PROJECT DUE (last day of classes)


Grading policy: