Meetings: MWF 12:10pm-1:00pm, PHYSICS 140.
Instructor: Jesús A. De Loera.
email: deloera@math.ucdavis.edu
http://www.math.ucdavis.edu/~deloera/TEACHING/MAT165/
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
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
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:
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 ).
(week 5-6) Groebner bases and Buchberger's algorithm
(week 9-10) Applications. Engineering problems (e.g. Robotics), Automatic Theorem proving.
THIRD PROJECT DUE (last day of classes)
Important: Each week I assign 5-10 problems for you to practice what is being covered. Although we wont collect those problems, you can count some will appear in each midterm and the final!!
http://www.math.ucdavis.edu/comp/class-accts
and follow the instructions. These accounts expire at the end of the quarter.
Here is the maple worksheet I showed in my introduction on the first day of the class.
Please read Computers and the meaning of Proof this article from Scientific American (a bit old now)
Here is the second MAPLE worksheet that I showed to introduce you to MAPLE on our first LAB session. maple_crashcourse.
Here is a third MAPLE worksheet about univariate polynomials.. Here you can also download more code to manipulate univariate polynomials, but not as a worksheet.
Here is pseudocode of the extended euclidean algorithm Also you can find a step by step example computation with some suggestion of MAPLE commands that will be useful when you implement it.
homework 2 Contains more problems for the first midterm
Here is a piece of MAPLE code that should help you with using Groebner
bases
and solving systems of polynomials Groebner MAPLE code .
Here is a list of some review problems for the first midterm
----------------MIDTERM 1 up to here-----------------------------
homework 3 contains problems for the second midterm.
homework 4 last set of problems to be covered in second midterm
Here are two pieces of MAPLE code that were demonstrated in class. The first is on how to use Groebner bases to solve system of equations Groebner commands and applications. You can also download code for the cyclohexane equations. Finally here is a second worksheet with applications to Graph theory and Logic
We are having our second Midterm on Friday May 20, at the
computer laboratory. Here are some review
problems for second midterm. Solutions for the computational
problems using MAPLE are posted here
Here is the MAPLE code that solves the numerical problems, first in
mw format,
then in a text version
(not for xmaple) text .
----------------MIDTERM 2 up to here-----------------------------
homework 5 Final homework!
We learned about Hilbert's Nullstellensatz and its applications to logic, graph theory, automatic theorem proving. Here are the lecture transparencies used in class to discuss the Linear Algebra approach to decide feasibility of polynomial systems
Here are the MAPLE solutions for problems 3, 2B,2A of midterm 2. Here is the text version.
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Our final exam will be a final project. You can choose from one of the 2 projects proposed in class (logic computation or integer programming) OR you can make your own project! For details and rules please consult the MAPLE worksheet about the final projects . NOTE: You must receive my approval if you are doing a project you designed.
You can find my transparencies about the logic satisfiability problem Davis Putnam and NP-completeness . Even ore information about the Davis-Putnam algorithm implementation to solve logic satisfiability problem is also available. You can also download the brilliant survey lecture by Bernd Sturmfels about Groebner bases . It includes our short introduction to integer programming.
All final Projects are due at 12:00noon June 9. They MUST be submitted in a single maple worksheet that will run at least 3 examples when executed.