Mathematics and Computers MAT 165
MWF 12:10 - 1 pm, BAINER 1130
Instructor : Amitabh Basu
Office Hours : Monday 2:00 - 3:00 pm, Friday 3:00 - 4:00 pm, email for appointment. Office Hours will be in my office : Mathematical Sciences Building (MSB) 3111.
Email : abasu [at] math [dot] ucdavis [dot] edu
Teaching Assistant : Our TA for this course will be Mark Junod. His email is : mjunod [at] math [dot] ucdavis [dot] edu.
Mark's office hours will be Wednesdays and Thurdays from 2:30pm to 4pm in his office MSB 2139.
Text : Required - Ideals, Varieties and Algorithms, by Cox, Little and O'Shea, Third Edition. The text is freely available electronically through the UC Davis library services: e-text. If the link does not work, simply search for the text in the library catalog at the UC Davis Library and use "Electronic Resources".
Other (more advanced, not requireed) 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 electronically (you do not need to buy this book!):
- Using Algebraic Geometry, by Cox, Little and O'Shea, Springer, GTM.
- Modern Computer Algebra, by von zur Gathen and Gerhard, Cambridge Univ.
- Solving Polynomial Equations, by Sturmfels, CBMS 97, American Math Soc.
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.
Syllabus and Schedule : We will follow the departmental syllabus closely.
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, the Kepler conjecture, 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 ).
- Programming Assignment I is up ! Please see below under "Homeworks and Programming Assignments".
- Practice Midterm I has been put up. Please see below under "Midterms and Final".
CLASS ACCOUNT FOR MAPLE
You can get free access to MAPLE by opening an account in the mathematics department. Please go to:
and follow the instructions. These accounts expire at the end of the quarter.
Here is the maple worksheet from the first lecture on Friday, Sept 28.
Here is the worksheet from the lecture on Monday, Oct. 1, 2012.
Here is a MAPLE worksheet on univariate polynomials. Some more commands for manipulating polynomials.
Here is the MAPLE worksheet from today's lecture (November 7, Wednesday) on Groebner Bases. More Groebner basis stuff from lecture on Friday, November 9.
Here is the MAPLE worksheet on Application of Groebner bases to Graph Theory and Mathematical Logic.
Lecture Slides on Hilbert Nullstellensatz.
EXAM AND GRADING INFORMATION
There will be 2 in-class examinations (Midterm I and Midterm II) and a Final exam. In addition, there will be 3 programming assigments. In addition, I will give homework assigments which will not be graded. However, seriously attempting these homework problems are imperative for your success in the class, and give an indication of the kind of problems on the tests.
Homeworks and Programming Assignments
Midterms and Final
- Homework Problems. This problem sheet will be continuously updated with new problems throughout the quarter.
- Midterm I will be on Wednesady, October 24, 2012 in class.
Practice Midterm I.
Solutions to Midterm I.
- Midterm II will be on Wednesday,
November 14 November 21, 2012 in class.
Practice Midterm II.
Solutions to Midterm II
- The Final exam is on Friday, December 14, 2012, 6 - 8 pm.
- There will be NO MAKE UP exams and a missed exam will result in a 0 grade. Please adjust your schedules around this.
- The lower of the two Midterm scores will be dropped from the calculation of the final grade.
- Both Midterms and the Final Exam will be closed book.
- Your final gradebased on the following weightage :
Programming Assignment - 30%
Midterm - 30%
Final - 40%
- SmartSite will be used to post the exam grades. You should be able to access your grades there.
You can use the form below to give me any feedback anonymously. Your feedback can be about anything related to course - pace of lectures, homework, exams etc. I welcome your suggestions !