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MA 522 "Computer Algebra I"

Instructor: Dr. Hoon Hong,
SAS 3274, hong@ncsu.edu
Office Hour: Tue 10:20-11:40, Thu 1:10-2:30

Lectures: Fall 2019 Tue, Thu 11:45-1:00, POE 636

Objectives: Learn fundamental mathematical theories and algorithms for tackling challenging problems in algebra.
  • Computer algebra is a vast area. Hence it is impossible to cover all aspects within a semester, let alone in a year.
  • Thus I have chosen three fundamental challenges (Counting, Solving, Eliminating). They are fundamental since numerous imporant and nontrivial problems in mathematics, science and engineering can be reduced to them.
  • You will be learning major breakthrough theories and algorithms for tackling the challenges.
Credit hours: 3
Prerequisites: (MA 407 or MA 521) and (MA 405 or MA 520)
GEP: Does not fulfill a General Education Program (GEP) category/co-reqisite

Textbook : No textbook will be required/used. The lectures will be self-contained
References : We will be covering some of the materials from the following books. They are not required, since the lecture will be self-contained. They are listed here in case you want to study some related topics on your own. Most of them are freely available electronically from the library or web sites.
Title Publisher Authors
Modern Computer Algebra Cambridge Uni Press     Gathen, Gerhard
Fundamental Problems of Algorithmic Algebra    Oxford Uni Press Yap
Ideals, Varieties and Algorithms Springer Cox, Little, O'Shea
Using Algebraic Geometry by Springer Cox, Little, O'Shea
Algorithms in Real Algebraic Geometry Springer Basu, Pollack, Roy
Software : Maple
  • One of the most effetive way to learn theories/algorithms is to carry out concrente computations
  • There are numerous computer algebra software. We will be using maple because it is eaiest to learn and most widely available on campus.
  • For graduate students (working as RA or TA) can download your own copy from https://software.ncsu.edu.
  • For other graduate students and undergraduate students, the software is available on almost all desk-top computers on campus. They are also available off campus via http:vcl.ncsu.edu. If you would like to buy one for yourself, it can be purchased at student price (roughly $99) at http:maplesoft.com

Grading: The letter grade will be determined from the total numeric grade as follows:
Letter Grade A+ A A- B+ B B- C+ C C- D+ D D- F
Total Numeric Grade >= 97 >= 93 >= 90 >= 87 >= 83 >= 80 >= 77 >= 73 >= 70 >= 67 >= 63 >= 60 < 60

The total numeric grade will be the sum of several numeric grades as follows:
Type Quizzes Projects Attendance Total
Max Numeric grade 30 66 4 100

Honor Pledge: Honor.pdf

Supplements: Maple Guide

Schedule: This is a tenative schedule. This might be updated depending on the progress and interest of the students.
Weeks      Challenges        Theories/algorithms by
1-5 Counting Descartes, Fourier, Sturm, Hermite, Hilbert
6-10 Solving Noether, Buchberger, Collins, Wu
10-15 Eliminating Sylvester, Macaulay, Tarski, Collins

Policy: We are required to adhere to University Policy. You are strongly recommended to read the policy to learn about your rights and duties.
Overall : http://policies.ncsu.edu/
Equality : http://policies.ncsu.edu/policy/pol-04-25-05
Accomodation : https://policies.ncsu.edu/regulation/reg-02-20-01
Absence : https://policies.ncsu.edu/regulation/reg-02-20-03
Incomplete : https://policies.ncsu.edu/regulation/reg-02-50-03
Credit-Only : https://policies.ncsu.edu/regulation/reg-02-20-15
Audit : https://policies.ncsu.edu/regulation/reg-02-20-04
Conduct : https://policies.ncsu.edu/policy/pol-11-35-01

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