Syllabus

1. Instructor:

Dr. Agnes Szanto
SAS Hall 4120
Tel: 515-7547
E-mail: aszanto

Meet

T-Th 11:45am-1:00pm
214 Poe Hall

Office Hours

T-W 2:00PM-3:00PM
or by appointment

2. Course Prerequisites

MA522 or permission from instructor

3. Goals and Objectives

The course will equip the graduate level students with advanced but well established material in algorithmic approach to algebra, such as algorithms for symbolic matrices, algorithms for commutative algebra and (real) algebraic geometry, and algorithms for polynomila factorization and/or for differential and difference equations, time permitting. Completing the course work, the students will be able to develop advanced algorithms in computer algebra, to read critically scientific articles published in journals and conferences, and to carry out original research in computer algebra or related subjects.

4. Textbook

Recommended Reading:

• Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) by David A. Cox, John Little and Donal O'Shea, 3rd edition (2007)
• Using Algebraic Geometry by David Cox, John Little and Donald O’Shea, Springer, 2nd edition (2005).
• Algorithms in Real Algebraic Geometry Sugata Basu, Richard Pollack, Marie-Francoise Roy, Springer, 2nd edition (2006).

5. Topics and estimated days allocated to each topics

• Algorithms for Complex and Real Algebraic Equations (5-6 weeks)
  • Groebner basis continued
  • Varieties and polynomial ideals
  • Representations of idelas and varieties
  • Wu's characteristic setts
  • Multivariate resultants
  • Cylindrical decomposition
    
  • Sums of squares and moment matrices
  • Lasserre hierarchy
    
    
    
• Presentations of course projects (1 week)

6. Tentative schedule of reading assignments

TBA

7. Tentative schedule of homework due dates, quizzes and tests

The grade will be given on the basis of successful completion of homework assignments given approximately every two weeks and a project. The project will involve giving an oral and written presentation of a recent paper or chapter from a book, which will be selected by the student subject to the approval of the instructor. Oral presentations of the projects will take place during the final week of classes and during the time scheduled for the final exam.

8. Determination of grades: + and - system

• Homework: 50%
• Course Project: 25%
• Final Exam 25%

9. Policy on incomplete grades and late assignments

Homework will be assigned and collected once every two or three weeks. It is the students' responsibility to do the homework. For the homework problems, check the course website. Late homework will NOT be accepted, since I may hand out solution sets on the due date.

10. Policy on absences (excused and unexcused) and scheduling makeup work

Students are expected to arrive on time, to contribute to group work and class discussions, and to stay until the class ends. Attendance at all meetings of the class is expected. Occasional absences will be approved if they meet University policy (see University policies).

11. Academic Integrity Statement:

Students are expected to follow university guidelines available at
http://www.ncsu.edu/policies/student_services/student_discipline/POL11.35.1.php

12. NC State policy on working with students with disabilities:

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.1) (link).

 

13. Statement on laboratory safety or risk assumption in courses requiring physical activity or field trips:

None

14. Statement on extra expenses or charges e.g. lane rental at bowling alley, field trip costs, etc.:

None

15. Transportation Information:

None

16. Class evaluation

Online class evaluations will be available for students to complete during the last two weeks of class.  Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations.  All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.

Evaluation website:
https://classeval.ncsu.edu

Student help desk: 
classeval@ncsu.edu

More information about ClassEval: 
http://www2.acs.ncsu.edu/UPA/classeval/index.htm