Holy Cross Mathematics and Computer Science
MATH 392 -- Seminar in Computational Commutative Algebra (and Algebraic Geometry, with Applications) -- Spring 2019
Syllabus and Schedule
Examples, Class Notes, Etc.
Assignments
- Problem Set 1: 1.1/2,5; 1.2/2,4 parts abdf only,6,13,14; 1.3/4,6,8,10 due: Friday, Feb. 1.
- First problem day: Ty Bramer 1.1/6, Jack Champagne 1.2/4 part e, Jennifer Collymore 1.2/7.
Be ready to present solutions of these in class on Friday, Feb. 1.
- First computer lab day, Feb. 4. Note this contains two exercises at the end
that you will submit with Problem Set 2, due Friday, Feb. 8.
- Problem Set 2: 1.4/1,2,3,8,16,19 and the two Maple exercises from the lab day (see above). due: Friday, Feb. 8.
- Second problem day: Kate Hegermiller: 1.4/6abc, Eliza May: 1.4/6de, Sarah McGuire: 1.4/11. Be ready to present solutions
of these in class on Friday, Feb. 8.
- Problem Set 3, due: Friday, Feb. 15. We'll resume the problem presentations the
following week on Friday, Feb. 22.
- Second computer lab day, Feb. 18. Note this contains two exercises at the end
that you will submit with Problem Set 4, due Friday, Feb. 22.
- Problem Set 4: 2.4/3,4,9 (Note what Corollary 6 on page 74 says: To show a relation is a monomial
order, you can show (1) and (2) in the definition, then show all α ≥ 0 instead of showing (3) in
the definition. This generally much easier!); 2.5/1,7,10, and the two Maple exercises from the second
computer lab day due: Friday, February 22. Note: Problem 9 in Section 2.5 has been postponed until next week's
problem set.
- Third problem day: Isabella Mongelli: 2.5/12, Zak Muse: 2.5/14, Victoria Roy: 2.5/16.
- Problem Set 5: 2.6/1; 2.7/2a, 10 (Note: this problem replaces the problem 2.5/9 that was postponed from last
week's problem set); Maple problems: 2.8/1, 3, 8, 9 (note this has a part c at the top of the following page!)
- Fourth problem day: Andrew Saunders: 2.6/3, Gabriella Uccelini: 2.6/9, Elena Wang: 2.7/12abc.
- Problem Set 6/Lab Day 3, due in class on Friday, March 15.
- Problem Set 7: 4.1/1, 2; 4.2/4, 7, 15; due in class on Friday, March 29.
- Fifth problem day: Melody: 4.1/4, Ty: 4.2/1, Jack: 4.2/3, Jennifer: 4.2/8. Be ready to present solutions
of these in class on Friday, March 29.
- Problem Set 8: 4.3/6, 8, 9, 11ab only. due: Friday, April 5.
- Sixth problem day: Katherine: 4.3/3 (It's not fair to use part b of the Proposition for this, but you
may use unique factorization as in equation (1).), Eliza: 4.3/7a, Sarah: 4.3/7b, Isabella: 4.3/12.
Be ready to present solutions
of these in class on Friday, April 5.
- Fourth Lab Day/Problem Set 9, due: Friday, April 12.
- Seventh problem day: Zak: 4.4/16a, Victoria: 4.4/16b , Andrew: 4.6/3,
Gabby: 4.6/4a, Melody: 4.6/4b (you can use part a),
Elena: 4.6/4c (you can use parts a,b) Be ready to present
solutions of these in class on Friday, April 12.
- Problem Set 10: 6.4/6, 7 , 13b, c. You'll want to do 6 and 7 by hand, then use your
polynomial translations in Maple for 13b, c. Also note: For 7 and 13c, the circumcenter
of a triangle is the unique point that is equidistant from the three vertices (so, a circle with that
center passes through the three vertices; that is the circumscribed circle of the triangle). The
circumcenter can be constructed by finding the intersection of any two of the perpendicular
bisectors of the sides of the triangle. (Do you see why?) due: Friday, April 26. This will be
the final problem set of the semester, and it will be treated as an Extra Credit assignment.
Any points earned here will be added to your problem set total, but the problem set average will be
computed by dividing by 9.
Final Projects
Information and Announcements
- CEF's for this class will be administered on Friday, April 26
- Final project presentations: April 29, May 1, 3, 6
- The textbook for the course is:
D. Cox, J. Little, and D. O'Shea, Ideals, Varieties, and Algorithms, 4th edition, Springer, ISBN 978-3319167206.
If you click on the link here, it will take you to the HC library system listing; then ``Click to view e-book.'' This will let you download a .pdf electronic version of the book free of charge. (The College library has purchased a large package of electronic books from this publisher for use on campus.) You can apparently
also download one chapter at a time. Conventional bound copies of the book are available
in any of the usual ways if you would prefer that.
Related Links
Downloading Information
The links for assignments and other handouts shown above lead in most cases
to documents in PDF format.
- Note: The Greek phrase appearing next to the heading of this page is one traditional rendering of
the reported inscription over the entrance to Plato's Academy in Athens
(founded about 387 BCE).
It means (roughly)
Let no one ignorant of geometry enter. This is a reflection of the foundational
role of geometry in Plato's ideas about knowledge and education.
Last modified: April 25, 2019