Mathematics 5385 (Introduction to Computational Algebraic Geometry)



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Required text: Ideals, Varieties and Algorithms, third edition by Cox, Little and O'Shea.

Course description: Algebraic Geometry studies solutions of systems of polynomial equations. This is a huge generalization of Linear Algebra, which studies solutions of systems of linear equations. There are algorithms for solving systems of polynomial equations, which are far-reaching generalizations of Gaussian elimination. The subject is rich and beautiful. We are going to cover Chapters 1 through 4 of the text.

Homework: Weekly homework assignments will be posted on this page. They are due on Monday of the following week in the beginning of class.

Exams: There will be two midterm exams on Wednesdays, March 2 and April 20, and a final exam on Monday, May 9, 4:00 -- 6:00, in the regular meeting room.

Make up exams: Will be allowed only under truly exceptional circumstances. You must notify the lecturer at least a week in advance.

Final grade: Homework counts for 40%, each of the midterm exams for 15% and the final exam for 30%.

Computers may be needed for some of the homework problems. You will use the program called Mathematica. It is available on the computers installed in the CSE and Math Department labs. Once you sit down at the machine and get the program running you get a window where you can type commands and see the answers. After you are done typing a command you execute it by doing a Shift-Return or Shift-Enter, that is, hold the Shift key down while pressing the Return or Enter key. Click for some examples

Lecture date Homework assignment Due date
Week 1
Wednesday
January 20 		p.5:
Problems 1, 2;
pp.12-14:
Problems 1,3,8
Monday
January 25
Week 2
Monday
January 25 		pp.12-14:
Problems 13, 15;
pp.23-28:
Problems 1,3,4
Monday
February 1
Wednesday
January 27 		pp.36-38:
Problems 2,3,7,8,15 		Monday
February 1
Week 3
Monday
February 1 		pp.36-38:
Problems 5,6,9,11 		Monday
February 8
Wednesday
February 3 		pp.46-48:
Problems 4,5,9 		Monday
February 8
Week 4
Monday
February 8 		pp.52-54:
Problems 1a,b,c, 2a, 3b, 4;
Read pp.54-57 		Monday
February 15
Wednesday
February 10 		pp.60-61:
Problems 1,2,7,10 		Monday
February 15
Week 5
Monday
February 15 		pp.68-69:
Problems 1,2		 Monday
February 22
Wednesday
February 17 		pp.73-75:
Problems 3,4,7,9 		Monday
February 22
Week 6
Monday
February 22 		pp.80-81:
Problems 1, 4, 5, 7, 11, 12, 13, 14, 15		 Monday
February 29
Wednesday
February 24 		pp.87-88:
Problems 5, 6, 8, 9a 		Monday
February 29
Week 7
Monday
February 29 		p. 94:
Problem 2 (do not use a computer algebra system)		 Monday
March 7
Wednesday
March 2 		Midterm 1
Monday
March 7 		p. 94-95:
Problems 3(click), 5, 6, 7, 9		 Monday
March 21
Wednesday
March 9 		pp. 121-122:
Problems 1, 2a,b, 3		 Monday
March 21
Monday
March 21 		pp. 121-122:
Problem 7a,b
p. 128
Problem 5 		Monday
March 28
Wednesday
March 23 		pp. 135-137:
Problems 6a,b, 14
You may have to use the computer program Mathematica
for this assignment. See above (right before the homework
assignments table) for instructions.		 Monday
March 28
Monday
March 28 		pp. 147-150:
Problems 1, 3, 4, 8
p. 159:
Problems 1, 2 		Monday
April 4
Wednesday
March 30 		pp. 159-162:
Problems 5, 7, 12, 15		 Monday
April 4
Monday
April 4 		pp. 166-168:
Problems 1, 2, 9		 Monday
April 11
Wednesday
April 6 		pp. 174-175:
Problems 1, 2, 4, 10		 Monday
April 11
Monday
April 11 		pp. 182-183:
Problems 1, 2, 3, 4, 5, 7, 11, 14		 Monday
April 18
Wednesday
April 13 		pp. 191-192:
Problems 1, 6, 7, 8, 12		 Monday
April 18
Monday
April 18 		pp. 203:
Problems 2, 3, 4, 5, 8		 Monday
April 25
Wednesday
April 20 		prepare for midterm 2
Monday
April 25 		pp. 209 - 210:
Problems 1, 2, 5, 8, 9		 Monday
May 2
Wednesday
April 27 		pp. 220 - 221:
Problems 8, 9
pp. 228 - 229:
1, 5, 6, 16		 Monday
May 2
Monday
May 2 		prepare for the final
Wednesday
May 4 		prepare for the final