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 4 and April 22, and a final exam on Monday, May 11, 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 21 		p.5:
Problems 1, 2;
pp.12-14:
Problems 1,3,8
Monday
January 26
Monday
January 26 		pp.12-14:
Problems 13, 15;
pp.23-28:
Problems 1,3,4
Monday
February 2
Wednesday
January 28 		pp.36-38:
Problems 2,3,7,8,15 		Monday
February 2
Monday
February 2 		pp.36-38:
Problems 5,6,9,11 		Monday
February 9
Wednesday
February 4 		pp.46-48:
Problems 4,5,9 		Monday
February 9
Monday
February 9 		pp.52-54:
Problems 1a,b,c, 2a, 3b, 4;
Read pp.54-57 		Monday
February 16
Wednesday
February 11 		pp.60-61:
Problems 1,2,7,10 		Monday
February 16
Monday
February 16 		pp.68-69:
Problems 1,2		 Monday
February 23
Wednesday
February 18 		pp.73-75:
Problems 3,4,7,9 		Monday
February 23
Monday
February 23 		pp.80-81:
Problems 1, 4, 5, 7, 11, 12, 13, 14, 15		 Monday
March 2
Wednesday
February 25 		pp.87-88:
Problems 5, 6, 8, 9a 		Monday
March 2
Monday
March 2 		p. 94:
Problem 2 (do not use a computer algebra system)		 Monday
March 9
Wednesday
March 4 		solutions for midterm 1
Monday
March 9 		p. 94-95:
Problems 3(click), 5, 6, 7, 9		 Monday
March 23
Wednesday
March 11 		pp. 121-122:
Problems 1, 2a,b, 3		 Monday
March 23
Monday
March 23 		pp. 121-122:
Problem 7a,b
p. 128
Problem 5 		Monday
March 30
Wednesday
March 25 		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 30
Monday
March 30 		pp. 147-150:
Problems 1, 3, 4, 8
p. 159:
Problems 1, 2 		Monday
April 6
Wednesday
April 1 		pp. 159-162:
Problems 5, 7, 12, 15		 Monday
April 6
Monday
April 6 		pp. 166-168:
Problems 1, 2, 9		 Monday
April 13
Wednesday
April 8 		pp. 174-175:
Problems 1, 2, 4, 10		 Monday
April 13
Monday
April 13 		pp. 182-183:
Problems 1, 2, 3, 4, 5, 7, 11, 14		 Monday
April 20
Wednesday
April 15 		pp. 191-192:
Problems 1, 6, 7, 8, 12		 Monday
April 20
Monday
April 20 		pp. 203:
Problems 2, 3, 4, 5		 Monday
April 27
Wednesday
April 22 		solutions for midterm 2
Monday
April 27 		pp. 209 - 210:
Problems 1, 2, 5, 8, 9		 Monday
May 4
Wednesday
April 29 		pp. 220 - 221:
Problems 8, 9
pp. 228 - 229:
1, 5, 6, 16		 Monday
May 4
Monday
May 4 		prepare for the final
Wednesday
May 6 		prepare for the final