Web pages: http://web.mit.edu/18.704/www or http://math.mit.edu/18.704.
Meetings: TR 1-2:30; Room 2-255.
Instructor: Steven L. KLEIMAN, 2-278, x3-4996, kleiman@math.mit.edu.
Instructor's office hours: TR 8:30-9:30 and 12:30-2:30 and by appointment.
TA: Martina Balagovic martinab@math.mit.edu.
TA's office hours: 8:00-9:00pm on Wednesdays in 2-251, and by appointment.
Text: "Ideals, Varieties, and Algorithms" by Cox, Little, and O'Shea, UTM Springer, third edition, 2007. Google books has most of the book online at the URL
Grades: Based equally on classwork, homework, and the term paper; no exams or final. Written work work will be graded in part on the quality of the writing. The term paper is to be ten-pages long in TeX: a full outline is due by Thursday, 30 October; a complete first draft, by Thursday, 20 November; and a revised final draft, by Tuesday, 9 December.
Homework: Problems with numbers between braces are to be written up formally in TeX and passed in by Thursday of the week after they are assigned; they may be emailed either in TeX form or dvi form directly to the TA.
| Assignments | ||||||
|---|---|---|---|---|---|---|
| Date | First lecture | Second lecture | ||||
| 1. R. 9/4 | Steve Kleiman | Sec. 1-1 | p.5: 2, {6b} | Steve Kleiman | Sec. 1-2 | p.12: {6}, 8, 10 |
| 2. T. 9/9 | Steve Kleiman | Sec. 1-3 | p.22: 1,3,4, {11} | ShinnYih Huang | Sec. 1-4 | p.34: 3b, {9}, 10 |
| 3. R. 9/11 | Yongjin Kim | Sec. 1-5 | p.46: {9}, 10 | Charles Tam | Sec. 2-1,2 | p.52: 5; p.60: {2}, 10 |
| 4. T. 9/16 | Oleg Kozhushnyan | Sec. 2-3 | p.68: {1} | Jia Wei | Sec. 2-4 | p.73: 3, {9} |
| 5. R. 9/18 | Ye Luo | Sec. 2-5 | p.80: {1}, 10 | Qingchun Ren | Sec. 2-6 | p.87: 1, {12} |
| 6. T. 9/23 | Amrik Kochhar | Sec. 2-7 | p.94: 2a, {3a} | Pablo Spivakovsky-Gonzalez | Sec. 2-8 | p.100: {1}, 7 |
| 7. R. 9/25 | ShinnYih Huang | Sec. 3-1 | p.121: 1, {6} | Yongjin Kim | Sec. 3-2 | p.127: {3}, 5 |
| 8. T. 9/30 | Charles Tam | Sec. 3-3 | p.135: 9, {11} | Oleg Kozhushnyan | Sec. 3-4 | p.148: 4, {10} |
| 9. R. 10/2 | Jia Wei | pp.150--153bot | p.159: 1, {4} | Ye Lu | pp.153bot--159 | p.159: 11, {17} |
| 10. R. 10/7 | Qingchun Ren | Sec. 3-6 | p.166: {2}, 3, 8 | Amrik Kochhar | Sec. 4-1 | p.174: 1, {2} |
| 11. T. 10/9 | Pablo Spivakovsky-Gonzalez | Sec. 4-2 | p.182: 2, {7a} | Sec. 4-3 | p.191: 1, {11a-d} | |
| T. 10/14 | Columbus Day -- No class | |||||
| 12. R. 10/16 | Sec. 4-4 | p.197: {1}, 4 | Sec. 4-5 | p.203: 5, {12} | ||
| 13. T. 10/21 | Sec. 4-6 | p.209: 1, {9} | Sec. 5-1 | p.220: 8, 10 | ||
| 14. R. 10/23 | Sec. 5-2 | p.228: 1, 6 | Sec. 5-3 | p.237: 6, {8} | ||
| 15. T. 10/28 | Sec. 5-4. Outline due. | p.246: 8, 9 | Sec. 5-5 | p.256: {9}, 10 | ||
| 16. R. 10/30 | Sec. 5-6 | p.263: {5}, 8 | Sec. 6-1,2 | p.269: 4; p.277: {4} | ||
| 17. T. 11/4 | Sec. 6-3 | p.287: {3}, 6 | Sec. 6-4 | p.303: 9, 13d | ||
| 18. R. 11/6 | Sec. 6-5 | p.315: 3, 6a | Sec. 7-1 | p.324: {8}, 14 | ||
| 19. T. 11/11 | Sec. 7-2 | p.333: 11, 14 | Sec. 7-3 | p.342: {5}, 7 | ||
| 20. R. 11/13 | Sec. 7-4 | p.354: 6, 13 | pp.357--371bot | p.375: 4, {7} | ||
| 21. T. 11/18 | pp.371bot--385. First draft due. | p.385: 15; p.385:{10} | Sec. 8-4 | p.391: {2}, 9 | ||
| 22. T. 11/20 | pp.393-400top | p.406: 7, {9} | pp.400top-406 | p.406: 17, 18 | ||
| 23. R. 11/25 | Sec. 8-6 | p.419: 7, 10, {15} | Sec. 9-1 | p.442: {2}, 5 | ||
| R. 11/27 | Thanksgiving -- No class | |||||
| 24. T. 12/2 | Sec. 9-2 | p.453: 3, 12 | Sec. 9-3 | p.465: 10, {12} | ||
| 25. R. 12/4 | Sec. 9-4. Deadline for late homework. | p.474: 6, 10 | Sec. 9-5 | p.482: 7, 13 | ||
| 26. T. 12/9 | Sec. 9-6 Final draft due. | p.493: 13, 17 | Sec. 9-7 | p.504: 6, 13 | ||