Math 437, Algebraic Geometry - Fall 2016

Instructor: Jack Huizenga

Jack Huizenga
Office: 324 McAllister
  • Meeting times: MWF 12:20-1:10, 302 Willard
  • First meeting: Monday, August 22
  • Office hours: Monday 3:30-5, Tuesday 12-1, or by appointment
  • Textbook: Robert Bix, Conics and Cubics, Second Edition. With your Penn State account you can get an eBook version for free here. However, the book is not exorbitantly expensive, and you should be reading it very carefully. I would strongly consider purchasing the hard copy.
Brief course description: We will cover the majority of the textbook. This course is a gentle introduction to algebraic geometry, focusing particularly on the theory of algebraic curves of small degree. We will begin by studying intersection multiplicities of curves in the Euclidean plane. We will also introduce the projective plane and study its transformations and intersections of curves in the projective plane. We then move on to the study of plane conics and cubics, which are the simplest algebraic curves. We discuss singularities, tangents, flexes, and the group law on a cubic curve. Successful students will learn to apply the general theory to analyze explicit problems and examples, as well as provide their own proofs of basic results in algebraic geometry.
Prerequisites: Math 311W, Concepts of Discrete Mathematics. Familiarity with proofs will be helpful, but will also be developed throughout the course.
Homework: Weekly homework assignments will be posted on the webpage most Wednesdays, and they are due in class the following Wednesday at the beginning of class. We may discuss solutions to problems after the homework has been turned in, so late homework will not be accepted. Please write your solutions clearly and carefully. If you have to miss class that day, you can turn in your assignment early to my box in the McAllister building. The lowest score will be dropped at the end of the semester.

Homework is by far the most important part of the course. The only way to learn advanced mathematics is to do advanced mathematics. Weekly homework assignements will consist both of problems from the book and additional questions not from the book.
Final project: In lieu of a final exam, you may opt to pursue an independent research/reading topic at the end of the semester. I will make several suggestions for possible topics after the second midterm. The goal of the project will be to explore a niche in algebraic geometry more thoroughly and produce a 5-10 page paper explaining your topic. I fully expect this option will be more challenging than preparing for a final; however, this is an excellent opportunity to explore the subject in greater depth.
Collaboration: You are encouraged to discuss homework problems with your fellow students. However, you have to write up your solutions by yourselves and show originality. Please write the names of any students you collaborated with on your assignment.
Attendance: Class attendance is strongly encouraged. If you must miss class you should make every effort to get notes from your fellow students. There is typically a very strong correlation between class attendance and performance on exams.
Exams, Grading, and Expectations: We will tentatively have exams on the following dates.

Week 6: Exam 1, Friday Sep. 30
Week 11: Exam 2, Friday Nov. 4
Final exam/project due date: TBD, during finals week

The homework and exams will count for the following portions of your grade.

Homework: 20%
Exam 1: 20%
Exam 2: 20%
Final exam OR project: 40%

Letter grades will be assigned based on the cumulative score; the ranges corresponding to letter grades will be determined based on the difficulty of the exams and the following rubric.

A: Able to perform basic computations in algebraic geometry and recite the definitions from the course. Demonstrates solid understanding of the theoretical aspects of the course.
B: Able to perform basic computations in algebraic geometry and recite the definitions from the course. Demonstrates some understanding of the theoretical aspects of the course.
C: Able to perform basic computations in algebraic geometry and recite the definitions from the course.
D/F: Fails to meet the expectations for a C.

Cumulative scores of 80/70/60 will receive at least an A/B/C; however, the final breakpoints may be lowered. Grade ranges will be discussed in more detail after each exam.

Make-up exams: All make-up exams for permissible excuses must be requested in advance of the exam. Travel scheduled on an exam date is not a permissible excuse. There will be no make-up exams for unexcused abscences. At the instructor's discretion, in the case of a missed midterm your other exam scores may be used to determine your grade.

Final exam scheduling: Conflicts for the final exam are determined by scheduling; they cannot be scheduled through the Mathematics Department. A student with a final exam conflict must take action to request a conflict exam through eLion during the final exam conflict filing period from Sep. 26 - Oct. 16.

Academic Integrity Statement: All Penn State policies regarding ethics and honorable behavior apply to this course.
Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. The Office for Disability Services Web site provides contact information for every Penn State campus: . For further information, please visit the Office for Disability Services Web site: .
Homework assignments (Solutions available on ANGEL) :
  • Problem Set 2 (Problems 4 and 5 updated slightly 9/6. Problem 5 due 9/14.)
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