Math 176: Algebraic Geometry

Fall 2016

Overview

Algebraic geometry is both old and amazingly active. In this course the goal is to become acquainted with the basics, affine and projective varieties, while keeping an eye on modern tools, such as moduli, and fun applications, such as enumerative geometry and number theory.

Instructor

Dagan Karp
Office: Shan 3414
Office hours: Monday 4-5 p.m., and open door

Lectures

This course will meet for lectures Monday and Wednesday, 1:15-2:30pm in Shanahan room 3465.

Textbook

We'll use Undergraduate Algebraic Geometry by Miles Reid.
Other good resources include Fulton's Algebraic Curves, An Invitation to Algebraic Geometry by Karen Smith, and the graduate texts (two distinct texts with the same title) Algebraic Geometry by Joe Harris and Robin Hartshorne.

Grading

Homework 80%
Final project 20%

Homework

Written homework will be due Wednesdays, and is posted below. Here are some useful tips for LaTeX homework formatting.

Portfolio Problems

The last problem on each assignment (aside from HW1) is a portfolio problem. This problem will generally be much more involved and will allow for creative freedom in approach. The written work for the portfolio problem will consist of reflection as well as mathematical analysis. The goal is to help you understand your own creative process, how you synthesize and create knowledge, and how you approach mathematics. Specific components and grades are as follows:

Critical Readings

In addition to the written homework, suggested readings will be posted on the homework page in conjunction with upcoming lectures.

Create a google document titled m176_f16-lastname, which will serve as a journal, and share it with my dkarp@g.hmc account. (If you prefer latex, please create an appropriately named folder instead.) Before each lecture, read the assigned material, and in your journal write one or two questions and/or comments. A brief note consisting of one or two sentences, saved the night before class is ideal.

The goals of the critical reading exercises are manifold: to better the student's independent intake of mathematical exposition, to train in independent learning, to increase the interactive nature of the course (by allowing the instructor to respond to the questions and comments), and to make the course more tailored to the specific curiosities of the class as a whole.

LaTeX

Students interested in using LaTeX are encouraged to do so, but it is not required.

Disabilities

It is the policy of The Claremont Colleges to accommodate students with temporary or permanent disabilities. Any student with a documented disability who requires reasonable accommodations should contact Deborah Kahn, Coordinator for Student Disability Resources at (909) 607-3148 or dkahn@hmc.edu, as soon as possible. Students from the other Claremont Colleges should contact their home college's disability officer.

Social Justice Demonstrations

The mission of Harvey Mudd College is to prepare leaders who understand the impact of their work on society. Our institution is a vibrant part of that society, and we might be affected by the violence in our world and the tumult of this political season. Social justice demonstrations are likely to occur at the Claremont Colleges this year, and we understand that some students may wish to take part in these activities. Therefore, we are willing to accommodate your reasonable participation in such events, so long as you coordinate with your instructor in advance, ideally at least 24 hours before the affected class meeting time or due date.

Notes


Homework and Critical Readings
  • CR 1. Due Mon Sep 5. Reid, Woffle and Section 1.
  • HW 1. Due Wed Sep 7.
    Reid 0.1, 0.2, 0.3.
  • CR 2. Due Mon Sep 12
    Re-read Reid Section 1, focusing on (1.7)-(1.14).
  • CR 3. Due Mon Sep 19.
    Hartshorne -- Section 1, through Proposition 1.2
    Munkres -- Chapter 2
    Reid -- Section 3, through (3.7).
  • CR 4. Due Mon Oct 10.
    Reid Section 4.
  • HW 4. Due Fri Oct 14.
    Reid 4.2, 4.4, 4.6
    Turn in homework to Jocelyn in the Math Dept office by 4:30pm on Friday.
  • CR 5. Due Mon Oct 24.
    Reid Section 5.
  • CR 6. Due Mon Nov 7.
    Reid Section 2.