MATH 3349 (2018)

Fridays 10am to 11:30am in the Meeting Room (JD 1117).

Here is a bi-weekly plan of our reading and homework. You should read and understand the assigned parts of the book, and test your understanding by trying the exercises. We will discuss the material and exercises when we meet on Fridays. On the last day of the second week, you must turn in complete solutions to 5 exercises of your choice.

1. Weeks 1 and 2 (19 Feb to 2 Mar): Chapter I (3 sections)
2. Weeks 3 and 4 (2 Mar to 16 Mar): I.3, II.1, II.2
3. Weeks 5 and 6 (16 Mar to 30 Mar): End of chapter II
4. Weeks 7 and 8 (30 Mar to 20 Apr): Finish chapter II, III.1, III.5.
5. Week 9 (27 Apr to 5 May): Chapter V.1
6. Week 10 (5 May to 12 May): Chapter IV.1, V.2, V.3
7. Week 11 (12 May to 19 May): V.3, V.4
8. Week 12 (19 May to 25 May): Read the statement of Riemann-Roch. Understand the meromorphic functions on a complex torus.

A short write up on [discrete valuation rings](DVR.pdf), to explain how the idea of ramification appears in extensions of number fields and maps of Riemann surfaces.

• Complex analysis: MATH 3328, or equivalent.
• Topology: Basic topology as covered in MATH 3320.
• Geometry: MATH 2242, MATH 3342, or equivalent.

We will meet once a week to discuss assigned readings from Miranda. Additionally, I highly encourage you to meet once or twice to discuss the material amongst yourselves. There will be written exercises due every two weeks.

Based on written exercises and participation in the group discussions.