18.786 | Spring 2010 | Graduate

Topics in Algebraic Number Theory

Readings and Lecture Notes

Readings come from the course texts:

[SAM] Samuel, Pierre. Algebraic Theory of Numbers. Translated by Allan J. Silberger. Mineola, NY: Dover, 2008. ISBN: 9780486466668.

[MIL] Milne, J. S. Algebraic Number Theory, 2009. (Available at Mathematics Site).

SES # READINGS LECTURE NOTES KEY DATES
1 [SAM] 1.1-1.3 (PDF)  
2 [SAM] 1.4-1.7 (PDF) Problem set 1 out
3 [SAM] 2.1-2.5 (PDF)  
4 [SAM] 2.6-2.9 (PDF)

Problem set 2 out

Problem set 1 due

5 [SAM] 3.1-3.5 (PDF)  
6 Valuations and completions lecture (PDF)

Problem set 3 out

Problem set 2 due

7

Local fields and GP/Sage sessions

Lecture notes

(PDF)

Problem set 4 out

Problem set 3 due

8 [SAM] 4.1-4.3 (PDF)  
9 [SAM] 4.4-4.7 (PDF)

Problem set 5 out

Problem set 4 due

10 [SAM] 5.1-5.2 (PDF)  
11 [SAM] 5.3-5.4 (PDF)

Problem set 6 out

Problem set 5 due

12 [SAM] 5.5-5.7 (PDF)  
13 [SAM] 6.1-6.5 [No notes] Problem set 6 due
14 [MIL] Introduction [No notes]  
15 Midterm (PDF) Problem set 7 out
16 [MIL] pg. 19-24, 86-93 [No notes]  
17 [MIL] pg. 55-65 [No notes]

Problem set 8 out

Problem set 7 due

18 [MIL] pg. 66-75 [No notes]  
19 [MIL] pg. 66-75 [No notes]

Problem set 9 out

Problem set 8 due

20 [MIL] pg. 95-104 [No notes]

Problem set 10 out

Problem set 9 due

21 [MIL] pg. 105-115 [No notes]  
22 [MIL] pg. 143-164 [No notes]

Problem set 11 out

Problem set 10 due

23 [MIL] pg. 165-176 [No notes]  
24 [MIL] pg. 195-204 [No notes] Problem Set 11 due
25 [MIL] pg. 204-211 [No notes]  
26 [MIL] pg. 211-221 [No notes] Take-home final due

Course Info

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Spring 2010
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