This is an archived course. A more recent version may be available at ocw.mit.edu.

Lecture Notes

The complete lecture notes This resource may not render correctly in a screen reader.Number Theory I (PDF - 8.4MB) can be used as the online textbook for this course.

LEC # TOPICS
1 This resource may not render correctly in a screen reader.Absolute values and discrete valuations (PDF)
2 This resource may not render correctly in a screen reader.Localization and Dedekind domains (PDF)
3 This resource may not render correctly in a screen reader.Properties of Dedekind domains, ideal class groups, factorization of ideals (PDF)
4 This resource may not render correctly in a screen reader.Étale algebras, norm and trace (PDF)
5 This resource may not render correctly in a screen reader.Dedekind extensions (PDF)
6 This resource may not render correctly in a screen reader.Ideal norms and the Dedekind-Kummer theorem (PDF)
7 This resource may not render correctly in a screen reader.Galois extensions, Frobenius elements, and the Artin map (PDF)
8 This resource may not render correctly in a screen reader.Complete fields and valuation rings (PDF)
9 This resource may not render correctly in a screen reader.Local fields and Hensel's lemmas (PDF)
10 This resource may not render correctly in a screen reader.Extensions of complete DVRs (PDF)
11 This resource may not render correctly in a screen reader.Totally ramified extensions and Krasner's lemma (PDF)
12 This resource may not render correctly in a screen reader.The different and the discriminant (PDF)
13 This resource may not render correctly in a screen reader.Global fields and the product formula (PDF)
14 This resource may not render correctly in a screen reader.The geometry of numbers (PDF)
15 This resource may not render correctly in a screen reader.Dirichlet's unit theorem (PDF)
16 This resource may not render correctly in a screen reader.Riemann's zeta function and the prime number theorem (PDF)
17 This resource may not render correctly in a screen reader.The functional equation (PDF)
18 This resource may not render correctly in a screen reader.Dirichlet L-functions and primes in arithmetic progressions (PDF)
19 This resource may not render correctly in a screen reader.The analytic class number formula (PDF)
20 This resource may not render correctly in a screen reader.The Kronecker-Weber theorem (PDF)
21 This resource may not render correctly in a screen reader.Class field theory: ray class groups and ray class fields (PDF)
22 This resource may not render correctly in a screen reader.The main theorems of global class field theory (PDF)
23 This resource may not render correctly in a screen reader.Tate cohomology (PDF)
24 This resource may not render correctly in a screen reader.Artin reciprocity in the unramified case (PDF)
25 This resource may not render correctly in a screen reader.The ring of adeles, strong approximation (PDF)
26 This resource may not render correctly in a screen reader.The idele group, profinite groups, infinite Galois theory (PDF)
27 This resource may not render correctly in a screen reader.Local class field theory (PDF)
28 This resource may not render correctly in a screen reader.Global class field theory and the Chebotarev density theorem (PDF)