Math 620 schedule

Monday Wednesday Friday

Sept. 7



In Lecture: No Class! Sept. 9



In Lecture: Algebraic numbers, algebraic integers and transcendental numbers

Associated Reading: Lang, Chapter I, sections 1.1 and 1.2

Hardy and Wright, section 11.7

Samuel, chapter 2, sections 2.1 to 2.5

Video of class

Video of class (downloadable) Sept. 11



In Lecture: No Class!

Sept. 14



In Lecture: Norms and Traces

Iintegral closures

Prime ideals and maximal ideals

Associated Reading: Lang, Chapter I, sections 1.2, 1.3, 1.4, 1.5.

Samuel, chapter 2.

Video of class

Video of class (downloadable) Sept. 16



In Lecture: Integral closures, continued

Traces and norms, finiteness of integral closures, continued

Dual bases

Associated Reading: Lang, chapter I, sections 1.2, 1.3, 1.4, 1.5

Lang, chapter 3, section 3.1.

Samuel, chapter 2.

Video of class

Video of class (downloadable) Sept. 18



In Lecture: No class!

Sept. 28



In Lecture: Fractional ideals of Dedekind rings form a group

Integral closures of Dedekind rings

Ideal class groups, elliptic curves, Jacobians of curves

Associated Reading: Samuel, chapter 3.

Samuel, chapter 5, sections 5.1 and 5.2.

Lang, chapter 1, section 1.6.

Hartshorne, chapters 1.6 and 2.6.

Video of class

Video of class (downloadable) Sept. 30



In Lecture: Applications of Dedekind rings: Fermat, Curves over fields and Dedekind rings

Decomposition of primes

Associated Reading: Washington, chapters 1 and 2.

Hartshorne, chapters 1.6 and 2.6

Samuel, chapter 5, sections 5.1 and 5.2.

Lang, chapter 1, section 1.6.

Video of class

Video of class (downloadable) Oct. 2



In Lecture: No Class!

Oct. 26



In Lecture: No class! Oct. 30



In Lecture: No class! Oct. 28



In Lecture: No class!

Nov. 9



In Lecture: No class! Nov. 11



In Lecture: Product formula

Geometry of numbers

Finiteness of class numbers, finite generation of unit groups

Associated Reading: Lang, chapters 2 and 5

Video of class (streaming)

Video of class (downloadable) Nov. 13



In Lecture: Geometry of numbers (continued)

Finiteness of class numbers, finite generation of unit groups (continued)

Associated Reading: Lang, chapters 2 and 5

Video of class (streaming)

Video of class (downloadable)