Notes will be posted here in the afternoons following the lecture.
Lecture Notes 
Date 
Topic 


#1  Wednesday, Sept. 3,  Outline of the course, sums of squares  
#2  Friday, Sept. 5,  Algebraic integers  
#3  Monday, Sept. 8,  Trace, norm, discriminant  
#4  Wednesday, Sept. 10,  integral bases  
#5  Friday, Sept. 12,  ideal factorization, Dedekind domains I  
#6  Monday, Sept. 15,  ideal factorization, Dedekind domains II  
#7  Wednesday, Sept. 17,  fractional ideals, class group, lattices  
#8  Friday, Sept. 19,  Minkowski's theory of lattices  
#9  Monday, Sept. 22,  Finiteness of class group, start of discussion on units  
#10  Wednesday, Sept. 24,  End of Dirichlet unit theorem, regulator  
#11  Friday, Sept. 26,  Factoring primes in Dedekind domains  
#12  Monday, Sept. 29,  Factoring primes in Dedekind domains II  
#13  Wednesday, Oct. 1,  Factoring primes in Galois extensions  
#14  Friday, Oct. 3,  Using SAGE to do computational algebraic number theory  
#15  Monday, Oct. 6,  Cyclotomic fields I  
#16  Wednesday, Oct. 8,  Cyclotomic fields II  
#17  Friday, Oct. 10,  Localization  
#18  Monday, Oct. 13,  Units and class groups in localizations  
#19  Wednesday, Oct. 15,  one dimensional Noetherian domains  
#20  Friday, Oct. 17,  Geometric intuition  
#21  Monday, Oct. 20,  Affine schemes for 1dimensional domains  
#22  Wednesday, Oct. 22,  Function fields  
#23  Friday, Oct. 24,  Introduction to valuation theory  
#24  Monday, Oct. 27,  completeness of padic numbers  
#25  Wednesday, Oct. 29,  classification of valuations  
#26  Friday, Oct. 31,  completions of number fields  
#27  Monday, Nov. 3,  nonarchimedean valuations, Hensel's lemma  
#28  Wednesday, Nov. 5,  Extensions of absolute values  
#29  Friday, Nov. 7,  Intro to local fields  
#30  Monday, Nov. 10,  Unit theorems  
#31  Wednesday, Nov. 12,  Logarithm in padic fields  
#32  Friday, Nov. 14,  Extensions of Henselian fields  
#33  Monday, Nov. 17,  The structure of unramified extensions  
#34  Wednesday, Nov. 19,  Extension of valuations in number fields  
#35  Friday, Nov. 21,  The fundamental identity of local extensions  
#36  Monday, Nov. 24,  Galois theory of local extensions  
#37  Monday, Dec. 1,  Formalism of profinite groups  
#38  Wednesday, Dec. 3,  Formalism of valuations  
#39  Friday, Dec. 5,  The reciprocity map  
#40  Monday, Dec. 8,  local class field theory and KroneckerWeber theorems  
#41  Wednesday, Dec. 10,  global class field theory 
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