Lecture Notes

Representation Theory and Character Theory
• Lecture 1 (01/28) Definitons
• Lecture 2 (01/30) Subrepresentations
• Lecture 3 (02/04) Irreducible representations and operations on representations
• Lecture 4 (02/06) The character of a representation (Classroom changed!)
• Lecture 5 (02/11) Schur's lemma and its applications
• Lecture 6 (02/13) Regular representations and irreducible representations
• Lecture 7 (02/20) The number of irreducible representations
• Lecture 8 (02/25) Dirichlet characters

Infinite Series, infinite products and logarithmic functions
• Lecture 9 (02/27) Proof of Dirichlet's Theorem (Sketch)
• Lecture 10 (03/04) The first log function
• Lecture 11 (03/06) The second log function
• Lecture 12 (03/11) Proof of Dirichlet's Theorem
• Lecture 13 (03/13) Real primitive Dirichlet characters

Number fields and class number formulas
• Lecture 14 (03/18) Noetherian rings and Noetherian modules
• Lecture 15 (03/20) Ring of integers
• Lecture 16 (04/01) The ring of integers is a Dedekind domain
• Lecture 17 (04/03) Dedekind domains
• Lecture 18 (04/08) Binary quadratic forms
• Lecture 19 (04/10) Class number formula: quadratic case
• Lecture 20 (04/15) Proof of class number formula I
• Lecture 21 (04/17) Proof of class number formula II
• Lecture 22 (04/22) Proof of class number formula III