Meeting 14: December 3

Back to quadratic reciprocity, quadratic forms, and cyclotomy

Characterizing structuralism

Contrast case studies

Meeting 13: November 19

Dedekind's theory of ideals

Meeting 12: November 12

Gauss 6 and cyclotomic extensions

The "meaning" of a number-theoretic fact

Meeting 11: November 5

Galois theory: comparison of Galois' and the modern approach

Theory of algebraic integers

Meeting 10: October 29

Finite fields

Algebraic number fields, modulo q

Specializing to cyclotomic fields, p(x) = (x^p-1)/(x - 1)

Meeting 9: October 22

Properties of the Galois group

Moving to higher reciprocity

Meeting 8: October 15

Galois' presentation of the Galois group

Discussion of Gauss' sixth proof

Meeting 7: October 8

Discussion of Sandborg's thesis

Gauss sums

Meeting 6: October 1

Views on calculation: Euler, Gauss, Galois, Dedekind, Kronecker, Siegal, Abhyankar, Edwards

Composition of binary quadratic forms

Galois theory

Meeting 5: September 24

More on quadratic forms

Quadratic reciprocity

Meeting 4: September 17

Back to aspects of mathematical understanding

Galois on computation and elegance: html

Back to quadratic forms

Meeting 3: September 10

Quadratic reciprocity

Quadratic forms

Meeting 2: September 3

Sums of squares

Aspects of mathematical understanding

Meeting 1: August 27

Philosophical issues

Historical overview