Assignments
December 3
This is the last meeting!
- Remember that we are meeting at Pitt, and at 9:30 instead of 10
- Continue reading Dedekind's 1877 monograph.
- Read the excerpts from Corry's book:
Chapter 1: pdf,
Chapter 2: pdf,
Chapter 3: pdf.
November 19
Continue reading Dedekind's 1877 monograph.
November 12
Continue reading Dedekind's 1877 monograph.
November 5
Read Dedekind's 1877 monograph, intro and chapter 2.
October 29
- Continue reading from October 22
- If you want to start reading about Dedekind's development of algebraic number theory, consider:
- Stillwell's translation of Dedekind's 1877 monograph (skip or skim chapter 1):
part 1: pdf,
part 2: pdf,
part 3: pdf.
- Edwards, Harold, "Mathematical Ideas, Ideals, and Ideology":
journal,
>pdf.
- Avigad, Jeremy, "Methodology and metaphysics in the development of Dedekind's theory of ideals":
pdf.
October 22
- Read Ed's translation of Dedekind's 1857 lectures on Galois theory:
pdf.
- Read Ed's translation of Dedekind's 1894 supplement on field extensions:
pdf.
- Read a modern account of Galois theory, such as the one in Milne's lecture notes:
html.
October 15
- Read Edwards' explanation of Galois' construction of the Galois group:
pdf.
- Take a look at Eisenstein's second and fourth proofs of quadratic reciprocity, using Gauss sums:
pdf.
October 8
- Read the excerpts from Sandborg's thesis:
Chapter 4: (and title page) pdf,
Chapter 5: pdf,
Chapter 6: pdf,
references: pdf.
- Read about Gauss sums, for example, in Everest and Ward's book: pdf.
Compute (g_1)^2, g_q, (g_1)^q.
October 1
Depending on your background and interests, read some of the following on Galois' theory of equations:
- Galois' memoir: pdf.
- Excerpts from Edwards, Galois Theory: pdf,
pdf,
pdf.
- An excerpt from Tignol's book: pdf
- Kiernan's historical overview: pdf.
September 24
- Look at the English translation of Gauss' third proof of QR: pdf
- Read the Lautenbacher and D. Pengelley article: JSTOR,
pdf.
- Continue reading the material on equivalence and composition of quadratic forms.
- If you would like, start reading Kiernan or Edwards on Galois theory (see the bibliography page).
September 17
- Continue reading Dirichlet on quadratic forms.
- Read the excerpts from Weil, Legendre's composition of quadratic forms:
pdf.
- Read the excerpt from Edwards, Fermat's Last Theorem, on composition of forms:
pdf.
- Take a look at Gauss on the composition of quadratic forms:
pdf.
September 10
- Read Gauss on quadratic reciprocity, DA 94-99 and 104-120 (n=-1, 2, 3): pdf.
- Continue reading chapters 5 and 12 of Goldman.
- Continue reading Dirichlet on quadratic forms.
- It is worthwhile spending some time with the first three sections of the DA:
pdf.
September 3
- Let us know if you want us to put you on an e-mail list.
- Read Cox on quadratic reciprocity:
JSTOR or
PDF.
- Read Edwards on Euler's proof of quadratic reciprocity:
JSTOR or
PDF.
- Read Avigad on sums of squares, in sections 2.2 and 2.3 of the following paper:
doi or
pdf.
Quadratic reciprocity and quadratic forms will occupy our attention for a while. As time allows, you may wish to consider
the following:
- Start reading Knoebel et al., Mathematical Masterpieces, Chapter 4, "Patterns in the Prime Numbers:
The Quadratic Reciprocity Law:" pdf.
- Start reading Stillwell's introduction to Dedekind's 1877 monograph on algebraic number theory:
pdf.
- Start reading Goldman, Chapters 5 and 12:
pdf,
pdf.
- Start reading Dirichlet's presentation of the theory of quadratic forms:
pdf.