Assignments

For the week of November 25:

• What are the philosophical issued raised by structural treatments of algebraic number theory, and Wedderburn's theorem?
• Be prepared to continue the discussion of Dedekind, Stein, Edwards, Gray.

For the week of November 18:

• Keep thinking about the Dedekind text, relying on these notes on Chapters 3 and 4: pdf, postscript, dvi. (Note that there are also short supplementary excerpts on Galois theory and the algebraic integers in the folder/drawer.)
• Keep thinking about division rings. (We still intend to make notes available soon.)
• Keep thinking about Dedekind, Stein, Edwards, and Gray.

For the week of November 11:

• Do your best to understand the background for the analysis of minimal finite dimensional division rings. Take a look at Wedderburn's paper and the excerpts from Lam's book. (We will supply additional notes.)
• Do your best to read Chapters 3 and 4 of Dedekind, with help from the supplementary excerpt from Stewart and Tall. (We will supply additional notes.)

For the week of November 4:

• Review Dedekind, Stein, Edwards, Gray.
• Review group actions.
• Feel free to discuss final paper topics with us.

For the week of October 28:

• Continue reading Chapter 2 of Dedekind, with help from the following notes: pdf, postscript, dvi.
• By ready to discuss Dedekind's methodological claims (most notably, in the introduction, and towards the end of Chapter 2). Also, be ready to compare and contrast views the analyses found in the articles by Stein, Edwards, and Gray.
• Start reading Dedekind's "Continuity and the irrational numbers," Kronecker's "On the concept of number," and Hilbert's "On the concept of number." Ewald's editorial notes and the other sources are optional background reading.

For the week of October 21:

• Continue reading Chapter 2 of Dedekind.
• Read Gray's "The nineteenth-century revolution in mathematical ontology," focusing on 12.2, 12.3, and 12.6.

For the week of October 14:

• Begin reading Chapter 2 of Dedekind.
• Review the introduction, focusing on methodological claims.

For the week of October 7:

• Read Edwards' "Mathematical ideas, ideals, and ideology."
• Continue reading the introduction and Chapter 1 of Dedekind. Supplementary notes: pdf, postscript, dvi

For the week of September 30:

• Look over Euler's "Power residues" one more time.
• Look over the Conway chapter one more time.
• Let us know if you are not comfortable with the notion of an algebraic extension of Q, etc., so we can help you understand it.
• Finish reading the translator's introduction to the Dedekind text.
• Read Dedekind's introduction.
• Start reading Chapter 1, "Auxilliary theorems from the theory of modules."

For the weeks of September 16 and 23 (in order of priority):

• Review the mathematical examples we have been discussing, and let us know if you would like additional help understanding them.
• Continue reading the translator's introduction to the Dedekind text.
• Finish reading the Conway chapter (the "afterthoughts" are optional).
• Be prepared to discuss Euler's "Power residues."

For the week of September 9 (in order of priority):

• Read the excerpt from Conway's The Sensual (Quadratic) Form, through page 12.
• Read Mac Lane's "Structures in mathematics."
• Read Euler's "Power residues" (in the excerpt from Struik's sourcebook).
• Read pages 48-51 of Wussing's The Genesis of the Abstract Group Concept.

For the week of September 2:

• If you want to be involved with this seminar, make sure you are on the mailing list (contact Jeremy Avigad at avigad@cmu.edu). Note that we will aim to reschedule for the weeks of Labor Day and Yom Kipur.
• If you are not sure whether you have the right mathematical background for this seminar, let us know, so we can make appropriate arrangements.
• Begin reading the translator's introduction to the Dedekind text.
• Read the Stein's "Logos, Logik, Logistike."
• Read the excerpt from Goldman's book.