Handouts

Handouts are available for xeroxing in the Philosophy Department's course drawer at the University of Pittsburgh, and under the mailboxes in the Philosophy Department's main office (Baker Hall 135) at Carnegie Mellon.

• An excerpt from John Conway's The Sensual (Quadratic) Form: the first lecture, "Can you see the values of 3x^2 + 6xy - 5y^2"
• Howard Stein's "Logos, Logic, and Logistike"
• An excerpt from Jay Goldman's The Queen of Mathematics: A historically motivated guide to number theory
• A two-page handout on philosophical themes, by Ken Manders
• Saunders Mac Lane's "Structures in Mathematics"
• An excerpt from Melvyn Nathanson's Elementary Methods in Mathematics. This is provided as a general reference for some of the topics we will discuss in number theory.
• An excerpt from Dirk Struik's A Source Book in Mathematics, 1200-1800. Only Euler's "Power residues" is required.
• An excerpt from Hans Wussing's The Genesis of the Abstract Group Concept. Only pages 48-51 are required.
• Israel Kleiner's "From Numbers to Rings: the early history of ring theory." Pitt and CMU students should be able to get this online from SpringerLink (e.g. search on "Israel Kleiner"). This is provided as background.
• An excerpt from Dedekind's "Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der höheren Kongruenzen." English translation: html, pdf, postscript, dvi.
• A handout on finite field extensions, algebraic integers, and the problem of factorization
• A collection of proofs of Fermat's little theorem and Wilson's theorem (gathered by Tyler Gibson).
• Harold Edwards, "Mathematical ideas, ideals, and ideology"
• Notes on Chapter 1 of Dedekind: pdf, postscript, dvi
• Short excerpts from Stewart and Tall, Algebraic Number Theory and Fermat's Last Theorem, and Hungerford, Algebra, on the structure of subgroups of a free abelian group, and Jay Goldman's The Queen of Mathematics. (These are optional supplements to Dedekind's Chapter 1.)
• Jeremy Gray, "The nineteenth-century revolution in mathematical ontology"
• Dedekind, "Continuity and the irrational numbers"
• Kronecker, "On the concept of number"
• Hilbert, "On the concept of number"
• Notes on Chapter 2 of Dedekind: pdf, postscript, dvi
• Notes on group actions
• Short excerpts from Lam, A first course on noncommutative rings, on division rings
• Weddernburn's 1905 paper, "A theorem on finite algebras." Pitt and CMU students should be able to get this online from JSTOR.
• An excerpt from Stewart and Tall, on the algebraic integers
• A short excerpt from Stillwell's Mathematics and its History, on the central idea of Galois theory
• Edwards, "Dedekind's inventions of ideals"
• Notes on Chapters 3 and 4 of Dedekind: pdf, postscript, dvi

The only assigned text, Dedekind's Theory of Algebraic Integers, is currently available at the Carnegie Mellon bookstore.