Unless otherwise specified, all readings are in RosenBook. As always, the future is uncertain, so you should take parts of the schedule that haven't happened yet with a grain of salt.
1. Detailed schedule
SetTheory. Naive set theory vs axiomatic set theory. Elements and subsets. Russell's paradox and the good parts of ZFC. Readings: §2.1.
More SetTheory. Operations on sets (∪, ∩, set difference, Cartesian product, etc.) and proving facts about sets. Readings: §2.2.
Functions. Readings: §2.3.
Still more GeneratingFunctions: how operations on sets of objects of differing weights translate to operations on generating functions. Extracting coefficients by differentiating. Extracting coefficients using the binomial theorem.
More GeneratingFunctions: extracting coefficients by partial fraction expansion and the cover-up method. Solving ugly recurrences.
Last of GeneratingFunctions: partial fraction expansion with repeated roots, Catalan numbers.
ProbabilityTheory basics: interpretations of probability, events, axioms, independence. Readings: §§6.1–6.2.
More ProbabilityTheory: inclusion-exclusion, conditional probabilities. Readings: §6.3.
RandomVariables and expectations. Readings: §6.4.
More RandomVariables: conditional expectations and applications.
Still more RandomVariables: Markov's inequality, variance, Chebyshev's inequality.
The midterm exam was given Wednesday, 2007-10-24, at the usual class time in room SCL 160. It was be a closed-book, cumulative exam covering all material discussed in lecture prior to the test date.
More RandomVariables: Computing variance of a sum; covariance.
Start of LinearAlgebra: matrices, matrix operations. Readings: §3.8.
More LinearAlgebra: inverting matrices.
More LinearAlgebra: vectors and vector operations. Dot-products. Mx equivalent to dot-product with rows or linear combination of columns.
Last of LinearAlgebra: linear combinations, linear independence, bases, and orthogonal projection.
Start of Relations: basic properties, equivalence relations. Readings: §8.1, §§8.3–8.5.
More Relations: partial orders. Readings: §8.6. See also footnote on definition for partial order in Relations notes. The completely tangential joke about "How to Draw like Leonardo Da Vinci" is originally due to Ben_Edlund, from a page that showed "How to Draw The_Tick" and advertised a sequel called "How to Draw like Albrecht_Dürer."
More Relations: More partial orders: maximum, maximal, minimal, and minimum elements; total orders, well orders, and lattices. Closure operations.
More NumberTheory: The Fundamental Theorem of Arithmetic; Euler's theorem and totients. Readings: §3.7.
More AlgebraicStructures: subalgebras, homomorphisms, products, congruences and quotients (i.e. subsets, functions, products, equivalence relations, and quotients that respect the algebra operations).
Start of GraphTheory: basic definitions; some standard graphs; graph homomorphisms. Readings: §§9.1—9.3.
More GraphTheory: paths, cycles, connectivity, and trees. Readings: §9.4, §10.1.
The final exam was given Thursday, December 20th, 2007, starting at 9:00 a.m., in AKW 200. It was a closed-book test covering all material discussed during the semester.