This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. This is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra.
There are many books on graph theory. Prof. Oporowski recommends the references listed above, but they are not absolutely necessary. He will present the lectures with his own notes, which will be available for download, and which should make good study material. However, the amount of detail in the lecture notes is less than that of either of the mentioned books. If your interest in the subject is anything more than superficial, you would be well advised to get at least one of those books - especially the first one listed.
This is an introduction to algebraic topology. In algebraic topology, topological questions are related to algebraic questions. Sometimes this allows one to answer the topological questions using algebra. We will discuss homotopy, homotopy type, the fundamental group, the Jordan curve theorem, Brouwer fixed point theorem, covering spaces, and time permitting elementary aspects of higher homotopy groups. We will study chapters 0 and 1 and perhaps the elementary parts of chapter 4. Munkres's Topology will be an alternative source.
This course is an introduction to algebraic topology, with an emphasis on homology and cohomology. The goal will be to cover as much of the material in chapters 2 and 3 of Hatcher's book as time permits. This includes simplicial, singular and cellular homology, excision, the Mayer-Vietoris sequence, cohomology groups, the Universal Coefficient Theorem, the cup product, and Poincare duality. 153554b96e