The course introduces students to vectors, vector spaces, linear transformations, and systems of linear equations. Using systems of linear equations, the course explores mathematical properties of a vector such as linear independence, bases, and dimension. Linear transformations are studied as relationships between vector spaces leading to the Rank-Nullity Theorem. The course also introduces students to eigenspaces and diagonalization.

The Mathematics of Logic. This text aims to give an introduction to select topics in mathematical logic at a level appropriate for first year undergraduate mathematics students, especially those who intend to teach secondary school mathematics. The text serves introduction to proofs, set theory and number systems. Most students who take the course plan to teach, although there are a handful of students who will go on to graduate school or study applied mathematics or computer science. For these students the current text hopefully is still of interest, but the intent is not to provide a solid mathematical foundation for computer science. The text provided here is intended to be used in a class taught using problem oriented or inquiry-based methods. During face to face interactions, I will assign sections for reading after first introducing them in class by using a mix of group work and class discussion on a few interesting problems. The text is meant to consolidate what we discover in class and serve as a reference for students as they master the concepts and techniques covered in the course unit. None-the-less, every attempt has been made to make the text sufficient for self-study as well, in a way that hopefully mimics an inquiry-based classroom. The topics covered in this text were chosen to match the needs of mathematics students as a pre-requisite for higher level mathematics courses. The main areas of study are number systems, set theory, notion of a mathematical proof, functions, mathematical arguments, logic and Boolean algebra, in that order. Apart from induction, proof techniques are covered at the end of the chapter on arguments. Induction is covered at the beginning of the course to provide enough common language to discuss the logical flow of proofs. While this selection and order of topics might be currently optimal for Foundations of Mathematics, you should endeavor to read deeper into the specific topics to broaden your scope of knowledge. There are occasionally examples and exercises that rely on earlier material and these can be understood without too much additional study. A lot of examples and more than 200 exercises are provided in the text, and these should make the text more useful for students for self-study and group work. The lecture material will continue to be improved during class sessions, and additions suggested by other readers and users will be incorporated. Thus, I encourage you to send along any suggestions and comments as you have them.