Lectures on Fundamental Concepts of Algebra and Geometry

Lectures on Universal Algebra

1 Algebras In this first section we will consider some common features of familiar algebraic structures such as groups, rings, lattices, and boolean algebras to arrive at a definition of a general algebraic structure. Recall that a group G consists of a nonempty set G, along with a binary operation · : G → G, a unary operation −1 : G → G, and a constant 1 G such that • x · (y · z) = (x · y) · z...

Lectures on Commutative Algebra

Lectures on Applied Algebra

Some motivation: In this age of computers, algebra may have replaced calculus (analysis) as the most important part of mathematics. For example: 1) Error correcting codes are built into the CD player and the computer. Who do you call to correct errors? The algebraist, that’s who! 2) Digital signal processing (such as that involved in medical scanners, weather prediction, the search for oil) is ...

Lectures on Symplectic Geometry

Lectures on Geometry