This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

Access also available here: http://abstract.ups.edu/contact.html

Table of Contents
Preliminaries
The Integers
Groups
Cyclic Groups
Permutation Groups
Cosets and Lagrange's Theorem
Introduction to Cryptography
Algebraic Coding Theory
Isomorphisms
Normal Subgroups and Factor Groups
Homomorphisms
Matrix Groups and Symmetry
The Structure of Groups
Group Actions
The Sylow Theorems
Rings
Polynomials
Integral Domains
Lattices and Boolean Algebras
Vector Spaces
Fields
Finite Fields
Galois Theory

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

Table of Contents
Systems of Linear Equations
Vectors
Matrices
Vector Spaces
Determinants
Eigenvalues
Linear Transformations
Representations
Preliminaries
Reference

Access also available here: http://linear.ups.edu/

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way.

Music Theory for the 21st–Century Classroom is an openly–licensed online college music theory textbook that is meant to take the student from the basics of reading and writing pitches and rhythms through twelve–tone technique and minimalism over the course of four semesters. This text differs from other music theory textbooks by focusing less on four–part (SATB) voiceleading and more on relating harmony to the phrase. Also, in traditional music theory textbooks, there is little emphasis on motivic analysis and analysis of melodic units smaller than the phrase. Whenever possible, examples from popular music and music from film and musical theater are included to illustrate melodic and harmonic concepts, usually within the context of the phrase. Practice exercises (with answers), homework exercises, and practice tests are included.

Music Theory for the 21st–Century Classroom is an openly–licensed online four–semester college music theory textbook. This text differs from other music theory textbooks by focusing less on four–part (SATB) voiceleading and more on relating harmony to the phrase. Also, in traditional music theory textbooks, there is little emphasis on motivic analysis and analysis of melodic units smaller than the phrase. In my opinion, this led to students having difficulty with creating melodies, since the training they are given is typically to write a “melody” in quarter notes in the soprano voice of part writing exercises. When the assignments in those texts ask students to do more than this, the majority of the students struggle to create a melody with continuity and with appropriate placement of harmonies within a phrase because the text had not prepared them to do so.