====================
Curricular Materials
====================

Textbooks
---------

`Abstract Algebra: Theory and Applications <http://abstract.ups.edu/beta/html/index.html/>`_ by Tom Judson
  :t:`Abstract Algebra: Theory and Applications` is an open-source textbook
  written by Tom Judson that is designed to teach the principles and
  theory of abstract algebra to college juniors and seniors in a
  rigorous manner. Its strengths include a wide range of exercises, both
  computational and theoretical, plus many nontrivial applications.

  The first half of the book presents group theory, through the Sylow
  theorems, with enough material for a semester-long course. The
  second-half is suitable for a second semester and presents rings,
  integral domains, Boolean algebras, vector spaces, and fields,
  concluding with Galois Theory.  
  `Book Website <http://abstract.ups.edu/>`_


`A First Course in Linear Algebra <http://linear.pugetsound.edu/html/fcla.html>`_ by Rob Beezer
  :t:`A First Course in Linear Algebra` is an introductory textbook
  designed for university sophomores and juniors. Typically such a
  student will have taken calculus, but this 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. Along the way, determinants and eigenvalues get fair
  time.  `Book Website <http://linear.pugetsound.edu/>`_

`Number Theory in Context <http://www.math-cs.gordon.edu/~kcrisman/mat338/>`_ by Karl-Dieter Crisman
  Introductory number theory course, in-progress.

`A Second Course in Linear Algebra <http://linear.ups.edu/scla/html/index.html>`_ by Rob Beezer
  Material for advanced undergraduates.

`Linear Algebra Workbook <http://theronhitchman.github.io/linear-algebra/course-materials/workbook/LinAlgWorkbook.html>`_ by Theron Hitchman
  Linear algebra material to support an inquiry-based learning approach.

`Elementary Number Theory: Primes, Congruences, and Secrets <http://modular.math.washington.edu/ent/>`_ by William Stein
  This is a textbook about classical elementary number theory and
  elliptic curves. The first part discusses elementary topics such as
  primes, factorization, continued fractions, and quadratic forms, in
  the context of cryptography, computation, and deep open research
  problems. The second part is about elliptic curves, their applications
  to algorithmic problems, and their connections with problems in number
  theory such as Fermats Last Theorem, the Congruent Number Problem, and
  the Conjecture of Birch and Swinnerton-Dyer. The intended audience of
  this book is an undergraduate with some familiarity with basic
  abstract algebra, e.g. rings, fields, and finite abelian groups.