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Curricular Materials
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Textbooks
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`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.
