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    <p>The text that you want here is <em>Abstract Algebra, A Computational Approach</em> by Chuck Sims. The author will recommend that you use the <a href="http://en.wikipedia.org/wiki/APL_(programming_language)" rel="noreferrer">APL</a> programming language. The book is out of print, but you can probably find it in your library.</p> <p>There is also the <a href="http://en.wikipedia.org/wiki/GAP_computer_algebra_system" rel="noreferrer">GAP Computer Algebra System</a> which is fun to use for group theory.</p> <p>Advanced resources:</p> <p><a href="http://en.wikipedia.org/wiki/Magma_computer_algebra_system" rel="noreferrer">Magma</a>: fairly sophisticated <a href="http://en.wikipedia.org/wiki/Computer_algebra_system" rel="noreferrer">CAS</a> that can handle a wide range of concepts from abstract algebra.<br> <a href="http://en.wikipedia.org/wiki/Macaulay_computer_algebra_system" rel="noreferrer">Macaulay 2</a>: used to study polynomial rings, especially <a href="http://en.wikipedia.org/wiki/Gr%F6bner_basis" rel="noreferrer">Gröbner bases</a>.<br> <a href="http://en.wikipedia.org/wiki/SINGULAR" rel="noreferrer">SINGULAR</a>: used to study polynomial rings.</p> <p>A key fact in studying group theory is that every group is isomorphic to a <a href="http://en.wikipedia.org/wiki/Permutation_group" rel="noreferrer">permutation group</a> by the regular action. Thus, the key to understanding group theory is to understand the permutation groups.</p> <p>Finally, any language that supports defining your own objects and defining a binary operator on two instances of the object will support learning the theory through programming.</p>
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    1. POAbstract algebra and Programming
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    1. USSam Hasler
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    1. COI just stumbled upon "Abstract Algebra, A Computational Approach" in the library today... can you recommend an APL implementation for the exercises?
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      1. USJørgen Fogh
    2. COThe NARS2000 implementation is great; I've used it successfully under Linux (it's runs on other systems too). I've heard (but have not experienced) that the VisualAPL (.NET implementation of APL) is fantastic.
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