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MATH 131-01, Mathematics Through Advanced Software, Fall 2010
Hamrick, Jeff
Hamrick, Jeff
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Syllabus, Curriculum, Academic departments, Text, Mathematics and Computer Science, Department of, 2010 Fall
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Abstract
A computer algebra system is a software program
that facilitates symbolic mathematics. Though the main purpose of a computer algebra
system is manipulation of mathematical expressions in symbolic form, over the past few decades
computer algebra systems have evolved to include formidable numerical and data analysis capabilities.
By “symbolic manipulation,” I mean simplification of certain expressions to some standard form
(with user-designated constraints often being possible). Computer algebra systems permit the
user to substitute symbols or numerical values in place of certain expressions, as well as to make
changes in the form of those expressions (partial and full factorization, representation as partial
fractions, rewriting trigonometric functions in terms of exponential functions, etc.). Many standard
tasks of calculus are well-handled by computer algebra systems: the symbolic computation of
limits, derivatives, integrals, and infinite sums; symbolic constrained and unconstrained local and
global optimization; and the calculation of Taylor expansions of analytic functions. Increasingly,
computer algebra systems are being used to power automated theorem-proving and theorem verification,
two tasks that are central components of the growing field of experimental mathematics.
Mathematica is just one example of a computer algebra system, but there are many others, including
Maple, Derive, Reduce, MuPAD, Magma, Axiom, and Maxima. Though proprietary (and,
arguably, expensive), Mathematica is the computer algebra system most frequently used at Rhodes
College (and, in fact, at many colleges, universities, corporations, and research laboratories). It was
originally conceived by Stephen Wolfram, a MacArthur fellow, physicist, and author of A New Kind
of Science, as a computer program called SMP (symbolic manipulation program). Mathematica
1.0, the successor to SMP, was released in 1988 and has improved incrementally with new major
releases in 1991, 1996, 1999, and 2003. With the release of Mathematica 6.0 in 2007, Mathematica
experienced enormous improvements in system stability, software documentation, dynamic interactivity,
and data computability. In 2009, Rhodes College upgraded its ten-year-old Mathematica
4.0 license to a new Mathematica 7.0 license. Today at Rhodes College, Mathematica is used for
undergraduate and faculty research, projects in upper-level courses in mathematics and the natural
sciences, and instruction in Math 115 (applied calculus).
Description
This syllabus was submitted to the Office of Academic Affairs by the course instructor. Uploaded by Archives RSA Josephine Hill.