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Much of modern algebra arose from attempts to prove Fermat's Last Theorem, which in turn has its roots in Diophantus' classification of Pythagorean triples. This book, designed for prospective and practicing mathematics teachers, makes explicit connections between the ideas of abstract algebra and the mathematics taught at high school level. Algebraic concepts are presented in historical order, and the book also demonstrates how other important themes in algebra arose from questions related to teaching. The focus is on number theory, polynomials, and commutative rings. Group theory is introduced near the end of the text to explain why generalizations of the quadratic formula do not exist for polynomials of high degree, allowing the reader to appreciate the work of Galois and Abel. Results are motivated with specific examples, and applications range from the theory of repeating decimals to the use of imaginary quadratic fields to construct problems with rational solutions.

Publisher:
Mathematical Association of America, [Washington, D.C.] : 2013

ISBN:
9781614446125

1614446121

9781939512017

1614446121

9781939512017

Branch Call Number:
REM

Characteristics:
1 online resource (xix, 459 p.) : ill

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