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
practising 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 generalisations
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.
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