id: 06193968
dt: b
an: 2014a.00668
au: Cuoco, Al; Rotman, Joseph J.
ti: Learning modern algebra. From early attempts to prove Fermat’s last
theorem.
so: MAA Textbooks. Washington, DC: The Mathematical Association of America
(MAA) (ISBN 978-1-939512-01-7/hbk; 978-1-61444-612-5/ebook). xix,
459~p. (2013).
py: 2013
pu: Washington, DC: The Mathematical Association of America (MAA)
la: EN
cc: H19 B50
ut: teacher education; teacher learning processes; comprehensive work in
algebra; methodology of mathematics; didactics; number theory; field
theory and polynomials; cyclotomic integers; Fermat’s last theorem
ci:
li:
ab: This book is destined for college students in the U.S. who intend to teach
mathematics in high school. The reviewer finds it even more apt as a
text for algebra courses. Special features in the book are side-notes
given and printed prominently at the margins of the pages, like: How to
think about it, Historical notes, Etymology of notions and words. One
finds chapters on: Early number theory (Greek: Euclid, Diophantus,
trigonometry, integration), Induction, Renaissance (classical formulae,
complex numbers, roots, powers, lattice point triangles), Modular
arithmetic (codes, rings, patterns in decimal expansions), Abstract
algebra, Arithmetic of polynomials, Quotients, fields, and classical
problems (ruler-compass constructions), Cyclotomic integers (Gauss,
Eisenstein, Fermat’s last theorem for exponent 3), Epilog references
(Abel, Galois, solvability by radicals, groups, Wiles and Fermat’s
last theorem, elliptic integrals, elliptic curves), and Appendices on
basic linear algebra and a cyclotomic integer calculator. The above
summing up, is by far not exhaustive. The reviewer considers the book a
refreshing reading among the vast amount of books dealing with similar
topics.
rv: Robert W. van der Waall (Huizen)