Pre-Calculus, Calculus, and Beyond

Pre-Calculus, Calculus, and Beyond
Author: Hung-Hsi Wu
Publisher: American Mathematical Soc.
Total Pages: 417
Release: 2020-10-26
Genre: Education
ISBN: 147045677X

This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. This volume distinguishes itself from others of the same genre in getting the mathematics right. In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles. It also provides details for extending the domain of definition of sine and cosine to all real numbers. It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians. In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs. An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator. This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.

Books In Print 2004-2005

Books In Print 2004-2005
Author: Ed Bowker Staff
Publisher: R. R. Bowker
Total Pages: 3274
Release: 2004
Genre: Reference
ISBN: 9780835246422

Joyce and Geometry

Joyce and Geometry
Author: Ciaran McMorran
Publisher: University Press of Florida
Total Pages: 195
Release: 2020-01-15
Genre: Literary Criticism
ISBN: 0813057396

In a paradigm shift away from classical understandings of geometry, nineteenth-century mathematicians developed new systems that featured surprising concepts such as the idea that parallel lines can curve and intersect. Providing evidence to confirm much that has largely been speculation, Joyce and Geometry reveals the full extent to which the modernist writer James Joyce was influenced by the radical theories of non-Euclidean geometry. Through close readings of Ulysses, Finnegans Wake, and Joyce’s notebooks, Ciaran McMorran demonstrates that Joyce’s experiments with nonlinearity stem from a fascination with these new mathematical concepts. He highlights the maze-like patterns traced by Joyce’s characters as they wander Dublin’s streets; he explores recurring motifs such as the topography of the Earth’s curved surface and time as the fourth dimension of space; and he investigates in detail the enormous influence of Giordano Bruno, Henri Poincaré, and other writers who were critical of the Euclidean tradition. Arguing that Joyce’s obsession with measuring and mapping space throughout his works encapsulates a modern crisis between geometric and linguistic modes of representation, McMorran delves into a major theme in Joyce’s work that has not been fully explored until now. A volume in the Florida James Joyce Series, edited by Sebastian D. G. Knowles

Modern Mathematics

Modern Mathematics
Author: Dirk De Bock
Publisher: Springer Nature
Total Pages: 615
Release: 2023-03-08
Genre: Education
ISBN: 3031111664

The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels—kindergarten to college graduate—in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17, some of the effects became entrenched. This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) “Nicolas Bourbaki.” In the United States, there emerged, during the 1950s various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching “Sputnik,” the first satellite. Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final “epilogue” chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends.