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It is often said that mathematics and music go together, and that people with a special aptitude for mathematics often have similar gifts in music. Some music is very profound, and listeners find that there is far more in it than they appreciated at a first hearing. A similar point can be made about an understanding of mathematics.
This book introduces the reader to various topics in mathematics and is intended for precocious high school students and college students just beginning their study of mathematics. The topics discussed in this book include a variety of results in number theory involving squares, and also complex numbers, early algebraic ideas such as the Euclidean algorithm, geometrical constructions created by the Greeks, and more recent topics such as group theory.
About the author
George Phillips is Professor of Mathematics at St. Andrews University, Scotland. He is the author of two previous books also published by Springer, Two Millenia of Mathematics (2000), and Interpolation and Approximation by Polynomials (2003).
Summary
This book introduces the reader to various topics in mathematics and is intended for precocious high school students and college students just beginning their study of mathematics. Topics include the Euclidean algorithm, geometrical constructions created by the Greeks, and ancient Babylonian and Chinese proofs of the Pythagorean theorem.
Additional text
From the reviews:
"The title of this book is an aphorism known by many concerned with the education of mathematicians, at many different levels. It is appropriate at all levels from primary school children ‘investigating’ to postgraduates generating and attempting to solve new problems. … The suggested audience is senior students in high school, students just beginning mathematics at university, and general readers no longer formally studying mathematics … . The content and style of the book matches this quite well and realistically." (John Baylis, The Mathematical Gazette, Vol. 91 (520), 2007)
"In this book, the author develops some (easy) mathematical concepts, which are suitable for high school students or non-mathematicians disciplines … . Each of the seven chapters is an invitation to learn new mathematical concepts. … The book is carefully written and a pleasure to read. … It is … an excellent prize to honor high school students for some extraordinary work in mathematics." (Alexander Pott, Zentralblatt MATH, Vol. 1140, 2008)
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From the reviews:
"The title of this book is an aphorism known by many concerned with the education of mathematicians, at many different levels. It is appropriate at all levels from primary school children 'investigating' to postgraduates generating and attempting to solve new problems. ... The suggested audience is senior students in high school, students just beginning mathematics at university, and general readers no longer formally studying mathematics ... . The content and style of the book matches this quite well and realistically." (John Baylis, The Mathematical Gazette, Vol. 91 (520), 2007)
"In this book, the author develops some (easy) mathematical concepts, which are suitable for high school students or non-mathematicians disciplines ... . Each of the seven chapters is an invitation to learn new mathematical concepts. ... The book is carefully written and a pleasure to read. ... It is ... an excellent prize to honor high school students for some extraordinary work in mathematics." (Alexander Pott, Zentralblatt MATH, Vol. 1140, 2008)
