The Method of Coordinates

Gelfand Correspondence Program in Mathematics

by Israel M. Gelfand

The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. As early as the 1960s, I. M. Gel'fand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this same content, unchanged by over thirty years of experience and mathematical development, are available in the present books to any student who is willing to read, to be stimulated and to learn. "The Method of Coordinates" is a way of transferring geometric images into formulas, a method for describing pictures by numbers and letters denoting constants and variables. It is fundamental to the study of calculus and other mathematical topics. Teachers of mathematics will find here a fresh understanding of the subject and a valuable path to the training of students in mathematical concepts and skills.

Genres: Mathematics, Reference, Geometry, Textbooks

84 pages, Paperback

First published January 1, 1967

About the author

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (Yiddish: ישראל געלפֿאַנד‎, Russian: Израиль Моисеевич Гельфанд ; 2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University.

Reviews

[Kate · Rating 5 out of 5]

I read the Dover edition of this book. It did take getting used to the cheaper printing and there were a few errors, but on the whole it was an acceptable publication.

I'm not sure how I would have fared without a bit of a math background. I think these books were originally written for high schoolers, but there's no way I could have waded through Method of Coordinates in high school. (I was not a particularly good math student, though.)

The first chunk of this book handled absolute value which was a challenge for me, but Gelfand gave superior explanations and problems to any other math text that I've seen cover absolute value. Next Gelfand covered coordinates in two dimensions and the distance formula. Gelfand spends a few pages on polar coordinates before he handles everything again in three dimensions and then finally in four dimensions. And then it's all over on page 69.

This is my second book in this series. I started with Trigonometry. These books really do give the student a deeper understanding of the material presented in high school and the problems give a much better preparation for Calculus.

[Bruno Oliveira · Rating 5 out of 5]

Uma obra prima que por aliar simplicidade e precisão deveria ser incorporada ao ensino básico. Merecedor de uma resenha mais detalhada que infelizmente agora não posso escrever.

[Maxim Perepelitsyn · Rating 5 out of 5]

Yet another great booklet from Gelfand, nice introduction to 4d space and cube.