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Geometry

Authors: Gelfand, Israel M., Alekseyevskaya (Gelfand), Tatiana

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  • The final book in Israel Gelfand's internationally renowned correspondence course
  • Focuses on geometric constructions and includes over 400 figures in order to develop students' geometrical intuition
  • Contains a large number of exercises with answers, as well as problems suggested for further study
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-1-07-160299-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-1-07-160297-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format – the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class.
Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject.  Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and “move” them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certain operations and the instruments to perform these operations are available for drawing objects and figures on the plane. This structure corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries, all the while ensuring students have the necessary tools to follow along.  
Geometry is suitable for a large audience, which includes not only high school geometry students, but also teachers and anyone else interested in improving their geometrical vision and intuition, skills useful in many professions. Similarly, experienced mathematicians can appreciate the book’s unique way of presenting plane geometry in a simple form while adhering to its depth and rigor. 
“Gelfand was a great mathematician and also a great teacher. The book provides an atypical view of geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how they move in the plane, leading us to a better understanding of what coordinate geometry and axiomatic geometry seek to describe.”  
- Mark Saul, PhD, Executive Director, Julia Robinson Mathematics Festival
“The subject matter is presented as intuitive, interesting and fun.  No previous knowledge of the subject is required. Starting from the simplest concepts and by inculcating in the reader the use of visualization skills, [and] after reading the explanations and working through the examples, you will be able to confidently tackle the interesting problems posed.  I highly recommend the book to any person interested in this fascinating branch of mathematics.” 
- Ricardo Gorrin, a student of the Extended Gelfand Correspondence Program in Mathematics (EGCPM)

About the authors

Israel Gelfand (1913-2009) is often considered one of the greatest mathematicians of the Twentieth Century.  He published dozens of books and over 400 articles in a variety of mathematical fields, including group theory, representation theory, and functional analysis.  Gelfand was known internationally as an outstanding and passionate teacher, as well as for his famous seminars in mathematics and biology, which were attended by the most prominent specialists in the field.  He had a remarkable ability to adapt his presentation of difficult concepts so they would be easily understood by his audience, whether that was children or experienced professors. 
In 1964, he created the Correspondence School in Mathematics (ZMSH) in Moscow, and later on, the Gelfand Correspondence Program in Mathematics (GCPM) at Rutgers University, both of which made mathematics available to a broad range of students.  His goal was to pass on to students his belief that mathematics is simple, beautiful, and a part of human culture which anyone can learn and enjoy, just like literature, poetry, art, and music.
Tatiana Alekseyevskaya (Gelfand) graduated from the Department of Cybernetics and Applied Mathematics at Kiev State University in Ukraine.  She then received her PhD in Mathematics in Moscow for her research on systems of quasi-linear equations and related geometrical constructions describing isotachophoresis, a process used in biological studies of protein molecules.  She has extensive experience teaching mathematics to undergraduate students in both Russia and the United States, and worked closely with Israel Gelfand at Rutgers University, preparing assignments to be used in the GCPM.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-1-07-160299-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-1-07-160297-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry
Authors
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
The Authors
eBook ISBN
978-1-07-160299-7
DOI
10.1007/978-1-0716-0299-7
Softcover ISBN
978-1-07-160297-3
Edition Number
1
Number of Pages
XXI, 420
Number of Illustrations
467 b/w illustrations
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works are not included.