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Portal through mathematics : journey to advanced thinking

Author: O A Ivanov; Robert G Burns
Publisher: Washington, D.C. : Mathematical Association of America, [2017] ©2017
Series: Anneli Lax new mathematical library, 47.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"A Portal Through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this  Read more...
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Genre/Form: Problems and exercises
Problems, exercises, etc
Document Type: Book
All Authors / Contributors: O A Ivanov; Robert G Burns
ISBN: 9780883856512 0883856514
OCLC Number: 967820964
Notes: Includes index.
Description: xiv, 304 pages : illustrations ; 23 cm.
Contents: Surprising and easy. Surprising right triangles --
Surprisingly short solutions of geometric problems --
A natural assertion with a surprising proof --
Surprising answers --
A surprising connection between three sequences --
Algebra, calculus, and geometry: problems. Five problems and a function --
Five solutions of a routine problem --
Equations of the form f (x, y) = g (x, y) and their generalizations --
The generalized version of Viète's formula --
Multiple roots of polynomials --
Non-routine applications of the derivative --
Complex numbers, polynomials, and trigonometry --
Complex numbers and geometry --
Areas of triangles and quadrilaterals --
Constructions in solid geometry --
Inequalities --
Diophantine equations --
Combinatorial tales --
Integrals --
Algebra, calculus, and geometry: theory (a little way beyond high school mathematics). Functional equations off elementary functions --
Sequences given by recurrence relations --
The "golden ratio" of solving equations of the form f (x) = x --
Convex functions: inequalities and approximations --
Taylor's formula, Euler's formula, and a combinatorial problem --
Derivatives and vector-functions --
Polynomials and trigonometric relations --
Areas and volumes as functions of co-ordinates --
Values of trigonometric functions and sequences satisfying a certain recurrence relation --
Do there exist further "numbers" beyond complex numbers? --
Solutions to supplementary problems.
Series Title: Anneli Lax new mathematical library, 47.
Other Titles: Matematika 10-11.
Responsibility: Oleg A. Ivanov, St. Petersburg State University ; translated by Robert G. Burns.

Abstract:

A collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. The book is organised into 29  Read more...

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Primary Entity

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    schema:description ""A Portal Through Mathematics is a collection of puzzles and problems mostly on topics relating to secondary mathematics. The problems and topics are fresh and interesting and frequently surprising. One example: the puzzle that asks how much length must be added to a belt around the Earth's equator to raise it one foot has probably achieved old chestnut status. Ivanov, after explaining the surprising answer to this question, goes a step further and asks, if you grabbed that too long belt at some point and raised it as high as possible, how high would that be? The answer to that is more surprising than the classic puzzle's answer. The book is organized into 29 themes, each a topic from algebra, geometry or calculus and each launched from an opening puzzle or problem. There are excursions into number theory, solid geometry, physics and combinatorics. Always there is an emphasis on surprise and delight. And every theme begins at a level approachable with minimal background requirements. With well over 250 puzzles and problems, there is something here sure to appeal to everyone. A Portal Through Mathematics will be useful for prospective secondary teachers of mathematics and may be used (as a supplementary resource) in university courses in algebra, geometry, calculus, and discrete mathematics. It can also be used for professional development for teachers looking for inspiration. However, the intended audience is much broader. Every fan of mathematics will find enjoyment in it." -- Publisher's description"@en ;
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