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Portal through Mathematics: Journey to Advanced Thinking
 

Translated by Robert G. Burns

Portal through Mathematics
MAA Press: An Imprint of the American Mathematical Society
This title is not currently available
Portal through Mathematics
Click above image for expanded view
Portal through Mathematics: Journey to Advanced Thinking

Translated by Robert G. Burns

MAA Press: An Imprint of the American Mathematical Society
This title is not currently available
  • Book Details
     
     
    Anneli Lax New Mathematical Library
    Volume: 472017; 304 pp

    Reprinted edition available: NML/52

    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.

    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.

  • Table of Contents
     
     
    • Cover
    • Half Title Page
    • Copyright
    • Title Page
    • Contributors
    • Anneli Lax New Mathematical Library
    • Contents
    • Foreword
    • Preface for anAmerican Readership
    • Author's Preface
    • Part I Surprising and Easy
    • 1 Surprising right triangles
    • 2 Surprisingly short solutions of geometric problems
    • 3 A natural assertion with a surprising proof
    • 4 Surprising answers
    • 5 A surprising connection between three sequences
    • Part II Algebra, Calculus, and Geometry: problems
    • 6 Five problems and a function
    • 7 Five solutions of a routine problem
    • 8 Equations of the form f(x, y) = g(x, y) and their generalizations
    • 9 The generalized version of Viete's formula
    • 10 Multiple roots of polynomials
    • 11 Non-routine applications of the derivative
    • 12 Complex numbers, polynomials, and trigonometry
    • 13 Complex numbers and geometry
    • 14 Areas of triangles and quadrilaterals
    • 15 Constructions in solid geometry
    • 16 Inequalities
    • 17 Diophantine equations
    • 18 Combinatorial tales
    • 19 Integrals
    • Part III Algebra, Calculus, and Geometry: theory (a little way beyond high school mathematics)
    • 20 Functional equations of elementary functions
    • 21 Sequences given by recurrence relations
    • 22 The "golden ratio" or solving equations of the form f( x) = x
    • 23 Convex functions: inequalities and approximations
    • 24 Taylor's formula, Euler's formula, and a combinatorial problem
    • 25 Derivatives of vector-functions
    • 26 Polynomials and trigonometric relations
    • 27 Areas and volumes as functions of co-ordinates
    • 28 Values of trigonometric functions and sequences satisfying certain recurrence relation
    • 29 Do there exist further "numbers" beyond complex numbers?
    • Solutions of the supplementary problems
    • Index
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 472017; 304 pp

Reprinted edition available: NML/52

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.

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.

  • Cover
  • Half Title Page
  • Copyright
  • Title Page
  • Contributors
  • Anneli Lax New Mathematical Library
  • Contents
  • Foreword
  • Preface for anAmerican Readership
  • Author's Preface
  • Part I Surprising and Easy
  • 1 Surprising right triangles
  • 2 Surprisingly short solutions of geometric problems
  • 3 A natural assertion with a surprising proof
  • 4 Surprising answers
  • 5 A surprising connection between three sequences
  • Part II Algebra, Calculus, and Geometry: problems
  • 6 Five problems and a function
  • 7 Five solutions of a routine problem
  • 8 Equations of the form f(x, y) = g(x, y) and their generalizations
  • 9 The generalized version of Viete's formula
  • 10 Multiple roots of polynomials
  • 11 Non-routine applications of the derivative
  • 12 Complex numbers, polynomials, and trigonometry
  • 13 Complex numbers and geometry
  • 14 Areas of triangles and quadrilaterals
  • 15 Constructions in solid geometry
  • 16 Inequalities
  • 17 Diophantine equations
  • 18 Combinatorial tales
  • 19 Integrals
  • Part III Algebra, Calculus, and Geometry: theory (a little way beyond high school mathematics)
  • 20 Functional equations of elementary functions
  • 21 Sequences given by recurrence relations
  • 22 The "golden ratio" or solving equations of the form f( x) = x
  • 23 Convex functions: inequalities and approximations
  • 24 Taylor's formula, Euler's formula, and a combinatorial problem
  • 25 Derivatives of vector-functions
  • 26 Polynomials and trigonometric relations
  • 27 Areas and volumes as functions of co-ordinates
  • 28 Values of trigonometric functions and sequences satisfying certain recurrence relation
  • 29 Do there exist further "numbers" beyond complex numbers?
  • Solutions of the supplementary problems
  • Index
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.