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Five-Minute Mathematics

Ehrhard Behrends Freie Universität Berlin, Berlin, Germany
Translated by David Kramer
Available Formats:
Softcover ISBN: 978-0-8218-4348-2
Product Code: MBK/53
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $32.80 Electronic ISBN: 978-1-4704-2484-8 Product Code: MBK/53.E List Price:$38.00
MAA Member Price: $34.20 AMS Member Price:$30.40
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $61.50 MAA Member Price:$55.35
AMS Member Price: $49.20 Click above image for expanded view Five-Minute Mathematics Ehrhard Behrends Freie Universität Berlin, Berlin, Germany Translated by David Kramer Available Formats:  Softcover ISBN: 978-0-8218-4348-2 Product Code: MBK/53  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$32.80
 Electronic ISBN: 978-1-4704-2484-8 Product Code: MBK/53.E
 List Price: $38.00 MAA Member Price:$34.20 AMS Member Price: $30.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$61.50 MAA Member Price: $55.35 AMS Member Price:$49.20
• Book Details

2008; 380 pp
MSC: Primary 00;

How much math can you cover in five minutes? Quite a bit, if you have a good guide. In this collection of one hundred short essays, Ehrhard Behrends offers a tour through contemporary and everyday mathematics. The topics range from pure mathematics to applications of mathematics to observations about the mathematics that surrounds us in daily life. Here, we read about the parable of grains of rice on a chessboard, the mathematics of the lottery, music and mathematics, intriguing paradoxes, the concept of infinity, the Poincaré conjecture, quantum computers, and plenty more.

Anyone who regularly reads the science section of a newspaper or magazine will find much to enjoy in Five-Minute Mathematics. Behrends makes very few assumptions about his readers, other than general curiosity and some familiarity with high school mathematics.

The vignettes originally appeared in the author's newspaper column. They have been extensively revised and expanded, and provided with attractive illustrations and photographs.

Undergraduates, graduate students, and research mathematicians interested in general topics in mathematics; the mathematics of everyday life.

This item is also available as part of a set:

• Chapters
• Chapter 1. You can’t beat the odds
• Chapter 2. Magical mathematics: The integers
• Chapter 3. How old is the captain?
• Chapter 4. Vertiginously large prime numbers
• Chapter 5. Loss plus loss equals win
• Chapter 6. When it comes to large numbers, intuition fails
• Chapter 7. The key for encryption is the telephone book
• Chapter 8. The village barber who shaves himself
• Chapter 9. Quit while you’re ahead?
• Chapter 10. Can a monkey create great literature?
• Chapter 11. The birthday paradox
• Chapter 12. Horror vacui
• Chapter 13. Sufficient difficulties with the logic of mathematics are in fact a necessity
• Chapter 14. To change or not to change? The Monty Hall problem
• Chapter 15. In Hilbert’s Hotel there is always a vacancy
• Chapter 16. That fascinating number pi
• Chapter 17. How random events become calculable quantities
• Chapter 18. A one-million-dollar prize: How are the prime numbers distributed?
• Chapter 19. The five-dimensional cake
• Chapter 20. One night stand
• Chapter 21. Fly me to the Moon
• Chapter 22. Using residues
• Chapter 23. Top secret!
• Chapter 24. Magical mathematics: Order amidst chaos
• Chapter 25. How does one approach genius?
• Chapter 26. On semitones and twelfth roots
• Chapter 27. Why am I always standing in the wrong line?
• Chapter 28. Zero: An undeservedly underrated number
• Chapter 29. I love to count!
• Chapter 30. Genius autodidact: The Indian mathematician Ramanujan
• Chapter 31. I hate mathematics because...
• Chapter 32. The traveling salesman: A modern odyssey
• Chapter 33. Squaring the circle
• Chapter 34. A step into the infinite
• Chapter 35. Mathematics in your CD player
• Chapter 36. The logarithm: A dying breed
• Chapter 37. Prizeworthy mathematics
• Chapter 38. Why axioms of all things?
• Chapter 39. Proof by computer?
• Chapter 40. The lottery: The small prizes
• Chapter 41. Formulas = concentrated thought
• Chapter 42. Endless growth
• Chapter 43. How do quanta compute?
• Chapter 44. Extremes!
• Chapter 45. Infinitely small?
• Chapter 46. Mathematical observations at the fire department
• Chapter 47. The first mathematical proof is 2,500 years old
• Chapter 48. There is transcendence in mathematics, though it has nothing to do with mysticism
• Chapter 49. Is every even number the sum of two primes?
• Chapter 50. Why we invert conditional probabilities incorrectly
• Chapter 51. Millionaire or billionaire?
• Chapter 52. Mathematics and chess
• Chapter 53. “The book of nature is written in the language of mathematics”
• Chapter 54. The search for Mersenne primes
• Chapter 55. Berlin, eighteenth century: A beatuful formula is discovered
• Chapter 56. The first really complicated number
• Chapter 57. P = NP: In mathematics, is luck sometimes unnecessary?
• Chapter 58. Happy 32nd birthday!
• Chapter 59. Buffon’s needle
• Chapter 60. Running hot and cold: Controlled cooling solves optimization problems
• Chapter 61. Who didn’t pay?
• Chapter 62. What can statistics tell us?
• Chapter 63. Arbitrage
• Chapter 64. Farewell to risk: Options
• Chapter 65. Is mathematics a reflection of the world?
• Chapter 66. Mathematics that you can hear
• Chapter 67. Chance as composer
• Chapter 68. Do dice have a guilty conscience?
• Chapter 69. Strawberry ice cream can kill you!
• Chapter 70. Prosperity for all
• Chapter 71. No risk, thank you!
• Chapter 72. A Nobel Prize in mathematics?
• Chapter 73. Chance as reckoner: Monte Carlo methods
• Chapter 74. Fuzzy logic
• Chapter 75. Secret messages in the Bible?
• Chapter 76. How knotted can a knot be?
• Chapter 77. How much mathematics does a person need?
• Chapter 78. Big, bigger, biggest
• Chapter 79. It is probably correct
• Chapter 80. Is the world a crooked place?
• Chapter 81. Is there a mathematical bureau of standards?
• Chapter 82. The butterfly that fluttered by
• Chapter 83. Guaranteed to make you rich
• Chapter 84. Don’t trust anyone over thirty
• Chapter 85. Equality in mathematics
• Chapter 86. Magical invariants
• Chapter 87. Mathematics goes to the movies
• Chapter 88. The lazy eight: Infinity
• Chapter 89. Books need bigger margins!
• Chapter 90. Visualizing internal organs with mathematics
• Chapter 91. A brain in the computer
• Chapter 92. Cogito, ergo sum
• Chapter 93. Does the world have a hole?
• Chapter 94. Complex numbers are not so complex as their name suggests
• Chapter 95. M. C. Escher and infinity
• Chapter 96. A one at the beginning is much more likely than a two
• Chapter 97. The Leipzig town hall and the sunflower
• Chapter 98. Information optimally packaged
• Chapter 99. Four colors suffice!
• Chapter 100. Mathematics makes billionaires

• Reviews

• This book, a breath of fresh air, makes mathematics a delight and fun for almost any reader. ... I highly recommend this book for any teacher looking for a way to get students interested in mathematics—again or for the first time.

Joyce Fischer, for NCTM's "Mathematics Teacher"
• The book has remarkable breadth. It covers probability theory, number theory, the history of mathematics, finance, computer science, topology, music, famous numbers, and on and on. ... This book is sure to be enjoyed by everyone who loves mathematics. With chapters 3–5 pages long, it is the perfect book to read before bedtime, on the beach, or on the train or bus while commuting to work or school.

MAA Reviews
• The columns have been carefully revised and extra material has been added when this seemed appropriate. The columns are a delight to read. They range very widely through mathematics. He has certainly raised public awareness with these fine columns, which are clearly and engagingly written, and he does not shy away from difficult topics whenhe can find a way to explain them at an appropriate level.

• One of the main achievements of this book, in the reviewer's opinion, is the fact that sophisticated mathematical ideas are presented in an accessible manner. The applications of mathematics are given much consideration, but the reader will also gain an appreciation for the beauty and power of the subject and the enjoyment that can be had from engaging with it. This book is aimed at the general reader and would be an excellent resource for mathematics teachers or anyone engaged in communicating mathematics to the general public.

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2008; 380 pp
MSC: Primary 00;

How much math can you cover in five minutes? Quite a bit, if you have a good guide. In this collection of one hundred short essays, Ehrhard Behrends offers a tour through contemporary and everyday mathematics. The topics range from pure mathematics to applications of mathematics to observations about the mathematics that surrounds us in daily life. Here, we read about the parable of grains of rice on a chessboard, the mathematics of the lottery, music and mathematics, intriguing paradoxes, the concept of infinity, the Poincaré conjecture, quantum computers, and plenty more.

Anyone who regularly reads the science section of a newspaper or magazine will find much to enjoy in Five-Minute Mathematics. Behrends makes very few assumptions about his readers, other than general curiosity and some familiarity with high school mathematics.

The vignettes originally appeared in the author's newspaper column. They have been extensively revised and expanded, and provided with attractive illustrations and photographs.

Undergraduates, graduate students, and research mathematicians interested in general topics in mathematics; the mathematics of everyday life.

This item is also available as part of a set:
• Chapters
• Chapter 1. You can’t beat the odds
• Chapter 2. Magical mathematics: The integers
• Chapter 3. How old is the captain?
• Chapter 4. Vertiginously large prime numbers
• Chapter 5. Loss plus loss equals win
• Chapter 6. When it comes to large numbers, intuition fails
• Chapter 7. The key for encryption is the telephone book
• Chapter 8. The village barber who shaves himself
• Chapter 9. Quit while you’re ahead?
• Chapter 10. Can a monkey create great literature?
• Chapter 11. The birthday paradox
• Chapter 12. Horror vacui
• Chapter 13. Sufficient difficulties with the logic of mathematics are in fact a necessity
• Chapter 14. To change or not to change? The Monty Hall problem
• Chapter 15. In Hilbert’s Hotel there is always a vacancy
• Chapter 16. That fascinating number pi
• Chapter 17. How random events become calculable quantities
• Chapter 18. A one-million-dollar prize: How are the prime numbers distributed?
• Chapter 19. The five-dimensional cake
• Chapter 20. One night stand
• Chapter 21. Fly me to the Moon
• Chapter 22. Using residues
• Chapter 23. Top secret!
• Chapter 24. Magical mathematics: Order amidst chaos
• Chapter 25. How does one approach genius?
• Chapter 26. On semitones and twelfth roots
• Chapter 27. Why am I always standing in the wrong line?
• Chapter 28. Zero: An undeservedly underrated number
• Chapter 29. I love to count!
• Chapter 30. Genius autodidact: The Indian mathematician Ramanujan
• Chapter 31. I hate mathematics because...
• Chapter 32. The traveling salesman: A modern odyssey
• Chapter 33. Squaring the circle
• Chapter 34. A step into the infinite
• Chapter 35. Mathematics in your CD player
• Chapter 36. The logarithm: A dying breed
• Chapter 37. Prizeworthy mathematics
• Chapter 38. Why axioms of all things?
• Chapter 39. Proof by computer?
• Chapter 40. The lottery: The small prizes
• Chapter 41. Formulas = concentrated thought
• Chapter 42. Endless growth
• Chapter 43. How do quanta compute?
• Chapter 44. Extremes!
• Chapter 45. Infinitely small?
• Chapter 46. Mathematical observations at the fire department
• Chapter 47. The first mathematical proof is 2,500 years old
• Chapter 48. There is transcendence in mathematics, though it has nothing to do with mysticism
• Chapter 49. Is every even number the sum of two primes?
• Chapter 50. Why we invert conditional probabilities incorrectly
• Chapter 51. Millionaire or billionaire?
• Chapter 52. Mathematics and chess
• Chapter 53. “The book of nature is written in the language of mathematics”
• Chapter 54. The search for Mersenne primes
• Chapter 55. Berlin, eighteenth century: A beatuful formula is discovered
• Chapter 56. The first really complicated number
• Chapter 57. P = NP: In mathematics, is luck sometimes unnecessary?
• Chapter 58. Happy 32nd birthday!
• Chapter 59. Buffon’s needle
• Chapter 60. Running hot and cold: Controlled cooling solves optimization problems
• Chapter 61. Who didn’t pay?
• Chapter 62. What can statistics tell us?
• Chapter 63. Arbitrage
• Chapter 64. Farewell to risk: Options
• Chapter 65. Is mathematics a reflection of the world?
• Chapter 66. Mathematics that you can hear
• Chapter 67. Chance as composer
• Chapter 68. Do dice have a guilty conscience?
• Chapter 69. Strawberry ice cream can kill you!
• Chapter 70. Prosperity for all
• Chapter 71. No risk, thank you!
• Chapter 72. A Nobel Prize in mathematics?
• Chapter 73. Chance as reckoner: Monte Carlo methods
• Chapter 74. Fuzzy logic
• Chapter 75. Secret messages in the Bible?
• Chapter 76. How knotted can a knot be?
• Chapter 77. How much mathematics does a person need?
• Chapter 78. Big, bigger, biggest
• Chapter 79. It is probably correct
• Chapter 80. Is the world a crooked place?
• Chapter 81. Is there a mathematical bureau of standards?
• Chapter 82. The butterfly that fluttered by
• Chapter 83. Guaranteed to make you rich
• Chapter 84. Don’t trust anyone over thirty
• Chapter 85. Equality in mathematics
• Chapter 86. Magical invariants
• Chapter 87. Mathematics goes to the movies
• Chapter 88. The lazy eight: Infinity
• Chapter 89. Books need bigger margins!
• Chapter 90. Visualizing internal organs with mathematics
• Chapter 91. A brain in the computer
• Chapter 92. Cogito, ergo sum
• Chapter 93. Does the world have a hole?
• Chapter 94. Complex numbers are not so complex as their name suggests
• Chapter 95. M. C. Escher and infinity
• Chapter 96. A one at the beginning is much more likely than a two
• Chapter 97. The Leipzig town hall and the sunflower
• Chapter 98. Information optimally packaged
• Chapter 99. Four colors suffice!
• Chapter 100. Mathematics makes billionaires
• This book, a breath of fresh air, makes mathematics a delight and fun for almost any reader. ... I highly recommend this book for any teacher looking for a way to get students interested in mathematics—again or for the first time.

Joyce Fischer, for NCTM's "Mathematics Teacher"
• The book has remarkable breadth. It covers probability theory, number theory, the history of mathematics, finance, computer science, topology, music, famous numbers, and on and on. ... This book is sure to be enjoyed by everyone who loves mathematics. With chapters 3–5 pages long, it is the perfect book to read before bedtime, on the beach, or on the train or bus while commuting to work or school.

MAA Reviews
• The columns have been carefully revised and extra material has been added when this seemed appropriate. The columns are a delight to read. They range very widely through mathematics. He has certainly raised public awareness with these fine columns, which are clearly and engagingly written, and he does not shy away from difficult topics whenhe can find a way to explain them at an appropriate level.