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Publisher:

Oxford University Press

Publication Date:

2014

Number of Pages:

198

Format:

Hardcover

Price:

44.95

ISBN:

9780198701811

Category:

Anthology

[Reviewed by , on ]

Charles Ashbacher

08/18/2014

The title would be a bit more accurate if it were to be “50 Brief Visions of Mathematics”: the longest “vision” is six pages long, with most being only 2 to 4 pages. The breadth of coverage is extensive, from brief biographies of some of the major mathematicians of the twentieth century to humor, recreational mathematics, major technical problems and their mathematical solutions and some mathematical philosophy.

While most amateur and professional mathematicians will be familiar with the majority of topics, the editor is to be commended for including some articles describing people and problems that are not as well known. I was unfamiliar with Sir James Lighthill, for example, yet he is described as arguably the preeminent applied mathematician of his generation.

The authors and editors make the excellent decision to include equations when they are needed to explain the topic, yet even with that nearly all of the visions will be clear and understandable to readers with a high school mathematics background. Crisp and understandable diagrams are also used to great effectiveness. The four page entry “Conic Section Hide and Seek” is simultaneously the best simple introduction to how GPS satellites work and a response to the student that says, “Why do we need to study conic sections?” In clear language and diagrams the reader learns the basics of how GPS works and why three satellite signals are needed.

There are many uses for this book; one of the best that I can think of is in high school mathematics classes. The instructor could assign most of these visions as a homework reading and then use it as the basis for a class discussion that the students would find interesting. It beats the sawdust out of having to constantly answer the question, “Why do we need to learn this math stuff?” Or equivalently, “What’s the use of this?”

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing *The Journal of Recreational Mathematics*. In his spare time, he reads about these things and helps his daughter in her lawn care business.

1. What's the problem with mathematics?, *David Acheson*

2. The mathematics of messages,*Alan J. Aw*

3. Decathlon: The art of scoring points,*John D. Barrow*

4. Queen Dido and the mathematics of the extreme,*Greg Bason*

5. Can strings tie things together?,*David Berman*

6. Grooves and knuckleballs,*Ken Bray*

7. Pigs didn't fly but swine flu,*Ellen Brooks-Pollock and Ken Eames*

8. Bill Tutte: Unsung Bletchley hero,*Chris Budd*

9. What's the use of a quadratic equation?,*Chris Budd and Chris Sangwin*

10. Tony Hilton Royle Skyrme,*Alan Champneys*

11. The mathematics of obesity,*Carson C. Chow*

12. It's a small world really,*Tony Crilly*

13. How does mathematics help at a murder scene?,*Graham Divall*

14. Mathematics: The language of the universe,*Marcus du Sautoy*

15. The troublesome geometry of CAT scanning,*Richard Elwes*

16. The mathematics of sports gambling,*Alistair Fitt*

Pythagoras's Theorem: a2

17. A conversation with Freeman Dyson,*Marianne Freiberger and Rachel Thomas*

18. A glass of bubbly,*Paul Glendinning*

19. The influenza virus: It's all in the packaging,*Julia Gog*

20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty,*Derek Moulton and Alain Goriely*

21. Solving the Bristol bridge problem,*Thilo Gross*

22. All ravens are black: Puzzles and paradoxes in probability and statistics,*David Hand*

23. The Tower of Hanoi: Where mathematics meets psychology,*Andreas Hinz and Marianne Freiberger*

24. Career: A sample path,*Philip* *Holmes*

25. Sweets in the jar,*Steve Humble*

26. Mary Cartwright,*Lisa Jardine*

27. The fallibility of mathematics,*Adam Jasko*

28. Anecdotes of Dr Barrow,*Tom Korner*

29. Finding Apollo,*Adam Kucharski*

30. The golden ratio in astronomy and astrophysics,*Mario Livio*

31. The high-power hypar,*Peter Lynch*

32. This is not a carrot: Paraconsistent mathematics,*Maarten McKubre-Jordens*

33. The mystery of Groombridge Place,*Alexander Masters and Simon Norton*

Pythagoras's Theorem: b2

34. Mysterious number 6174,*Yutaka Nishiyama*

35. Percolating possibilities,*Colva Roney-Dougal & Vince Vatter*

36. Milestones on a non-Euclidean journey,*Caroline Series*

37. Simpson's rule,*Simon Singh*

38. Risking your life,*David Spiegelhalter*

39. Networks and illusions,*Ian Stewart*

40. Emmy Noether: Against the odds,*Danielle Stretch*

41. Of catastrophes and creodes: How maths benefits from collaboration with other fields,*Paul Taylor*

42. Conic section hide and seek,*Rachel Thomas*

43. Sir James Lighthill: A life in waves,*Ahmer Wadee*

44. Fail safe or fail dangerous,*Ahmer Wadee and Alan Champneys*

45. Leapfrogging into the future: How child's play is at the heart of weather and climate models,*Paul Williams*

46. Motorway mathematics,*Eddie Wilson*

47. The philosophy of applied mathematics,*Phil Wilson*

48. Mighty Morphogenesis,*Thomas Woolley*

49. Called to the barcode,*Andrew Wrigley*

50. Roughly fifty-fifty?,*Gunter Ziegler*

Pythagoras's Theorem: c2

2. The mathematics of messages,

3. Decathlon: The art of scoring points,

4. Queen Dido and the mathematics of the extreme,

5. Can strings tie things together?,

6. Grooves and knuckleballs,

7. Pigs didn't fly but swine flu,

8. Bill Tutte: Unsung Bletchley hero,

9. What's the use of a quadratic equation?,

10. Tony Hilton Royle Skyrme,

11. The mathematics of obesity,

12. It's a small world really,

13. How does mathematics help at a murder scene?,

14. Mathematics: The language of the universe,

15. The troublesome geometry of CAT scanning,

16. The mathematics of sports gambling,

Pythagoras's Theorem: a2

17. A conversation with Freeman Dyson,

18. A glass of bubbly,

19. The influenza virus: It's all in the packaging,

20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty,

21. Solving the Bristol bridge problem,

22. All ravens are black: Puzzles and paradoxes in probability and statistics,

23. The Tower of Hanoi: Where mathematics meets psychology,

24. Career: A sample path,

25. Sweets in the jar,

26. Mary Cartwright,

27. The fallibility of mathematics,

28. Anecdotes of Dr Barrow,

29. Finding Apollo,

30. The golden ratio in astronomy and astrophysics,

31. The high-power hypar,

32. This is not a carrot: Paraconsistent mathematics,

33. The mystery of Groombridge Place,

Pythagoras's Theorem: b2

34. Mysterious number 6174,

35. Percolating possibilities,

36. Milestones on a non-Euclidean journey,

37. Simpson's rule,

38. Risking your life,

39. Networks and illusions,

40. Emmy Noether: Against the odds,

41. Of catastrophes and creodes: How maths benefits from collaboration with other fields,

42. Conic section hide and seek,

43. Sir James Lighthill: A life in waves,

44. Fail safe or fail dangerous,

45. Leapfrogging into the future: How child's play is at the heart of weather and climate models,

46. Motorway mathematics,

47. The philosophy of applied mathematics,

48. Mighty Morphogenesis,

49. Called to the barcode,

50. Roughly fifty-fifty?,

Pythagoras's Theorem: c2

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