# Great Moments in Mathematics: After 1650

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*Howard Eves*

MAA Press: An Imprint of the American Mathematical Society

What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is a fascinating collection of pivotal points in the historical development of mathematics...The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics.

—Herbert Fremont, The Mathematics Teacher

Eves is never less than tantalizing and usually inspiring...each 'great moment' has detailed exercises following it, as these have been carefully chosen to illustrate the depth of the ideas in question.

—C. W. Kilmister, The London Times, Higher Education Supplement

As is usual with Eves' work, the books are well written and entertaining. They give an historical background to many of the best known mathematical results, and, in addition, provide interesting pieces of information about the mathematicians involved. Eves includes relevant exercises at the end of each chapter. These are a good source of different, interesting problems, and when combined with the material in the chapter, could form the basis for a mathematical project...Eves' book provides an interesting, well-written, and enjoyable account. You won't be disappointed.

—David Parrott, The Australian Mathematics Teacher

#### Reviews & Endorsements

What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is fascinating collection of pivotal points in the historical development of mathematics. The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics.

-- Herbert Fremont in The Mathematics Teacher

As usual with Eves' work, the books are well written and entertainging. They give an historical background to many of the best known mathematical results, and in addition provide interesting pieces of information about the mathe mathematicians involved. Eves includes relevent exercises at the end of each chapte. These are a good source of different, interesting problems, and when combined with the matieral in the chapter could form the basis for a mathematical project...Eves' book provides an ineresting well-written, and enjoyable account. You won't be disappointed!

-- David Parrott The Australian Mathematics Teacher

# Table of Contents

## Great Moments in Mathematics: After 1650

- Front Cover Cover11
- Great Moments in Mathematics (After 1650) iii5
- Copyright Page iv6
- A Grateful Acknowledgment vi8
- Preface ix11
- Contents xi13
- Lecture 21. Order within disorder 115
- Lecture 22. Moving pictures versus still pictures 1125
- Lecture 23. Like opening and closing a door 2842
- Lecture 24. Power(ful) series 4054
- Lecture 25. Yea + Yea + Yea + Yea 5266
- Lecture 26. The liberation of geometry, I 6377
- Lecture 27. The liberation of geometry, II 7690
- Lecture 28. The liberation of algebra, I 88102
- Lecture 29. The liberation of algebra, II 98112
- Lecture 30. An important atomic structure 110124
- Lecture 31. A remarkable codification 119133
- Lecture 32. Pythagoras justified 132146
- Lecture 33. Digging deeper 146160
- Lecture 34. Beyond the finite 159173
- Lecture 35. Some remarkable definitions 171185
- Lecture 36. Some clarifying examples 181195
- Lecture 37. The third level 189 189203
- Lecture 38. Mathematics as a branch of theology 200214
- Lecture 39. The dream that came true 209223
- Lecture 40. Apology and regrets 221235
- Hnts for the Solution of Some of the Exercises 230244
- Index 251265