Mathematical Conversations - Selections from The Mathematical Intelligencer [Hardcover]

Robin Wilson (Author), Jeremy Gray (Author)

Book Description

ISBN-10: 0387986863 | ISBN-13: 978-0387986869 | Publication Date: October 12, 2000 | Edition: 1

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

Editorial Reviews

Review

"Popular mathematical expositions aim to render exciting, deep mathematics comprehensible to a wide audience (hard!). Since even professional mathematicians can expect to penetrate the technicalities of only a small fraction of mathematical breakthroughs, publications such as The Mathematical Intelligencer, the Bulletin of the American Mathematical Society, Sugaku, and LÉnseignement Mathmatique (Mathematique) address themselves to at least a wide audience of mathematicians. The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. The balance of topics reflects the broad spectrum of mathematical activity, and especially, great recent achievements (the Mordell conjecture, the Bieberbach conjecture, the Jones polynomial). Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. For example, every student of advanced calculus should read Felipe Acker's essay on Stokes's theorem and the mean value theorem. This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer. Upper-division undergraduates and up."
D.V. Feldman, University of New Hampshire in CHOICE Reviews, June 2001

Product Details

• Hardcover: 495 pages
• Publisher: Springer; 1 edition (October 12, 2000)
• Language: English
• ISBN-10: 0387986863
• ISBN-13: 978-0387986869
• Product Dimensions: 10 x 7.1 x 1.1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,532,833 in Books (See Top 100 in Books)

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3 of 11 people found the following review helpful:

3.0 out of 5 stars Narrenfreiheit, February 16, 2007

By 

Viktor Blasjo - See all my reviews
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This review is from: Mathematical Conversations - Selections from The Mathematical Intelligencer (Hardcover)

This collection has some pretty interesting articles. Everyone should read at least van Dalen's wonderful article on how the aged Hilbert felt it necessary to dismiss Brouwer as associate editor of the Annalen. Displays of loyalty and back-stabbing worthy of a Shakespeare drama ensued, and with no less literary quality, as we may illustrate by this Einstein quotation: "I consider [Brouwer], with all due respect for his mind, a psychopath ... I would say: 'Sire, give him the liberty of a jester [Narrenfreiheit]!' If you cannot bring yourself to this, because his behaviour gets too much on your nerves, for God's sake do what you have to do." Also interesting is Williams's article on the Baptistery of San Giovanni. The baptistery is octagonal. A classic construction of a regular octagon is this: start with a square; set the radius of the compass to half the diameter and draw the circles centred at the vertices; these circles cut the square at 8 points, the vertices of a regular octagon (as is easily proved using symmetry and Pythagoras's theorem). There is also an inner octagon on the baptistery pavement, which is constructed as follows. The octagon, and thus the square from which it was constructed, has a natural inner square. And the octagon walls naturally accommodate two squares: one connecting the midpoints of the slanted sides and one connecting the midpoints of the straight sides. The inner squares of these two squares make up the inner octagon. In another article Ibragimov surveys Lie's theory of differential equations. All the transformations of the x-y-plane that leave the essence of a differential equation (including boundary conditions, etc.) invariant make a group. Surely a solution will be invariant under this group, so we can solve the differential equation by finding the group and studying its invariants. Also, whatever invariants we can find of the most general groups of physical equations will be physical laws, and Kepler's laws of equal area and T^2/r^3 may be deduced in this manner.