Yearning for the Impossible The Surprising Truths of Mathematics pdf
Yearning for the Impossible The Surprising Truths of Mathematics pdf : Pages 329
By John Stillwell
Publisher: CRC Press, Year: 2018
ISBN: 1138586102, 9781138586109
Yearning for the Impossible: The Surprising Truth of Mathematics, Second Edition
explores the history of mathematics from the perspective of the creative tension between common sense and the « impossible » as the author follows the discovery or invention of new concepts that have marked mathematical progress. The author puts these creations into a broader context involving related « impossibilities » from art, literature, philosophy, and physics. This new edition contains many new exercises and commentaries, clearly discussing a wide range of challenging subjects.
This course is a novel introduction to mathematics and its history. It puts the difficulties of the subject upfront by enthusiastically tackling the most important ones: the seemingly impossible concepts of irrational and imaginary numbers, the fourth dimension, curved space, and infinity. Similar « impossibilities » arise in music, art, literature, philosophy, and physics—as we will see—but math has the precision to separate actual impossibilities from those that are merely apparent. In fact, « impossibility » has always been a spur to the creativity of mathematicians, and a major influence on the development of math. By focusing reason and imagination on several apparent impossibilities, the course aims to show interesting math to students whose major may be in another field, and to widen the horizons of math students whose other courses are necessarily rather narrowly focused.