The Calculus Gallery: Masterpieces from Newton to Lebesgue
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"The Calculus Gallery is one of the best efforts at mathematical exposition I have ever read! Dunham presents in detail and in his own words the sequence of ideas of classical giants of mathematics, but each new idea is described in modern terms and notation, so I had absolutely no trouble following along. Furthermore—and this is an astounding achievement—the entire work has a tightly woven development. If it were a detective story I would say it had a plot with no loose ends. An amazing feat. I wish I could plan a single lecture, never mind a course or a book, that well!"—Henry Pollak, Teachers College, Columbia University"What a fine resource! All of the famous functions that have shaped calculus and analysis parade before the reader in the original words of their creators. Bill Dunham has produced an excellent volume that teachers and students will enjoy and appreciate."—Thomas Banchoff, Brown University"Bill Dunham has done it again. The Calculus Gallery is a masterly journey through the works of thirteen mathematicians who formulated, formalised, and reformed the calculus into the modern analysis we learn today. Readers of his earlier books have learned to expect a clarity of exposition that few others can attain: they will not be disappointed."—Robin Wilson, author of Four Colors Suffice"This is an excellent book—an amazing mathematical page-turner. William Dunham has done the seemingly impossible: he has taken some difficult, advanced mathematics and, without sacrificing the technical details, written a lively, readable book about it."—Barry Cipra, author of Misteaks . . . and How to Find Them Before the Teacher Does"Pedagogically excellent and extremely well written, The Calculus Gallery bridges the gap between general histories and detailed studies of individual mathematicians. Dunham has described mathematical developments in an engaging style rarely found in literature of this kind."—Annette Imhausen, Trinity Hall, Cambridge"A welcome addition to the literature. The idea of presenting a 'museum of mathematics' is new. It allows the author to present a nonstandard selection of theorems, so that even mathematicians with a strong historical background will learn a few things."—Franz Lemmermeyer, Bilkent University, author of Reciprocity Laws: From Euler to Eisenstein Eberhard Knobloch - Zentralblatt MATH Database A fascinating, competent visit too the calculus gallery.
Ch. 1Newton5Ch. 2Leibniz20Ch. 3The Bernoullis35Ch. 4Euler52Ch. 5First interlude69Ch. 6Cauchy76Ch. 7Riemann96Ch. 8Liouville116Ch. 9Weierstrass128Ch. 10Second interlude149Ch. 11Cantor158Ch. 12Volterra170Ch. 13Baire183Ch. 14Lebesgue200
