At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that ...
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At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol- ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note- worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
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Add this copy of Lecture Notes on Elementary Topology and Geometry to cart. $26.83, good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1967 by Scott Foresman and Company.
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First Springer edition, first printing, 232 pp., hardcover, light wear to spine, faint age-toning to endpapers and pastedowns else text clean & binding tight. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
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This book is a bridge between Spivak's Calculus on Manifolds and Warner's Foundations of Differential Manifolds and Lie Groups. It's a must for undergrads planning to go to math graduate school. The material on manifolds is excellent. It has some very nice material on algebraic topology and contains a proof of the Gauss-Bonnet theorem. The... material on separation axioms in point set topology is also very interesting. This book has been a classic since it first appeared in 1967. It is beautifully produced and the diagrams are superb. A real pleasure to read. A jewel.
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