This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving meth... read more
History of Mathematics, Vol. I by David E. Smith Volume 1 of a two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Non-technical chronological survey with thousands of biographical notes, critical evaluations, contemporary opinions on over 1,100 mathematicians.
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The World of Mathematics, Vol. 1 by James R. Newman Vol. 1 of a monumental 4-volume set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, more.
The World of Mathematics, Vol. 2 by James R. Newman Vol. 2 of a monumental 4-volume set covers mathematics and the physical world, mathematics and social science, and the laws of chance, with non-technical essays by eminent mathematicians, economists, scientists, and others.
The World of Mathematics, Vol. 3 by James R. Newman Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and more.
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A Concise History of Mathematics: Fourth Revised Edition by Dirk J. Struik Compact, well-written survey ranges from the ancient Near East to 20th-century computer theory, covering Archimedes, Pascal, Gauss, Hilbert, and many others. "A work which is unquestionably one of the best." — Nature.
A Long Way from Euclid by Constance Reid Lively guide by a prominent historian focuses on the role of Euclid's Elements in subsequent mathematical developments. Elementary algebra and plane geometry are sole prerequisites. 80 drawings. 1963 edition.
Makers of Mathematics by Stuart Hollingdale Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 edition.
100 Great Problems of Elementary Mathematics by Heinrich Dörrie Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, etc. Features squaring the circle, pi, similar problems. No advanced math is required. Includes 100 problems with proofs.
The Art of Mathematics by Jerry P. King Clear, concise, and superbly written, this book reveals the beauty at the heart of mathematics, illustrating the fundamental connection between aesthetics and mathematics. "Witty, trenchant, and provocative." — Mathematical Association of America.
A Bridge to Advanced Mathematics by Dennis Sentilles This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
Discovering Mathematics: The Art of Investigation by A. Gardiner With puzzles involving coins, postage stamps, and other commonplace items, readers are challenged to explain perplexing mathematical phenomena. Simple methods are employed to capture the essentials of mathematical discovery. Solutions.
The Historical Roots of Elementary Mathematics by Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems examines their origins in early Egyptian, Babylonian, and Greek sources.
Lectures on Elementary Mathematics by Joseph Louis Lagrange One of the 18th century's greatest mathematicians delivered these lectures at a training school for teachers. An exemplar among elementary expositions, they combine original ideas and elegant expression. 1898 edition.
Mathematics and the Physical World by Morris Kline Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Mathematics: The Man-Made Universe by Sherman K. Stein Highly readable volume covers number theory, topology, set theory, geometry, algebra, and analysis, plus the primes, fundamental theory of arithmetic, probability, and more. Solutions manual available upon request. 1994 edition.
The Nature of Mathematics by Philip E. B. Jourdain Anyone interested in mathematics will appreciate this survey, which explores the distinction between the body of knowledge known as mathematics and the methods used in its discovery. 1913 edition.
A Short Account of the History of Mathematics by W. W. Rouse Ball This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
A Source Book in Mathematics by David Eugene Smith The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.
This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.
Reprint of the The MIT Press, Cambridge, Massachusetts, 1981 edition.
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