Bibliography - Numbers and Functions: Steps into Analysis - page 347

Cohen, D., 1988, Calculus By and For Young People . Published by the author at 809
Stratford Drive, Champaign, Ill. 61821, USA.
A numerical approach to sequences, series and graphs, said to be for those aged 7
and upwards. Just right for thesixth form!
Cohen, L. W. and Ehrlich, G., 1963,

T he structure of the Real Number System , van

Nostrand Reinhold.
A detailed, thorough and modern account of the number system from the Peano
postulates to the various forms of completeness.
Courant, R. and John, F., 1965, Introduction to Calculus and Analysis , vol. 1, New York:
Wiley. Reprinted 1989, Berlin: Springer.
Excellent text and diagrams. Style of discussion consonant with a good sixth form
text. Gives integration before differentiation. Strong on applications.
Dedekind, R., 1963, Essays on the theory of numbers , Dover.
First published 1872 and 1887, these are two of the historically seminal documents in
thearithmtisation of analysis.
Dieudonne´ , J., 1960, Foundations of Modern Analysis , Academic Press.
For 'further reading' only.
du Bois-Reymond, P., 1882, Die allgemeine Funktionentheorie , Laupp, Tu¨ bingen. French
translation 1887, The´orie Ge´ne´rale des Fonctions ,Ni¸oise, Nice. Reprint 1995, Jacques
Gabay, Paris.
This is not a textbook but a discussion of numbers and functions favouring infinite
decimals. It has a fine and full discussion of completeness.
Dugac, P., 1978, Sur les fondements de l'Analyse de Cauchy a` Baire, doctoral thesis,
Universite´ Pierre et Marie Curie, Paris.
A masterly survey of the foundation of analysis during the nineteenth century,
particularly informative on the contribution of Weierstrass.
Edwards, C. H., 1979, he Historical Development of the Calculus , Springer.

Strong on the seventeenth and eighteenth centuries. Written to generate interest in
mathematics.
Ferrar, W. L., 1938, Convergence , Oxford University Press.
Gardiner, A., 1982, Infinite Processes , Springer.
An attempt to bridge the gap between sixth form and undergraduate thinking on
three fronts: numbers, geometry and functions.
Gelbaum, B. R. and Olmsted, J. M. H., 1964, Counterexamples in Analysis , Holden-Day.
A rich collection of correctives to the untutored intuition.
Grabiner, J. V., 1981, The Origins of Cauchy ' s Rigorous Calculus , MIT.
Thedefinitiveintroduction to Cauchy's analysis and calculus. Strong on thelate
eighteenth and early nineteenth century.
Grattan-Guinness, I. (ed.), 1980, From the Calculus to Set Theory , 1630—1910 , Duckworth.
Strong on the nineteenth century, but you must know the mathematics before you
start reading this history topic.
Hairer, E. and Wanner, G., 1995, Analysis by its history , Springer.
The historical remarks in this topic are useful, and the diagrams quite outstanding.
Hardy, G. H., 1st edition 1908, Pure Mathematics , Cambridge University Press.
Until about 1960, this (2nd edition, 1914, onwards) was the leading English language
text on analysis. The text is hard going but the exercises offer a rich and broad diet.
Hardy, G. H., Littlewood, J. E., and Po´ lya, G., 1952, Inequalities , CambridgeUnivrsity
Press.
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