Books by P. J. Hilton

The mathematical ideas involved are des cribed in this book, and only the student familiar with the corresponding ideas for functions of a single variable should attempt to understand the extension of the method of the differential calculus to several variables.

THIS book is intended to provide the university student in the physical sciences with information about the differential calculus which he is likely to need. Formulae for differentiating 21 Exerc-bses 2 3 3 Maxima and Minima and Taylor's Theorem 34 I.

This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers.

These notes constitute a faithful record of a short course of lectures given in Sao Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.