ABOUT THE This book is based on courses of lectures on Elementary Analysis given at Queen’s College, Galway, during each of the sessions 1902-1907. But additions have naturally been made in preparing the manuscript. In Particular the whole of chapter XI and greater part of the appendices have been added. This historic book may have numerous typos and missing text. In Chapter 1., a preliminary account is given of the notions of a limit and of convergence. I have not in this chapter attempted to supply arithmetic proofs of the fundamental theorems concerning the existence of limits, but have allowed their truth to rest on an appeal to the readers intuition, in the hope that the discussion may thus be made more attractive to beginners. An arithmetic treatment will be found in Appendix-I., where Dedekind’s definition of irrational numbers is adopted as fundamental, this method leads at once the monotonic principle of convergence, from which the existence limits is deduced. ABOUT THE Thomas John I’Anson Bromwich was born on 8 February 1875, in Wolverhampton, England. He was descended from Bryan I’Anson, of Ashby St. Legers, Sheriff of London and father of the 17th century 1st Baronet Sir Bryan I’Anson of Bassetbury. His parents emigrated to South Africa, where in 1892 he graduated from high school. He attended St John’s College, Cambridge, where in 1895 he became Senior Wrangler. In 1897, he became a lecturer at St. John’s. From 1902 to 1907, he was a Professor of mathematics at Queen’s College, Galway. In 1906, he was elected a Fellow of the Royal Society. In 1907, he returned to Cambridge and again became a Fellow and lecturer at St. John’s. He was a vice president of the Royal Society in 1919 and 1920. He died in Northampton on 24 August 1929. The Title 'An Introduction to the Theory of Infinite Series written/authored/edited by T . J. I’A. Bromwich', published in the year 2017. The ISBN 9789351285946 is assigned to the Paperback version of this title.

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