Overview
Designed to enable the student an opportunity to engage in mathematical problem solving at the highest level
Includes exercises at every level
Versatile pedagogical usage
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
- J.S. Mac Nerney text
- textbook functional analysis
- textbook complex analysis
- functional analysis
- complex analysis
- Moore method
- extended complex plane
- linear-fractional transformations
- meromorphic functions
- branch-points
- analytic surfaces
- connectedness
- independent study functional analysis
- independent study complex analysis
- convexity
- analyticity
- analytic inverses
- homotopy groups
- automorphic functions
- singularities
About this book
When first published in 1959, this book was the basis of a two-semester course in complex analysis for upper undergraduate and graduate students. J. S. Mac Nerney was a proponent of the Socratic, or “do-it-yourself” method of learning mathematics, in which students are encouraged to engage in mathematical problem solving, including theorems at every level which are often regarded as “too difficult” for students to prove for themselves. Accordingly, Mac Nerney provides no proofs. What he does instead is to compose and arrange the investigation in his own unique style, so that a contextual proof is always available to the persistent student who enjoys a challenge. The central idea is to empower students by allowing them to discover and rely on their own mathematical abilities. This text may be used in a variety of settings, including: the usual classroom or seminar, but with the teacher acting mainly as a moderator while the students present their discoveries, a small-group setting in which the students present their discoveries to each other, and independent study.
The Editors, William E. Kaufman (who was Mac Nerney’s last PhD student) and Ryan C. Schwiebert, have composed the original typed Work into LaTeX ; they have updated the notation, terminology, and some of the prose for modern usage, but the organization of content has been strictly preserved. About this Book, some new exercises, and an index have also been added.
Authors, Editors and Affiliations
About the editors
William E. Kaufman received his PhD from the University of Houston in 1979 under J. S. Mac Nerney. His primary areas of research are Hilbert space operator theory and the structure of Banach spaces. He worked on mathematical software for the first Space Shuttle at the Johnson Space Center. He is also interested in functional analysis in general, topological vector spaces, and is currently actively pursuing problems in the theory of nonseparable Banach spaces.
Ryan C. Schwiebert received his PhD from Ohio University in 2011 under Sergio López-Permouth and Gregory Oman. His areas of research are in the theory of rings and modules. He has an ongoing interest in applications of abstract algebra to other fields and the creation of software to enhance progress in mathematical research.
Bibliographic Information
Book Title: An Introduction to Analytic Functions
Book Subtitle: With Theoretical Implications
Authors: John Sheridan Mac Nerney
Editors: William E. Kaufman, Ryan C. Schwiebert
DOI: https://doi.org/10.1007/978-3-030-42085-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: University of Houston and Trinity College 2020
Softcover ISBN: 978-3-030-42084-0Published: 31 May 2020
eBook ISBN: 978-3-030-42085-7Published: 30 May 2020
Edition Number: 1
Number of Pages: XIX, 92
Number of Illustrations: 12 b/w illustrations
Additional Information: Copyright University of Houston and Trinity College
Topics: Functional Analysis