|
Showing 1 - 3 of
3 matches in All Departments
This text gives a rigorous treatment of the foundations of
calculus. In contrast to more traditional approaches, infinite
sequences and series are placed at the forefront. The approach
taken has not only the merit of simplicity, but students are well
placed to understand and appreciate more sophisticated concepts in
advanced mathematics. The authors mitigate potential difficulties
in mastering the material by motivating definitions, results and
proofs. Simple examples are provided to illustrate new material and
exercises are included at the end of most sections. Noteworthy
topics include: an extensive discussion of convergence tests for
infinite series, Wallis's formula and Stirling's formula, proofs of
the irrationality of and e and a treatment of Newton's method as a
special instance of finding fixed points of iterated functions.
This is not a traditional work on topological graph theory. No
current graph or voltage graph adorns its pages. Its readers will
not compute the genus (orientable or non-orientable) of a single
non-planar graph. Their muscles will not flex under the strain of
lifting walks from base graphs to derived graphs. What is it, then?
It is an attempt to place topological graph theory on a purely
combinatorial yet rigorous footing. The vehicle chosen for this
purpose is the con cept of a 3-graph, which is a combinatorial
generalisation of an imbedding. These properly edge-coloured cubic
graphs are used to classify surfaces, to generalise the Jordan
curve theorem, and to prove Mac Lane's characterisation of planar
graphs. Thus they playa central role in this book, but it is not
being suggested that they are necessarily the most effective tool
in areas of topological graph theory not dealt with in this volume.
Fruitful though 3-graphs have been for our investigations, other
jewels must be examined with a different lens. The sole requirement
for understanding the logical development in this book is some
elementary knowledge of vector spaces over the field Z2 of residue
classes modulo 2. Groups are occasionally mentioned, but no
expertise in group theory is required. The treatment will be
appreciated best, however, by readers acquainted with topology. A
modicum of topology is required in order to comprehend much of the
motivation we supply for some of the concepts introduced."
This text provides a detailed presentation of the main results for
infinite products, as well as several applications. The target
readership is a student familiar with the basics of real analysis
of a single variable and a first course in complex analysis up to
and including the calculus of residues. The book provides a
detailed treatment of the main theoretical results and applications
with a goal of providing the reader with a short introduction and
motivation for present and future study. While the coverage does
not include an exhaustive compilation of results, the reader will
be armed with an understanding of infinite products within the
course of more advanced studies, and, inspired by the sheer beauty
of the mathematics. The book will serve as a reference for students
of mathematics, physics and engineering, at the level of senior
undergraduate or beginning graduate level, who want to know more
about infinite products. It will also be of interest to instructors
who teach courses that involve infinite products as well as
mathematicians who wish to dive deeper into the subject. One could
certainly design a special-topics class based on this book for
undergraduates. The exercises give the reader a good opportunity to
test their understanding of each section.
|
You may like...
Goldfinger
Honor Blackman, Lois Maxwell, …
Blu-ray disc
R53
Discovery Miles 530
|