AMS/MAA Textbooks Volume: 35
2017; 161 pp; Softcover
Print ISBN: 978-1-93951-213-0
A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.
A lovely little book for beginning mathematics majors and other students encountering proofs for the first time. Students should find the text appealing, and it contains many good exercises that a professor can build a course around. … Overall, a most satisfying book for a beginning class in mathematical proofs.
-- Curt Bennett, Professor of Mathematics at Loyola Marymount University and 2010 Haimo Award Winner
A TeXas Style Introduction to Proof by Ron Taylor and Patrick X. Rault is truly delightful-full of humanizing charm that softens the hard edge of mathematical rigor. It is gentle, lively, clear, and warm. … From this book, students and their instructors will find many proofs of the joy of mathematics.
-- Michael Starbird, University Distinguished Teaching Professor ofMathematics at The University of Texas at Austin and 2007 Haimo Award Winner
Taylor and Rault skillfully guide students through basic proof-writing techniques so that the student createsand discovers the content. The book is well-written, the integration of LaTeX is unique, and the authors have a fantastic sense of humor.
-- Amanda Croll, Assistant Professor of Mathematics, Concordia University, Irvine
Spectrum Volume: 86
2017; 176 pp; Softcover
Print ISBN: 978-0-88385-589-8
Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (Φ,Π,e and i)
, each of which has recently been the individual subject of historical and mathematical expositions. But here we discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus.
This material offers an excellent excuse to display the power of calculus to reveal elegant truths that are not often seen in college classes. These truths are described here via the work of such luminaries as Nilakantha, Liu Hui, Hemachandra, Khayyam, Newton, Wallis, and Euler.
Due 2018-01-22
1st ed. 2017, XIII, 198 p. 9illus.
Hardcover ISBN 978-3-319-70820-1
Series Trends in Logic
Variations on the Propositional Logic of William T. Parry
Offers a monograph-length investigation into the logics of analytic implication
Supports the rehabilitation of the work of William Parry
Studies analytic implication in the contexts of computer science and philosophy
This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is
the only full-length investigation into Parry-type propositional logics. A central tenet of the
monograph is that the sheer diversity of the contexts in which the mereological analogy
emerges ? its effervescence with respect to fields ranging from metaphysics to computer
programming ? provides compelling evidence that the study of logics of analytic implication
can be instrumental in identifying connections between topics that would otherwise remain
hidden. More concretely, the book identifies and discusses a host of cases in which analytic
implication can play an important role in revealing distinct problems to be facets of a larger,
cross-disciplinary problem.It introduces an element of constancy and cohesion that has
previously been absent in a regrettably fractured field, shoring up those who are sympathetic
to the worth of mereological analogy. Moreover, it generates new interest in the field by
illustrating a wide range of interesting features present in such logics ? and highlighting these
features to appeal to researchers in many fields.
Due 2018-03-14
1st ed. 2018, XII, 291 p. 1illus.
Softcover
ISBN 978-3-319-72325-9
Springer Undergraduate Mathematics Series
Provides a hands-on approach to learning Galois theory, focusing on problemsolving
exercises
Features almost 500 exercises with hints, answers or solutions
Includes Maple tutorials and exercises
This textbook offers a unique introduction to classical Galois theory through many concrete
examples and exercises of varying difficulty (including computer-assisted exercises). In addition
to covering standard material, the book explores topics related to classical problems such as
Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of
non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of
Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed,
including exercises related to the inverse Galois problem and cyclotomic fields. The author
presents proofs of theorems, historical comments and useful references alongside the
exercises, providing readers with a well-rounded introduction to the subject and a gateway to
further reading. A valuable reference and a rich source of exercises with sample solutions, this
book will be useful to both students and lecturers. Its original concept makes it particularly
suitable for self-study.
Due 2018-02-15
1st ed. 2018, VII, 111 p. 1illus.
Hardcover
ISBN 978-3-319-71833-0
Series Springer INdAM Series
Highlights recent advances in those areas of Convex Geometry that are
currently most intensively researched
Includes contributions by the leading experts in the field
Presents open problems that can be of great interest to young researchers
This book presents the proceedings of the international conference Analytic Aspects in
Convexity, which was held in Rome in October 2016. It offers a collection of selected articles,
written by some of the world’s leading experts in the field of Convex Geometry, on recent
developments in this area: theory of valuations; geometric inequalities; affine geometry; and
curvature measures. The book will be of interest to a broad readership, from those involved in
Convex Geometry, to those focusing on Functional Analysis, Harmonic Analysis, Differential
Geometry, or PDEs. The book is a addressed to PhD students and researchers, interested in
Convex Geometry and its links to analysis.