Copyright 2024
Hardback
ISBN 9780367555016
547 Pages 44 B/W Illustrations
December 19, 2023
Abstract Algebra: An Inquiry-Based Approach, Second Edition not only teaches abstract algebra, but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think.
The second edition of this unique, flexible approach builds on the success of the first edition. The authors offer an emphasis on active learning, helping students learn algebra by gradually building both their intuition and their ability to write coherent proofs in context.
Allowing the flexibility to begin the course with either groups or rings.
Introducing the ideas behind definitions and theorems to help students develop intuition.
Helping students understand how mathematics is done. Students will experiment through examples, make conjectures, and then refine or prove their conjectures.
Assisting students in developing their abilities to effectively communicate mathematical ideas.
Actively involving students in realizing each of these goals through in-class and out-of-class activities, common in-class intellectual experiences, and challenging problem sets.
Streamlining of introductory material with a quicker transition to the material on rings and groups.
New investigations on extensions of fields and Galois theory.
New exercises added and some sections reworked for clarity.
More online Special Topics investigations and additional Appendices, including new appendices on other methods of proof and complex roots of unity.
Encouraging students to do mathematics and be more than passive learners, this text shows students the way mathematics is developed is often different than how it is presented; definitions, theorems, and proofs do not simply appear fully formed; mathematical ideas are highly interconnected; and in abstract algebra, there is a considerable amount of intuition to be found.
In the series De Gruyter Textbook
Suitable for introductory and advanced courses, Lectures on Linear Algebra presents the topic in a clear and concise manner. Chapters include exercises, non-trivial and practical applications. In-depth explorations pertaining to differential equations, calculus, and differential geometry are provided. A solution manual available to instructors covers discussion of additional topics, including Perron-Frobenius theorem, and Gram determinants..
Clear and concise approach based on the authors extensive lecture notes.
Well suited for introductory and advanced courses on linear algebra.
Contains a large number of exercises with selected solutions
Author / Editor information
Philip Korman is Professor of Mathematics at the University of Cincinnati. He is the author of over one hundred research articles in differential equations and the author of Global Solution Curves for Semilinear Elliptic Equations, World Scientific, 2012 and Lectures on Differential Equations, SIAM, 2019. Korman has served on the editorial boards of Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM Review, and Differential Equations and Applications and Mathematica Slovaca.
In the series De Gruyter Series on the Applications of Mathematics in Engineering and Information Sciences
Graph Theory is one of the most prolific branches of mathematics, that has immense applications to almost all disciplines including physical sciences, chemical sciences, social sciences, different streams of engineering. This book provides researchers with a good reference on the emerging areas.
Author / Editor information
N. Sudev, J.V.Kureethara, C. Dominic, J.Kok, CHRIST (Deemed to be University), India.
Combinatorics and Graph Theory
Computer Sciences
Fundamentals of Computer Sciences
Information Technology
Mathematics
Numerical and Computational Mathematics
Essays in Geometry cover
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This volume consists in a collection of essays dedicated to Norbert A'Campo on the occasion of his 80th birthday. The subject is geometry in the broadest sense. The topics include hyperbolic and super hyperbolic geometry, 3-manifolds, metric geometry, mapping class groups, linear groups, Riemann surfaces, Teichmuller spaces, high-dimensional complex geometry, differential topology, symplectic geometry, singularity theory, number theory, algebraic geometry, dynamics, mathematical physics and philosophy of mathematics. The book gives a fairly comprehensive overview of the wealth of current research in geometry.
Format: Paperback / softback, 454 pages, height x width: 279x210 mm, LXXXI, 454 p.,
Pub. Date: 08-Sep-2023
ISBN-13: 9783031053573
This volume explores A.P. Morsefs (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morsefs works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morsefs publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editorfs commentary serves to outline Morsefs goals, give informal explanations of Morsefs formal language, and compare Morsefs often unique approaches to more traditional approaches. Minor corrections to Morsefs previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editorfs introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morsefs methods.
A.P. Morsefs Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morsefs unique perspective and in the history of mathematics will also find this book to be of interest.
Preface.- Editor's Introduction.- Language and Inference.- Logic.- Set Theory.- Elementary Analysis.- Metrics.- Measure.- Linear Measure and Total Variation.- Integration.- Product Measures.- Web Derivatives.- Classical Differentiation.- The Construction of Definition.- The Consistency of the Axiom of Size.- Suggested Reading.- Publications of A.P. Morse.- Errata to A Theory of Sets, Second Edition.- Integration with Respect to Addor Functions.- The Henstock-Kurzweil Integral.
Format: Hardback, 216 pages, height x width: 235x155 mm, 92 Illustrations, black and white; XVII, 216 p. 92 illus.
Series: Studies in Fuzziness and Soft Computing 429
Pub. Date: 28-Sep-2023
ISBN-13: 9783031397554
One of the most preeminent ways of applying mathematics in real-world scenario modeling involves graph theory. A graph can be undirected or directed depending on whether the pairwise relationships among objects are symmetric or not. Nevertheless, in many real-world situations, representing a set of complex relational objects as directed or undirected is not suc cient. Weighted graphs oer a framework that helps to over come certain conceptual limitations. We show using the concept of an isomorphism that weighted graphs have a natural connection to fuzzy graphs. As we show in the book, this allows results to be carried back and forth between weighted graphs and fuzzy graphs. This idea is in keeping with the important paper by Klement and Mesiar that shows that many families of fuzzy sets are lattice isomorphic to each other. We also outline the important work of Head and Weinberger that show how results from ordinary mathematics can be carried over to fuzzy mathematics. We focus on the concepts connectivity, degree sequences and saturation, and intervals and gates in weighted graphs.
Graphs and Weighted Graphs.- Connectivity.- More on Connectivity.- Cycle Connectivity.- Distance and Convexity.- Degree Sequences and Saturation.- Intervals and Gates.- Weighted Graphs and Fuzzy Graphs.- Fuzzy Results from Crisp Results.
Format: Hardback, 500 pages, height x width: 235x155 mm, 20 Tables, color; 83 Illustrations, color;
35 Illustrations, black and white; XVIII, 500 p. 118 illus., 83 illus. in color.
Series: Behaviormetrics: Quantitative Approaches to Human Behavior 17
Pub. Date: 31-Oct-2023
ISBN-13: 9789819953288
This collection of essays is in honor of Shizuhiko Nishisato on his 88th birthday and consists of invited contributions only. The book contains essays on the analysis of categorical data, which includes quantification theory, cluster analysis, and other areas of multidimensional data analysis, covering more than half a century of research by the 41 interdisciplinary and international researchers who are contributors. Thus, it offers the wisdom and experience of work past and present and attracts a new generation of researchers to this field. Central to this wisdom and experience is that of Prof. Nishisato, who has spent much of the past 60 years mentoring and providing leadership in the research of quantification theory, especially that of gdual scalingh. The book includes contributions by leading researchers who have worked alongside Prof. Nishisato, published with him, been mentored by him, or whose work has been influenced by the research he has undertaken over his illustrious career. This book inspires researchers young and old as it highlights the significant contributions, past and present, that Prof. Nishisato has made in his field.
Gratitude: A Life Relived.- Nishisato's Psychometric World.- My
Recollections of People in the World of Data Science.- A Straightforward
Approach to Chi-Squared Analysis of Associations in Contingency Tables.-
Contrasts for Neyman's Modified Chi-Square Statistic in One-Way Contingency
Tables.