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Author : John Joseph Del Grande,J. C. Egsgard
Publisher : Unknown
Page : 454 pages
File Size : 48,9 Mb
Release : 1979
Category : Conic sections
ISBN : 0771536380
Author : Myra McFadden
Publisher : Unknown
Page : 326 pages
File Size : 43,9 Mb
Release : 1963
Category : Algebra
ISBN : UOM:39015017316426
Author : Helena Rasiowa
Publisher : Elsevier
Page : 352 pages
File Size : 50,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483274720
Introduction to Modern Mathematics focuses on the operations, principles, and methodologies involved in modern mathematics. The monograph first tackles the algebra of sets, natural numbers, and functions. Discussions focus on groups of transformations, composition of functions, an axiomatic approach to natural numbers, intersection of sets, axioms of the algebra of sets, fields of sets, prepositional functions of one variable, and difference of sets. The text then takes a look at generalized unions and intersections of sets, Cartesian products of sets, and equivalence relations. The book ponders on powers of sets, ordered sets, and linearly ordered sets. Topics include isomorphism of linearly ordered sets, dense linear ordering, maximal and minimal elements, quasi-ordering relations, inequalities for cardinal numbers, sets of the power of the continuum, and Cantor's theorem. The manuscript then examines elementary concepts of abstract algebras, functional calculus and its applications in mathematical proofs, and propositional calculus and its applications in mathematical proofs. The publication is a valuable reference for mathematicians and researchers interested in modern mathematics.
Author : Kenneth O, May
Publisher : Dover Publications
Page : 627 pages
File Size : 48,7 Mb
Release : 2019-11-13
Category : Mathematics
ISBN : 9780486836577
An unusually thoughtful and well-constructed introduction to the serious study of mathematics, this book requires no background beyond high school courses in plane geometry and elementary algebra. From that starting point, it is designed to lead readers willing to work through its exercises and problems to the achievement of basic mathematical literacy. The text provides a fundamental orientation in modern mathematics, an essential vocabulary of mathematical terms, and some facility in the use of mathematical concepts and symbols. From there, readers will be equipped to move on to more serious work, and they'll be well on the way to having the tools essential for work in the physical sciences, engineering, and the biological and social sciences. Starting with elementary treatments of algebra, logic, and set theory, the book advances to explorations of plane analytic geometry, relations and functions, numbers, and calculus. Subsequent chapters discuss probability, statistical inference, and abstract mathematical theories. Each section is enhanced with exercises in the text and problems at the end. Answers to the exercises and some of the problems are included at the end of each section.
Author : Edna Ernestine Kramer
Publisher : Princeton University Press
Page : 790 pages
File Size : 43,8 Mb
Release : 1982
Category : Mathematics
ISBN : 0691023727
Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.
Author : Myra McFadden,J. William Moore,Wendell I. Smith
Publisher : Unknown
Page : 299 pages
File Size : 53,9 Mb
Release : 1963
Category : Algebra
ISBN : OCLC:230085495
Author : Paul Roman
Publisher : Elsevier
Page : 426 pages
File Size : 50,8 Mb
Release : 2014-05-09
Category : Mathematics
ISBN : 9781483187372
Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.
Author : José Ferreirós
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 52,7 Mb
Release : 2008-10-04
Category : Mathematics
ISBN : 9783764383503
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century." --Bulletin of Symbolic Logic (Review of first edition)
Author : Albert Monjallon
Publisher : Unknown
Page : 248 pages
File Size : 46,7 Mb
Release : 1967
Category : Abelian groups
ISBN : UOM:39015065666326
Author : Danilo R. Diedrichs,Stephen Lovett
Publisher : CRC Press
Page : 552 pages
File Size : 53,8 Mb
Release : 2022-05-22
Category : Mathematics
ISBN : 9781000581669
This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments Relations Part II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master’s degree in civil engineering from the Ecole Polytechnique Fédérale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).
Author : Max D. Larsen
Publisher : Unknown
Page : 168 pages
File Size : 46,5 Mb
Release : 1970
Category : Arithmetic
ISBN : CORNELL:31924001504228
Author : John Edward Hafstrom
Publisher : Courier Corporation
Page : 209 pages
File Size : 54,6 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486497297
An in-depth overview of some of the most readily applicable essentials of modern mathematics, this concise volume is geared toward undergraduates of all backgrounds as well as future math majors. Topics include the natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.
Author : Jose Ferreiros
Publisher : Birkhäuser
Page : 459 pages
File Size : 47,9 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9783034850490
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 52,8 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 3540225250
This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Théorie des Ensembles (1970).