Elements Of Mathematics
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Elements Of Mathematics
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Author : John Stillwell
language : en
Publisher: Princeton University Press
Release Date : 2017-11-07
Elements Of Mathematics written by John Stillwell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
An exciting look at the world of elementary mathematics Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics—but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.
Elements Of Mathematics
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Author : Gabor Toth
language : en
Publisher: Springer Nature
Release Date : 2021-09-23
Elements Of Mathematics written by Gabor Toth and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.
This textbook offers a rigorous presentation of mathematics before the advent of calculus. Fundamental concepts in algebra, geometry, and number theory are developed from the foundations of set theory along an elementary, inquiry-driven path. Thought-provoking examples and challenging problems inspired by mathematical contests motivate the theory, while frequent historical asides reveal the story of how the ideas were originally developed. Beginning with a thorough treatment of the natural numbers via Peano’s axioms, the opening chapters focus on establishing the natural, integral, rational, and real number systems. Plane geometry is introduced via Birkhoff’s axioms of metric geometry, and chapters on polynomials traverse arithmetical operations, roots, and factoring multivariate expressions. An elementary classification of conics is given, followed by an in-depth study of rational expressions. Exponential, logarithmic, and trigonometric functions complete the picture, driven by inequalities that compare them with polynomial and rational functions. Axioms and limits underpin the treatment throughout, offering not only powerful tools, but insights into non-trivial connections between topics. Elements of Mathematics is ideal for students seeking a deep and engaging mathematical challenge based on elementary tools. Whether enhancing the early undergraduate curriculum for high achievers, or constructing a reflective senior capstone, instructors will find ample material for enquiring mathematics majors. No formal prerequisites are assumed beyond high school algebra, making the book ideal for mathematics circles and competition preparation. Readers who are more advanced in their mathematical studies will appreciate the interleaving of ideas and illuminating historical details.
Elements Of Mathematics
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Author : Nicolas Bourbaki
language : en
Publisher:
Release Date : 1966
Elements Of Mathematics written by Nicolas Bourbaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Euclid S Elements
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Author : Euclid
language : en
Publisher:
Release Date : 2002
Euclid S Elements written by Euclid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
"The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Elements Of Advanced Mathematics Third Edition
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2012-03-19
Elements Of Advanced Mathematics Third Edition written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-19 with Mathematics categories.
For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant. This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques. Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.
Elements Of The History Of Mathematics
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Elements Of The History Of Mathematics written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.
Elements Of Modern Mathematics
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Author : Kenneth O, May
language : en
Publisher: Dover Publications
Release Date : 2019-11-13
Elements Of Modern Mathematics written by Kenneth O, May and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-13 with Mathematics categories.
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.
Elements Of Mathematics For Economics And Finance
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Author : Vassilis C. Mavron
language : en
Publisher: Springer Nature
Release Date : 2023-11-20
Elements Of Mathematics For Economics And Finance written by Vassilis C. Mavron and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.
Based on over 15 years’ experience in the design and delivery of successful first-year courses, this book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The book starts with a summary of basic skills and takes its readers as far as constrained optimisation helping them to become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems in economics and finance.Designed as both a course text and a handbook, the book assumes little prior mathematical knowledge beyond elementary algebra and is therefore suitable for students returning to mathematics after a long break. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics. Features of the book include: a systematic approach: ideas are touched upon, introduced gradually and thenconsolidated through the use of illustrative examples; several entry points to accommodate differing mathematical backgrounds; numerous problems, with full solutions, and exercises to illustrate the theory and applications; key learning objectives and self-assessment questions provided for each chapter; full solutions to exercises, available to lecturers via the Springer Nature Extramaterial - Lecturer Material website. Vass Mavron is Emeritus Professor of Mathematics at Aberystwyth University. Tim Phillips is Professor of Applied Mathematics in the School of Mathematics at Cardiff University.
Elements Of Number Theory
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-12-13
Elements Of Number Theory written by John Stillwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-13 with Mathematics categories.
Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
Topological Vector Spaces
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Topological Vector Spaces written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This [second edition] is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory).