Journey Into Mathematics

Author : Joseph J. Rotman
Publisher : Courier Corporation
Page : 386 pages
File Size : 41,6 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151687

Get Book

Journey into Mathematics by Joseph J. Rotman Pdf

Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. Journey into Mathematics offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.

Author : D. J. Acheson
Publisher : Oxford University Press, USA
Page : 200 pages
File Size : 51,6 Mb
Release : 2002
Category : Mathematics
ISBN : 0198516231

Get Book

1089 and All that by D. J. Acheson Pdf

This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.

Author : William Dunham
Publisher : Penguin Books
Page : 324 pages
File Size : 51,8 Mb
Release : 1991-08
Category : Biography & Autobiography
ISBN : PSU:000023719095

Get Book

Journey Through Genius by William Dunham Pdf

Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov

Author : Erna Yackel,Koeno Gravemeijer,Anna Sfard
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 50,7 Mb
Release : 2010-11-30
Category : Education
ISBN : 9789048197293

Get Book

A Journey in Mathematics Education Research by Erna Yackel,Koeno Gravemeijer,Anna Sfard Pdf

Our objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb’s own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb’s contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb’s work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb’s work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers’ constant pursuit of new insights.

Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 53,8 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688

Get Book

Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth Pdf

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.

Author : Enrique A. González-Velasco
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 55,9 Mb
Release : 2011-08-08
Category : Mathematics
ISBN : 9780387921549

Get Book

Journey through Mathematics by Enrique A. González-Velasco Pdf

This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

Author : Owen Byer,Deirdre L. Smeltzer,Kenneth L. Wantz
Publisher : MAA Press
Page : 388 pages
File Size : 50,6 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470449129

Get Book

Journey Into Discrete Mathematics by Owen Byer,Deirdre L. Smeltzer,Kenneth L. Wantz Pdf

Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.

Author : Joseph J. Rotman
Publisher : Unknown
Page : 237 pages
File Size : 49,6 Mb
Release : 2024-06-12
Category : Proof theory
ISBN : OCLC:1150132726

Get Book

Journey Into Mathematics: an Introduction with Proofs by Joseph J. Rotman Pdf

Author : Martin Loebl,Jaroslav Nešetřil,Robin Thomas
Publisher : Springer
Page : 810 pages
File Size : 42,7 Mb
Release : 2017-10-11
Category : Computers
ISBN : 9783319444796

Get Book

A Journey Through Discrete Mathematics by Martin Loebl,Jaroslav Nešetřil,Robin Thomas Pdf

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Author : Allison K. Henrich,Emille D. Lawrence,Matthew A. Pons,David George Taylor
Publisher : Unknown
Page : 136 pages
File Size : 52,9 Mb
Release : 2019
Category : Academic achievement
ISBN : 1470452812

Get Book

Living Proof by Allison K. Henrich,Emille D. Lawrence,Matthew A. Pons,David George Taylor Pdf

Wow! This is a powerful book that addresses a long-standing elephant in the mathematics room. Many people learning math ask ``Why is math so hard for me while everyone else understands it?'' and ``Am I good enough to succeed in math?'' In answering these questions the book shares personal stories from many now-accomplished mathematicians affirming that ``You are not alone; math is hard for everyone'' and ``Yes; you are good enough.'' Along the way the book addresses other issues such as biases and prejudices that mathematicians encounter, and it provides inspiration and emotional support for mathematicians ranging from the experienced professor to the struggling mathematics student. --Michael Dorff, MAA President This book is a remarkable collection of personal reflections on what it means to be, and to become, a mathematician. Each story reveals a unique and refreshing understanding of the barriers erected by our cultural focus on ``math is hard.'' Indeed, mathematics is hard, and so are many other things--as Stephen Kennedy points out in his cogent introduction. This collection of essays offers inspiration to students of mathematics and to mathematicians at every career stage. --Jill Pipher, AMS President This book is published in cooperation with the Mathematical Association of America.

Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 46,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437

Get Book

Proofs from THE BOOK by Martin Aigner,Günter M. Ziegler Pdf

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Author : Chase Orton
Publisher : Corwin Press
Page : 210 pages
File Size : 45,9 Mb
Release : 2022-02-24
Category : Education
ISBN : 9781071841556

Get Book

The Imperfect and Unfinished Math Teacher [Grades K-12] by Chase Orton Pdf

The system won’t do it for us. But we have each other. In The Imperfect and Unfinished Math Teacher: A Journey to Reclaim Our Professional Growth, master storyteller Chase Orton offers a vulnerable and courageous grassroots guide that leads K-12 math teachers through a journey to cultivate a more equitable, inclusive, and cohesive culture of professionalism for themselves...what he calls professional flourishment. The book builds from two bold premises. First, that as educators, we are all naturally imperfect and unfinished, and growth should be our constant goal. Second, that the last 40 years of top-down PD efforts in mathematics have rarely supplied teachers with what they need to equitably grow their practice and foster classrooms that are likewise empowered, inclusive, and cohesive. With gentle humanity, this book inspires teachers to break down silos, observe each others’ classrooms, interrogate their own biases, and put students at the center of everything they do in the math classroom. This book: Weaves raw and authentic stories—both personal and those from other educators—into a relatable and validating narrative Offers interactive opportunities to self-reflect, build relationships, seek new vantage on our teaching by observing others’ classrooms and students, and share and listen to other’s stories and experiences Asks teachers to give and accept grace as they work collaboratively to better themselves and the system from within, so that they can truly serve each of their students authentically and equitably Implementing the beliefs and actions in this book will position teachers to become more active partners in each other’s professional growth so that they can navigate the obstacles in their professional landscape with renewed focus and a greater sense of individual and collective efficacy. It equips teachers—and by extension, their students—to chart their own course and author their own equitable and joyful mathematical and professional stories.

Author : A. Gardiner
Publisher : Courier Corporation
Page : 226 pages
File Size : 52,5 Mb
Release : 2006-01-26
Category : Mathematics
ISBN : 9780486452999

Get Book

Discovering Mathematics by A. Gardiner Pdf

The term "mathematics" usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen. With puzzles involving coins, postage stamps, and other commonplace items, students are challenged to account for the simple explanations behind perplexing mathematical phenomena. Elementary methods and solutions allow readers to concentrate on the way in which the material is explored, as well as on strategies for answers that aren't immediately obvious. The problems don't require the kind of sophistication that would put them out of reach of ordinary students, but they're sufficiently complex to capture the essential features of mathematical discovery. Complete solutions appear at the end.

Author : Catalin Barboianu
Publisher : PhilScience Press
Page : 315 pages
File Size : 42,9 Mb
Release : 2021-01-18
Category : Education
ISBN : 9789731991986

Get Book

What is Mathematics: School Guide to Conceptual Understanding of Mathematics by Catalin Barboianu Pdf

This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.

Author : Owen D. Byer,Deirdre L. Smeltzer,Kenneth L. Wantz
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 52,7 Mb
Release : 2018-11-13
Category : Combinatorial analysis
ISBN : 9781470446963

Get Book

Journey into Discrete Mathematics by Owen D. Byer,Deirdre L. Smeltzer,Kenneth L. Wantz Pdf

Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject.