a transition to abstract mathematics learning mathematical thinking and writing

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A Transition To Abstract Mathematics

Author : Randall Maddox
ISBN : 9780080922713
Genre : Mathematics
File Size : 25. 26 MB
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Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. A Transition to Abstract Mathematics teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction Explains identification of techniques and how they are applied in the specific problem Illustrates how to read written proofs with many step by step examples Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter

Mathematical Thinking And Writing

Author : Randall B. Maddox
ISBN : 9780124649767
Genre : Mathematics
File Size : 80. 66 MB
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The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision.

A Transition To Abstract Mathematics Learning Mathematical Thinking And Writing

Author : CTI Reviews
ISBN : 9781478422501
Genre : Education
File Size : 41. 51 MB
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Facts101 is your complete guide to A Transition to Abstract Mathematics, Learning Mathematical Thinking and Writing. In this book, you will learn topics such as Sets and Their Properties, Functions, The Real Numbers, and Sequences of Real Numbers plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Student Solutions Manual For A Transition To Abstract Mathematics

Author : Randall Maddox
ISBN : 9780123748881
Genre : Science
File Size : 78. 93 MB
Format : PDF, Kindle
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Student Solutions Manual for A Transition to Abstract Mathematics

Mathematik F R Software Engineering

Author : Stephan Dreiseitl
ISBN : 9783662567333
Genre : Computers
File Size : 76. 22 MB
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Warum müssen InformatikerInnen und SoftwareentwicklerInnen im Studium eigentlich Mathe hören? Wie kann ihnen die Mathematik beim Programmieren helfen? Dieses Lehrbuch vermittelt StudienanfängerInnen die Sprache und Methode der Mathematik als Grundlage strukturierten Problemlösens, welches essenziell für das Entwickeln von Softwaresystemen ist. Deshalb liegt der didaktische Fokus hier darauf aufzuzeigen, wie mathematische Konzepte aufeinander aufbauen, welche Muster sich daraus ergeben, und welche klar strukturierten Regeln es in der mathematischen Argumentation (dem Beweisen) gibt. Dieses Buch richtet den inhaltlichen Fokus auf Logik, Mengenlehre, diskrete Strukturen und Wahrscheinlichkeitsrechnung und orientiert sich damit an den Empfehlungen von ACM und IEEE zur Mathematikausbildung im Software-Engineering-Studium. Da man Mathematik - ebenso wie die Softwareentwicklung - nicht durch Lesen, sondern nur durch Tun erlernt, schließt jeder Abschnitt mit einer Reihe von Verständnisfragen und Übungsaufgaben. Es eignet sich daher bestens zum Nacharbeiten einer Vorlesung und zur Prüfungsvorbereitung. Durch den verständlichen Schreibstil und die Lösungen auf der Webseite des Autors kann dieses Buch aber auch gut zum Selbststudium genutzt werden.

Discrete Mathematics Introduction To Mathematical Reasoning

Author : Susanna S. Epp
ISBN : 9780495826170
Genre : Mathematics
File Size : 31. 45 MB
Format : PDF
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Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING, provides the same clear introduction to discrete mathematics and mathematical reasoning as her highly acclaimed DISCRETE MATHEMATICS WITH APPLICATIONS, but in a compact form that focuses on core topics and omits certain applications usually taught in other courses. The book is appropriate for use in a discrete mathematics course that emphasizes essential topics or in a mathematics major or minor course that serves as a transition to abstract mathematical thinking. The ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. This book offers a synergistic union of the major themes of discrete mathematics together with the reasoning that underlies mathematical thought. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Brain Literacy For Educators And Psychologists

Author : Virginia Wise Berninger
ISBN : 012092871X
Genre : Education
File Size : 65. 51 MB
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Although educators are expected to bring about functional changes in the brain--the organ of human learning--they are given no formal training in the structure, function or development of the brain in formal or atypically developing children as part of their education. This book is organized around three conceptual themes: First, the interplay between nature (genetics) and nurture (experience and environment) is emphasized. Second, the functional systems of the brain are explained in terms of how they lead to reading, writing and mathematics and the design of instruction. Thirdly, research is presented, not as a finished product, but as a step forward within the field of educational neuropsychology. The book differs from neuropsychology and neuroscience books in that it is aimed at practitioners, focuses on high incidence neuropsychological conditions seen in the classroom, and is the only book that integrates both brain research with the practice of effective literacy, and mathematics instruction of the general and special education school-aged populations.

Discovering Group Theory

Author : Tony Barnard
ISBN : 9781315405773
Genre : Mathematics
File Size : 88. 15 MB
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Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking. ? Features Full proofs with all details clearly laid out and explained Reader-friendly conversational style Complete solutions to all exercises Focus on deduction, helping students learn how to construct proofs "Asides" to the reader, providing overviews and connections "What you should know" reviews at the end of each chapter

Einf Hrung In Das Mathematische Denken

Author : Friedrich Waismann
ISBN : STANFORD:36105033140034
Genre : Mathematics
File Size : 44. 66 MB
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Abstracts Of Papers Presented To The American Mathematical Society

Author :
ISBN : CORNELL:31924099658993
Genre : Mathematics
File Size : 27. 80 MB
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