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 : 33. 81 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

A Transition To Abstract Mathematics Learning Mathematical Thinking

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File Size : 82. 5 MB
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Mathematical Thinking And Writing

Author : Randall B. Maddox
ISBN : 9780124649767
Genre : Mathematics
File Size : 51. 97 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.

Student Solutions Manual For A Transition To Abstract Mathematics

Author : Randall Maddox
ISBN : 9780123748881
Genre : Science
File Size : 25. 18 MB
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Student Solutions Manual for A Transition to Abstract Mathematics

Brain Literacy For Educators And Psychologists

Author : Virginia Wise Berninger
ISBN : 012092871X
Genre : Education
File Size : 32. 50 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.

Discrete Mathematics Introduction To Mathematical Reasoning

Author : Susanna S. Epp
ISBN : 9781133417071
Genre : Mathematics
File Size : 79. 26 MB
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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.

Abstracts Of Papers Presented To The American Mathematical Society

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ISBN : CORNELL:31924099658993
Genre : Mathematics
File Size : 71. 61 MB
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The Nuts And Bolts Of Proofs

Author : Antonella Cupillari
ISBN : 9780123822178
Genre : Mathematics
File Size : 68. 97 MB
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The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems. New chapter on proof by contradiction New updated proofs A full range of accessible proofs Symbols indicating level of difficulty help students understand whether a problem is based on calculus or linear algebra Basic terminology list with definitions at the beginning of the text

Children S Mathematical Thinking In Primary Years

Author : Julia Anghileri
ISBN : 0826479111
Genre : Education
File Size : 45. 69 MB
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This popular Continuum series, intended chiefly for teachers and trainee teachers, places strong emphasis on practice but at the same time incorporates the latest research in the field. The book demonstrates a strong belief in the ability of children to learn, and in the ability of teachers to increase children's learning potential. The series authors are distinguished practitioners in their fields who write with authority, but without jargon. With the increasingly popular constructivist framework for learning, teachers are coming to recognize the limitations of taught procedures and to find ways to encourage children to generate their own knowledge and understanding in mathematics. The challenge for teachers is to promote an environment that encourages mathematical thinking in which pupils of all abilities are able to achieve their full potential. This text brings together experiences of teachers and researchers who examine the ways children work mathematically, in order to provide an enhanced learning environment within the classroom. It also addresses key issues in current maths teaching.

Books In Print

Author : R.R. Bowker Company
ISBN : UOM:39015054035236
Genre : American literature
File Size : 44. 78 MB
Format : PDF
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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

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