Number Theory Through Inquiry

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Number Theory Through Inquiry

Author : David C. Marshall
ISBN : 9780883857519
Genre : Mathematics
File Size : 29.22 MB
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This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.
Category: Mathematics

Topology Through Inquiry

Author : Michael Starbird
ISBN : 9781470462611
Genre : Education
File Size : 69.8 MB
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Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
Category: Education

The Whole Truth About Whole Numbers

Author : Sylvia Forman
ISBN : 9783319110356
Genre : Mathematics
File Size : 69.30 MB
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The Whole Truth About Whole Numbers is an introduction to the field of Number Theory for students in non-math and non-science majors who have studied at least two years of high school algebra. Rather than giving brief introductions to a wide variety of topics, this book provides an in-depth introduction to the field of Number Theory. The topics covered are many of those included in an introductory Number Theory course for mathematics majors, but the presentation is carefully tailored to meet the needs of elementary education, liberal arts, and other non-mathematical majors. The text covers logic and proofs, as well as major concepts in Number Theory, and contains an abundance of worked examples and exercises to both clearly illustrate concepts and evaluate the students’ mastery of the material.
Category: Mathematics

A Radical Approach To Lebesgue S Theory Of Integration

Author : David M. Bressoud
ISBN : 9780521884747
Genre : Mathematics
File Size : 21.61 MB
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Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
Category: Mathematics

A Pythagorean Introduction To Number Theory

Author : Ramin Takloo-Bighash
ISBN : 9783030026042
Genre : Mathematics
File Size : 44.56 MB
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Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.
Category: Mathematics

Conceptions Of Inquiry

Author : Stuart Brown
ISBN : 9781134948260
Genre : Philosophy
File Size : 41.30 MB
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First Published in 1981. Routledge is an imprint of Taylor & Francis, an informa company.
Category: Philosophy

Teaching High School Science Through Inquiry

Author : Douglas Llewellyn
ISBN : 0761939385
Genre : Education
File Size : 36.4 MB
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Acknowledging the importance of national standards, offers case studies, tips, and tools to encourage student curiosity and improve achievement in science.
Category: Education

Teaching High School Science Through Inquiry And Argumentation

Author : Douglas Llewellyn
ISBN : 9781452279640
Genre : Education
File Size : 79.1 MB
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Proven ways to teach next generation science! To ensure our students achieve scientific literacy, we need to know what works in science teaching. One thing we know for certain: inquiry and argumentation are key. This groundbreaking book for Grades 9–12 addresses the new direction of science standards by emphasizing both inquiry-based and argument-based instruction. Filled with case studies and vignettes, this edition features: Exceptional coverage of scientific argumentation Enhanced chapters on assessment and classroom management Questioning techniques that promote the most learning Activities that emphasize making claims and citing evidence New examples of inquiry investigations New approaches to traditional labs
Category: Education

Euclidean And Transformational Geometry A Deductive Inquiry

Author : Shlomo Libeskind
ISBN : 9781449650094
Genre : Mathematics
File Size : 43.22 MB
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Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.
Category: Mathematics

Phenomenological Inquiry

Author :
ISBN : STANFORD:36105017876900
Genre : Phenomenology
File Size : 24.63 MB
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Category: Phenomenology

Sophie Germain

Author : L.L. Bucciarelli
ISBN : 9789400990517
Genre : History
File Size : 48.72 MB
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Why should the story of a woman's role in the development of a scientific theory be written? Is it to celebrate, as some have done, the heroism of a woman's struggle in a man's world? Or is it, rather~to demonstrate that gender is irrelevant to the march of scientific ideas? This book hopes to do neither. Rather, it intends to do justice both to the professional life of a woman in science and to the development of the theory with which she was engaged. Technically, this essay centers on Sophie Germain's analysis of the modes of vibration of elastic surfaces, work which won a competition set by the French Academy of Sciences in 1809. It also evaluates related work on the mathematical theory of elasticity done by men of the Academy. Biographically, it is about a woman who believed in the greatness of science and strove, with some measure of success, to participate in that noble, but wholly male-dominated, enterprise. It explores her failures, analyzes her success, and describes how the members of the Parisian scientific community dealt with her offerings, contributions and demands.
Category: History

Essays On The Theory And Practice Of Index Numbers

Author : Kam Yu
ISBN : 9783639212372
Genre : Econometrics
File Size : 63.46 MB
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Economic measurement has over the years become an important subject in academic and policy researches. Debates in the development of macroeconomic theory and public policy rely on accurate feedback of aggregate data. This book fills the gap between the theory and practice in index numbers. It reviews and explores several important topics which lead to improvement in measuring price and output indices. These include econometric problems in hedonic regression, treatment of seasonal goods in the CPI, output and productivity measurement of government services, efficiency analysis of the health care sector, and a novel approach in calculating the cost-of-living indices for products involving risk and uncertainty. The book serves as a valuable references for academic economists, policy analysts, and economic statisticians.
Category: Econometrics

Language Form And Inquiry

Author : James F. Ward
ISBN : UOM:39015056107959
Genre : Social Science
File Size : 82.60 MB
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Category: Social Science

Number Shape Symmetry

Author : Diane L. Herrmann
ISBN : 9781466554641
Genre : Mathematics
File Size : 30.94 MB
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Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Category: Mathematics

Correspondence H Z

Author : Kurt Gödel
ISBN : 0198500750
Genre : Computers
File Size : 84.5 MB
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The collected works of Kurt Godel is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.
Category: Computers

Kurt G Del Collected Works

Author : Kurt Gödel
ISBN : 9780191003776
Genre : Mathematics
File Size : 43.88 MB
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Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.
Category: Mathematics

Computer And Intrusion Forensics

Author : George M. Mohay
ISBN : 1580536301
Genre : Computers
File Size : 88.81 MB
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Annotation A comprehensive and broad introduction to computer and intrusion forensics, covering the areas of law enforcement, national security and corporate fraud, this practical book helps professionals understand case studies from around the world, and treats key emerging areas such as stegoforensics, image identification, authorship categorization, and machine learning.
Category: Computers