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Author: Benjamin Hutz
Publisher: American Mathematical Soc.
ISBN: 1470430975
Category : Mathematics
Languages : en
Pages : 330
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Book Description
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Author: Benjamin Hutz
Publisher: American Mathematical Soc.
ISBN: 1470430975
Category : Mathematics
Languages : en
Pages : 330
Get Book Here
Book Description
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Author: Victor H. Moll
Publisher: American Mathematical Soc.
ISBN: 0821887955
Category : Mathematics
Languages : en
Pages : 530
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Book Description
New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to discover and interesting properties of these functions. The book provides a transition between elementary mathematics and more advanced topics, trying to make this transition as smooth as possible. Many topics occur in the book, but they are all part of a bigger picture of mathematics. By delving into a variety of them, the reader will develop this broad view. The large collection of problems is an essential part of the book. The problems vary from routine verifications of facts used in the text to the exploration of open questions. Book jacket.
Author: Gary E. Schwartz
Publisher: Simon and Schuster
ISBN: 0743477413
Category : Philosophy
Languages : en
Pages : 324
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Book Description
Can science lead to God? Esteemed scientist and theoretician Dr. Gary Schwartz tackles this question as he takes readers on a journey of discovery to the miraculous place where science and spirituality meet. Illustrations throughout.
Author: Edmund Harriss
Publisher: The Experiment
ISBN: 1615196846
Category : Juvenile Nonfiction
Languages : en
Pages : 40
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Book Description
Learning meets wonder when you invite numbers to come play in your imagination! First think of One peeking out from the night Like a point, or a dot, or a shimmering light. But when One finds a friend to run from or run to, Then we can’t call both “One”—that new One must be Two! And should you want something to go in between, You’ll need a new number, a number like Three. Four makes a square when it’s standing around, But what would you see if it flies off the ground? And then when another new One comes to mind, Yell out its name if you know it . . . it’s Five! Do you like the way that these numbers are sounding? Then join our adventure to count beyond counting! Hello Numbers! What Can You Do? is not like any other counting book. As each “new One” appears on the scene, the numbers’ antics hint at ever-deeper math. Young readers ages 3 to 6 will not only count along, but begin to wonder about symmetry, angles, shapes, and more. Written by the mathematician-and-poet team Edmund Harriss and Houston Hughes, and illustrated by longstanding New York Times artist Brian Rea, this rollicking, rhyming book will take you to a whole new world of numbers.
Author: Larry L. Orr
Publisher: SAGE
ISBN: 9780761912958
Category : Computers
Languages : en
Pages : 284
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Book Description
Intended to provide a basic understanding not only of how to design and implement social experiments, but also of how to interpret their results once they are completed, author Larry L. Orr's Social Experiments is written in a friendly, how-to manner. Through the use of illustrative examples, how-to exhibits and cases, and boldface key words, Orr provides readers with a grounding in the experimental method, including the rational and ethical issues of random assignment; designs that best address alternative policy questions; maximizing the precision of the estimates; implementing the experiment in the field; data collection; estimating and interpreting program impacts, costs, and benefits; dealing with potential biases; and the use and misuse of experimental results in the policy process. This book will be useful not only to those who plan to conduct experiments, but also to the much larger group who will, at one time or another, want to understand the results of experimental evaluations.
Author: Fernando Rodriguez Villegas
Publisher: Oxford University Press, USA
ISBN: 0198528221
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, are provided along with exercises and selected solutions.
Author: Sarwar Beg
Publisher: Springer Nature
ISBN: 9813343516
Category : Medical
Languages : en
Pages : 190
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Book Description
This book volume provides complete and updated information on the applications of Design of Experiments (DoE) and related multivariate techniques at various stages of pharmaceutical product development. It discusses the applications of experimental designs that shall include oral, topical, transdermal, injectables preparations, and beyond for nanopharmaceutical product development, leading to dedicated case studies on various pharmaceutical experiments through illustrations, art-works, tables and figures. This book is a valuable guide for all academic and industrial researchers, pharmaceutical and biomedical scientists, undergraduate and postgraduate research scholars, pharmacists, biostatisticians, biotechnologists, formulations and process engineers, regulatory affairs and quality assurance personnel.
Author: Gebhard Böckle
Publisher: Springer
ISBN: 3319705660
Category : Mathematics
Languages : en
Pages : 753
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Book Description
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
Author: James Bicheno Francis
Publisher:
ISBN:
Category : Hydraulic motors
Languages : en
Pages : 372
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Book Description
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1264
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Book Description
