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Author: James McKee
Publisher: Springer Nature
ISBN: 3030800318
Category : Mathematics
Languages : en
Pages : 444
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Book Description
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Author: James McKee
Publisher: Springer Nature
ISBN: 3030800318
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Author: Ralph Emerson
Publisher: American Roots
ISBN: 9781429096249
Category : Nature
Languages : en
Pages : 0
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Book Description
Transcendentalist Ralph Waldo Emerson's 1841 essay "Circles" reflects on the endless circles found in nature, and the fluidity of the universe. He encourages the embracing of new thoughts and ideas: "No truth so sublime but it may be trivial to-morrow in the light of new thoughts. People wish to be settled; only as far as they are unsettled is there any hope for them." This short work is part of Applewood's American Roots, series, tactile mementos of American passions by some of America's most famous writers and thinkers.
Author: National Academy of Sciences (U.S.)
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 452
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Book Description
The Proceedings of the National Academy of Sciences (PNAS) publishes research reports, commentaries, reviews, colloquium papers, and actions of the Academy. PNAS is a multidisciplinary journal that covers the biological, physical, and social sciences.
Author: Timothy Rasinski
Publisher: Teacher Created Materials
ISBN: 1425896308
Category : Language Arts & Disciplines
Languages : en
Pages : 195
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Book Description
Expand your students' content-area vocabulary and improve their understanding with this roots-based approach! This standards-based resource, geared towards secondary grades, helps students comprehend informational text on grade-level topics mathematics using the most common Greek and Latin roots. Each lesson provides tips on how to introduce the selected roots and offers guided instruction to help easily implement the activities. Students will be able to apply their knowledge of roots associated with specific subject areas into their everyday vocabulary.
Author: Becca Piastrelli
Publisher: Sounds True
ISBN: 1683647734
Category : Body, Mind & Spirit
Languages : en
Pages : 0
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Book Description
A beautifully illustrated guide for connecting with the earth, your ancestors, and your communities as you come home to your whole self Despite our best efforts, our modern world leaves so many of us feeling isolated, unworthy, and alone. We’re unrooted from the land, untethered from our lineages, disconnected from our communities, and separated from our deepest sense of self. In Root and Ritual, Becca Piastrelli offers a pathway back to connection and wholeness through rituals, recipes, and ancestral wisdom. “Though we live in a radically different-looking world, the needs of our bodies and spirits are the same as the ancestors we came from.” Divided into four parts—Land, Lineage, Community, and Self—this book takes you on a journey for engaging more deeply with your life: Part 1 introduces practices for reconnecting with the land, including seasonal recipes, crafting with plants, and tending your homeIn Part 2, you’ll learn to reclaim the gifts of your lineage as you understand past harms and explore the traditional folklore, foods, and arts of those who came beforePart 3 centers around community, helping you cultivate sisterhood and celebrate meaningful rites of passageIn Part 4, you’ll return to yourself as you open your intuition, tune in to your body, and awaken the wild woman within A rich and dynamic treasure chest of timeless teachings, Root and Ritual is a beautiful guide for knowing who you are—and that you belong here.
Author: Talal Ghannam
Publisher: Talal Ghannam
ISBN: 1477678417
Category : Science
Languages : en
Pages : 319
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Book Description
What is it that brings all these different things together? The subatomic particles and the Vedic square. The hydrogen atom and the golden section. Fibonacci numbers, consciousness, and alchemy. Nikola Tesla, music, and the ether. Electromagnetism, gravity, and the fourth dimension. The procession of the equinox, the Mayan dooms day, the Hindu Brahma cycle, and Atlantis. It is Numbers, or more precisely; their Digital Root. In this book the author examines the amazing world of numbers, particularly those which have intrigued and fascinated ancient and modern mathematicians alike. However, he does it from a very novel point of view; by implementing the digital root operation, in which the individual digits of any of these numbers are summed up until a single digit is left over. The author will show that when applying this simple operation to magical numbers, and to many other groups of numbers, an amazing world of hidden interconnections; repetition cycles; numerical symmetries; and geometrical patterns emerge. Especially when the geometrical (the circle) and the numerical aspects of the digital root world are combined together. It is in this circular/numerical world where numbers, individually and collectively, exist in their most basic, yet perfect and symmetrical states, and where the basic nine numbers are differentiated into three groups of amazing properties, which will be shown to underlie the essence of the whole universe; from the atom and its forces to the solar system and its geometry. This book will take us on a numerical and spiritual journey: starting from prime and figurate numbers; to Fibonacci sequence and the golden section; to alchemy and the Mayan calendar; to the atoms and its forces, along with the ether and the fourth dimension. In addition, the author will show how these new revelations of the digital root world are corroborating the numerological and mystical qualities that have been attributed to numbers by philosophers and mystics throughout the ages. This book will paint a so holistic and meaningful image of the world that will forever change our perception, not only towards numbers, but towards the whole universe as well.
Author: J.M. McNamee
Publisher: Elsevier Inc. Chapters
ISBN: 012807700X
Category : Mathematics
Languages : en
Pages : 87
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Book Description
This chapter treats several topics, starting with Bernoulli’s method. This method iteratively solves a linear difference equation whose coefficients are the same as those of the polynomial. The ratios of successive iterates tends to the root of largest magnitude. Special versions are used for complex and/or multiple roots. The iteration may be accelerated, and Aitken’s variation finds all the roots simultaneously. The Quotient-Difference algorithm uses two sequences(with a similar one for ). Then, if the roots are well separated, . Special techniques are used for roots of equal modulus. The Lehmer–Schur method uses a test to determine whether a given circle contains a root or not. Using this test we find an annulus which contains a root, whereas the circle does not. We cover the annulus with 8 smaller circles and test which one contains the roots. We repeat the process until a sufficiently small circle is known to contain the root. We also consider methods using integration, such as by Delves–Lyness and Kravanja et al.
Author:
Publisher: Prestwick House Inc
ISBN: 9781580498708
Category : English language
Languages : en
Pages : 260
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Book Description
Each chapter includes two to four Greek or Latin roots, up to a dozen vocabulary words, word histories and common phrases. Matching exercises, word searches, crossword puzzles, and writing exercises provide review.
Author: Tsuruichi Hayashi
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Author: John Michels (Journalist)
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 742
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Book Description
