Around the Unit Circle PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Around the Unit Circle PDF full book. Access full book title Around the Unit Circle by James McKee. Download full books in PDF and EPUB format.
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: 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: Encyclopaedias
Publisher:
ISBN:
Category :
Languages : en
Pages : 1388
Get Book Here
Book Description
Author:
Publisher: Prestwick House Inc
ISBN: 9781580498708
Category : English language
Languages : en
Pages : 260
Get Book Here
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:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 736
Get Book Here
Book Description
Vols. for 1911-13 contain the Proceedings of the Helminothological Society of Washington, ISSN 0018-0120, 1st-15th meeting.
Author: Edinburgh Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 848
Get Book Here
Book Description
Author: J.M. McNamee
Publisher: Elsevier Inc. Chapters
ISBN: 012807700X
Category : Mathematics
Languages : en
Pages : 87
Get Book Here
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: Timothy Rasinski
Publisher: Teacher Created Materials
ISBN: 1425896294
Category : Language Arts & Disciplines
Languages : en
Pages : 179
Get Book Here
Book Description
Expand your students' content-area vocabulary and improve their understanding with this roots-based approach! This standards-based resource, geared towards fifth grade, helps students comprehend informational text on grade-level topics in science, social studies, and 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:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 300
Get Book Here
Book Description
Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.
Author: Charles Baker
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 438
Get Book Here
Book Description
Author: Robert Kourik
Publisher:
ISBN: 9780961584863
Category :
Languages : en
Pages : 225
Get Book Here
Book Description
Understanding Roots uncovers one of the greatest mysteries underground—the secret lives and magical workings of the roots that move and grow invisibly beneath our feet. Roots, it seems, do more than just keep a plant from falling over: they gather water and nutrients, exude wondrous elixirs to create good soil, make friends with microbes and fungi, communicate with other roots, and adapt themselves to all manner of soils, winds, and climates, nourishing and sustaining our gardens, lawns, and woodlands. Understanding Roots contains over 115 enchanting and revealing root drawings that most people have never seen, from prairies, grasslands, and deserts, as well as drawings based on excavations of vegetable, fruit, nut, and ornamental tree roots. Every root system presented in this book was drawn by people literally working in the trenches, sketching the roots where they grew. The text provides a verydetailed review of all aspects of transplanting; describes how roots work their magic to improve soil nutrients; investigates the hidden life of soil microbes and their mysterious relationship to roots; explores the question of whether deep roots really gather more unique nutrients than shallow roots; shares the latest research about the mysteries of mycorrhizal (good fungal) association; shows you exactly where to put your fertilizer, compost, water, and mulch to help plants flourish; tells you why gray water increases crop yields more than fresh water; and, most importantly, reveals the science behind all the above (with citations for each scientific paper). This book contains at least eighty percent more new information, more results of the latest in-depth and up-to-date explorations, and even more helpful guidelines on roots than the author’s previous book (Roots Demystified: Change Your Garden Habits to Help Roots Thrive). This is not a revised edition—it’s a whole new stand-alone book.
