Download or read book The Equidistribution of Lattice Shapes of Rings of Integers of Cubic Quartic and Quintic Number Fields written by Piper Harron and published by Birkhäuser. This book was released on 2018-11-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to explain the author’s joint work with Manjul Bhargava in a fun and accessible way. On its face, the subject matter concerns properties of number fields, namely the shape (literally and mathematically) of their rings of integers. The result says essentially that the ring of integers of a random number field should not have any special symmetries when viewed as a lattice in real space. The proof requires a parametrization, a counting method, an understanding of conditions mod p, a way to isolate the things we actually want to count, and a volume calculation. This has all been presented to the experts in an eleven page paper. The real purpose of this book, then, is not to present the results and the proof, but to really attempt to explain not just the math but also the struggles, that go into the result.
Download or read book Change and Stability in Thesis and Dissertation Writing written by Brian Paltridge and published by Bloomsbury Publishing. This book was released on 2023-12-14 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining recent changes in the once stable genre of doctoral thesis and dissertation writing, this book explores how these changes impact on the nature of the doctoral thesis/dissertation itself. Covering different theories of genre, Brian Paltridge and Sue Starfield focus on the concepts of evolution, innovation and emergence in the context of the production and reception of doctoral theses and dissertations. Specifically concerned with this genre in the humanities, social sciences and visual and performing arts, this book also investigates the forces which are shaping changes in this high-stakes genre, as well as those which act as constraints. Employing textography as its methodological approach, the book provides multiple perspectives on the ways in which doctoral theses and dissertations are subject to forces of continuity and change in the academy. Analyses of the 'new humanities' doctorate, professional doctorates, practice-based doctorates, and the doctorate by publication contribute to understandings of new variants of the doctoral dissertation genre. The book paves the way for a new generation of doctoral students and asks, 'what might the doctorate of the future look like?'.
Download or read book Creative Research Methods written by Kara, Helen and published by Policy Press. This book was released on 2020-09-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Creative research methods can help to answer complex contemporary questions which are hard to answer using conventional methods alone. Creative methods can also be more ethical, helping researchers to address social injustice. This bestselling book, now in its second edition, is the first to identify and examine the five areas of creative research methods: • arts-based research • embodied research • research using technology • multi-modal research • transformative research frameworks. Written in an accessible, practical and jargon-free style, with reflective questions, boxed text and a companion website to guide student learning, it offers numerous examples of creative methods in practice from around the world. This new edition includes a wealth of new material, with five extra chapters and over 200 new references. Spanning the gulf between academia and practice, this useful book will inform and inspire researchers by showing readers why, when, and how to use creative methods in their research. Creative Research Methods has been cited over 500 times.
Download or read book Qualitative Research for Quantitative Researchers written by Helen Kara and published by SAGE. This book was released on 2022-01-12 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approaching qualitative research for the first time and unsure how to get started? This book captures what you need to know to jump into effective qualitative or mixed methods research. The book gets you up to speed on the specifics of qualitative research, while showing how it complements quantitative research and how to draw on and hone your existing skills to conduct impactful research. It covers the whole research process, from explaining what theories are for and planning your research design, through gathering and working with your data, to developing good practice in research reporting and dissemination. The book also: • Showcases the value of qualitative research, helping you understand its relevance, credibility and validity. • Grapples with how to decolonise your approach, do research in an ethical and inclusive way, and debias your thinking. • Challenges you to rethink how you conduct research and choose the most appropriate methods for your project. Giving you a fuller understanding of methods and methodologies to benefit your work regardless of the approach you choose, this book encourages you to discover the joy of qualitative research.
Download or read book A Conversation on Professional Norms in Mathematics written by Pamela E. Harris and published by American Mathematical Soc.. This book was released on 2021-10-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas. This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.
Download or read book The Female Artist in Academia written by Anastasia Kamanos and published by Rowman & Littlefield. This book was released on 2019-11-07 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book delves into the conflicts, contradictions and paradoxes inherent in the lives of women who, as artists and academics, seek to connect their personal and professional lives in their work. It explores how creativity and the pursuit of self-knowledge relate to their lives and arises from the author's own experience as a woman, writer, and academic. Inquiries into creativity and feminist critical and cultural theory provide the framework for examining how the identity of the female artist is shaped within the patriarchal institution of academia. These inquiries allow a deeper understanding of the impact of this institution on the life and work of the female artist both within and beyond academia. As an auto-ethnographic study, Kamanos' distinctive voice is developed through narratives, journals, letters and a development of personal metaphors, as well as with a dialogue with others. As performative text, the narratives map a process of transformation that traces the artist's path from silence to voice. This book has important implications for women in higher education as self-study is revealed to be an essential methodological instrument for the articulation of alternative, authentic perspectives of marginalized and under-represented women. Moreover, the acknowledgement of the academic/ artist paradigm in teacher education opens the path for a re-viewing of the metaphors of self-denial, impersonation and masks that are part of the landscape of teacher knowledge.
Download or read book Creative Writing for Social Research written by Phillips, Richard and published by Policy Press. This book was released on 2021-01-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This groundbreaking book brings creative writing to social research. Its innovative format includes creatively written contributions by researchers from a range of disciplines, modelling the techniques outlined by the authors. The book is user-friendly and shows readers: • how to write creatively as a social researcher; • how creative writing can help researchers to work with participants and generate data; • how researchers can use creative writing to analyse data and communicate findings. Inviting beginners and more experienced researchers to explore new ways of writing, this book introduces readers to creatively written research in a variety of formats including plays and poems, videos and comics. It not only gives social researchers permission to write creatively but also shows them how to do so.
Download or read book A Survey Of Trace Forms Of Algebraic Number Fields written by P E Conner and published by World Scientific. This book was released on 1984-07-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every finite separable field extension F/K carries a canonical inner product, given by trace(xy). This symmetric K-bilinear form is the trace form of F/K.When F is an algebraic number field and K is the field Q of rational numbers, the trace form goes back at least 100 years to Hermite and Sylvester. These notes present the first systematic treatment of the trace form as an object in its own right. Chapter I discusses the trace form of F/Q up to Witt equivalence in the Witt ring W(Q). Special attention is paid to the Witt classes arising from normal extensions F/Q. Chapter II contains a detailed analysis of trace forms over p-adic fields. These local results are applied in Chapter III to prove that a Witt class X in W(Q) is represented by the trace form of an extension F/Q if and only if X has non-negative signature. Chapter IV discusses integral trace forms, obtained by restricting the trace form of F/Q to the ring of algebraic integers in F. When F/Q is normal, the Galois group acts as a group of isometries of the integral trace form. It is proved that when F/Q is normal of prime degree, the integral form is determined up to equivariant integral equivalence by the discriminant of F alone. Chapter V discusses the equivariant Witt theory of trace forms of normal extensions F/Q and Chapter VI relates the trace form of F/Q to questions of ramification in F. These notes were written in an effort to identify central problems. There are many open problems listed in the text. An introduction to Witt theory is included and illustrative examples are discussed throughout.
Download or read book Quadratic Number Fields written by Franz Lemmermeyer and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
Download or read book Asymptotics of Cubic Number Fields with Bounded Second Successive Minimum of the Trace Form written by Gero Brockschnieder and published by diplom.de. This book was released on 2018-06-26 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number fields, particularly of small degree n, have been treated in detail in several publications during the last years. The subject that has been investigated the most is the computation of lists of number fields K with field discriminant d(K) less than or equal to a given bound D and the computation of the minimal value of the discriminant for a given degree n (and often also signature (r1, r2)) of the number fields. The distinct cases of different degrees, as well as the different numbers of real and complex embeddings, respectively, are usually treated independently of each other since each case itself offers a broad set of problems and questions. In some of the cases the applied methods and algorithms have been notably improved over the years. Each value for the degree n of the investigated fields represents a huge and interesting set of problems and questions that can be treated on its own. The case we will concentrate on in this thesis is n = 3. Algebraic number fields of degree 3 are often referred to as cubic fields and, in a way, their investigation is easier than the investigation of higher degree fields since the higher the degree of the field, the higher the number of possible signatures (i.e. combinations of real and complex embeddings of the field). In this thesis, we will concentrate only on totally real cubic fields. Totally real fields are those fields K for which each embedding of K into the complex numbers C has an image that lies inside the real numbers R. The purpose of this thesis is to show that the number of isomorphism classes of cubic fields K whose second successive minima M2(K), as introduced by Minkowski, are less than or equal to a given bound X is asymptotically equal (in X) to the number of cubic polynomials defining these fields modulo a relation P which will be explained in detail.
Download or read book Representations of Integers as Sums of Squares written by E. Grosswald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.
Download or read book On Representation of Integers by Binary Quadratic Forms in Algebraic Number Fields written by Stig Christofferson and published by . This book was released on 1962 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 4 Ranks of K2 of Rings of Integers in Quadratic Number Fields written by Anthony M. Vazzana and published by . This book was released on 1998 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Normsets and Rings of Algebraic Integers written by James Barker Coykendall and published by . This book was released on 1995 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Quadratic Forms written by Larry J. Gerstein and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics - particularly group theory and topology - as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest - with special attention to the theory over the integers and over polynomial rings in one variable over a field - and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Download or read book Rational Quadratic Forms written by John William Scott Cassels and published by . This book was released on 1978 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids written by William Duke and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
