› › The Equidistribution Of Lattice Shapes Of Rings Of Integers Of Cubic Quartic And Quintic Number Fields

The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields

Author : Piper Harron

Publisher : Birkhäuser

Page : pages

File Size : 10,52 MB

Release : 2018-11-12

Category : Mathematics

ISBN : 9783319765310

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Book Description

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.



Qualitative Research for Quantitative Researchers

Author : Helen Kara

Publisher : SAGE

Page : 222 pages

File Size : 14,49 MB

Release : 2022-01-12

Category : Social Science

ISBN : 1529786193

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Book Description

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.



Change and Stability in Thesis and Dissertation Writing

Author : Brian Paltridge

Publisher : Bloomsbury Publishing

Page : 297 pages

File Size : 44,63 MB

Release : 2023-12-14

Category : Language Arts & Disciplines

ISBN : 1350146587

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Book Description

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?'.



Creative Research Methods

Author : Kara, Helen

Publisher : Policy Press

Page : 320 pages

File Size : 45,15 MB

Release : 2020-09-16

Category : Social Science

ISBN : 1447356748

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Book Description

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.



A Conversation on Professional Norms in Mathematics

Author : Pamela E. Harris

Publisher : American Mathematical Soc.

Page : 138 pages

File Size : 33,74 MB

Release : 2021-10-19

Category : Education

ISBN : 1470467135

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Book Description

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.



Creative Writing for Social Research

Author : Phillips, Richard

Publisher : Policy Press

Page : 224 pages

File Size : 43,48 MB

Release : 2021-01-20

Category : Social Science

ISBN : 1447355989

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Book Description

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.



The Female Artist in Academia

Author : Anastasia Kamanos

Publisher : Rowman & Littlefield

Page : 135 pages

File Size : 11,28 MB

Release : 2019-11-07

Category : Education

ISBN : 1793604118

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Book Description

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.



Analytic Number Theory

Author : Henryk Iwaniec

Publisher : American Mathematical Soc.

Page : 615 pages

File Size : 49,27 MB

Release : 2021-10-14

Category : Education

ISBN : 1470467704

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Book Description

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.



Love and Math

Author : Edward Frenkel

Publisher : Basic Books

Page : 314 pages

File Size : 35,1 MB

Release : 2013-10-01

Category : Mathematics

ISBN : 0465069959

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Book Description

An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.



Spectral Methods of Automorphic Forms

Author : Henryk Iwaniec

Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain

Page : 220 pages

File Size : 39,24 MB

Release : 2021-11-17

Category : Mathematics

ISBN : 1470466228

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Book Description

Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.