New Books Purchased by Campbell Library

by Daniel Kipnis on 2020-10-30T13:00:00-04:00 | 0 Comments

Number Theory Revealed by Andrew Granville

ISBN: 1470441586

Publication Date: 2019-01-04

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ``Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.

An Introduction to Symmetric Functions and Their Combinatorics by Eric S. Egge

ISBN: 1470448998

Publication Date: 2020-01-10

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution $\omega$; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal--familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

The Infinite Book by John D. Barrow

ISBN: 9780375422270

Publication Date: 2005-08-02

An examination of Infinity — in history and science — with excursions into literature, philosophy and religion, written by one of the most successful writers of popular science. Infinity is surely the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Or is infinity just a label for something that is never reached, no matter how long you go on counting? Can you do an infinite number of things in a finite amount of time? Is the universe infinite? But infinity is also the place where things happen that don’t. All manner of strange paradoxes and fantasies characterize an infinite universe. So what is it like to live in a Universe where nothing is original, where you can live forever, where anything that can be done, is done, over and over again? These are some of the deep questions that the idea of the Infinite pushes us to ask. Throughout history, the Infinite has been a dangerous idea. Many have lost their lives, their careers, or their freedom for talking about it. The Infinite Book will take you on a tour of these dangerous questions and the strange answers that scientists, mathematicians, philosophers, and theologians have come up with to deal with its threats to our sanity.

Knowledge and the Philosophy of Number by Keith Hossack; Christopher Gauker (Series edited by); Johannes Brandl (Series edited by); Mark Textor (Series edited by); Max Kolbel (Series edited by)

ISBN: 9781350102903

Publication Date: 2020-02-20

If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects- must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects- they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.

Leadership and Women in Statistics by Amanda L. Golbeck (Editor); Ingram Olkin (Editor); Yulia R. Gel (Editor)

ISBN: 1482236443

Publication Date: 2015-08-03

Learn How to Infuse Leadership into Your Passion for Scientific Research Leadership and Women in Statistics explores the role of statisticians as leaders, with particular attention to women statisticians as leaders. By paying special attention to women's issues, this book provides a clear vision for the future of women as leaders in scientific and technical fields. It also shows how emerging and current leaders of both genders in many disciplines can expand their leadership potentials. Featuring contributions from leadership experts and statisticians at various career stages, this unique and insightful text: Examines leadership within the roles of statistician and data scientist from international and diverse perspectives Supplies a greater understanding of leadership within teams, research consulting, and project management Encourages reflection on leadership behaviors, promoting both natural and organizational leadership Identifies existing opportunities to foster creative outputs and develop strong leadership voices Includes real-life stories about overcoming barriers to leadership Leadership and Women in Statistics explains how to convert a passion for statistical science into visionary, ethical, and transformational leadership. Although the context focuses on statistics, the material applies to almost all fields of endeavor. This book is a valuable resource for those ready to consider leadership as an important element of their careers, and for those who are already leaders but want to deepen their perspectives on leadership. It makes an ideal text for group leadership training as well as for individual professional development.

Pioneering Women in American Mathematics by Judy Green; Jeanne LaDuke

ISBN: 9780821843765

Publication Date: 2008-12-16

More than 14 percent of the PhD's awarded in the United States during the first four decades of the twentieth century went to women, a proportion not achieved again until the 1980s. This book is the result of a study in which the authors identified all of the American women who earned PhD's in mathematics before 1940, and collected extensive biographical and bibliographical information about each of them. By reconstructing as complete a picture as possible of this group of women, Green and LaDuke reveal insights into the larger scientific and cultural communities in which they lived and worked. The book contains an extended introductory essay, as well as biographical entries for each of the 228 women in the study. The authors examine family backgrounds, education, careers, and other professional activities. They show that there were many more women earning PhD's in mathematics before 1940 than is commonly thought. Extended biographies and bibliographical information are available from the companion website for the book: http://www.ams.org/bookpages/hmath-34. The material will be of interest to researchers, teachers, and students in mathematics, history of mathematics, history of science, women's studies, and sociology. The data presented about each of the 228 individual members of the group will support additional study and analysis by scholars in a large number of disciplines.

Power in Numbers by Talithia Williams

ISBN: 1631064851

Publication Date: 2018-05-08

Bringing to life such eminent mathematicians as the astronomer-philosopher Hypatia, theoretical physicist Emmy Noether, and rocket scientist Annie Easley, The Women of Mathematics is an affirmation of female genius and a celebration of the boundless applications of mathematics.

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