A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given.
This is a very readable introduction to number theory, with particular emphasis on diophantine equations, and requires only a school knowledge of mathematics. The exposition is admirably clear. More advanced or recent work is cited as background, where relevant c [T]here are welcome novelties: Gauss's own evaluation of Gauss's sums, which is still perhaps the most elegant, is reproduced apparently for the first time. There are 180 examples, many of considerable interest, some of these being little known.
AMS Chelsea Publishing, Volume: 163;
1964; 309 pp; Softcover
Print ISBN: 978-1-4704-6324-3
Product Code: CHEL/163.S
Not yet published
Expected publication date January 30, 2021
A co-publication of the AMS and Centre de Recherches Mathematiques
The Seventh ARTA (gAdvances in Representation Theory of Algebras VIIh) conference took place at the Instituto de Matematicas of the Universidad Nacional Autonoma de Mexico, in Mexico City, from September 24?28, 2018, in honor of Jose Antonio de la Pena's 60th birthday.
Papers in this volume cover topics Professor de la Pena worked on, such
as covering theory, tame algebras, and the use of quadratic forms in representation
theory. Also included are papers on the categorical approach to representations
of algebras and relations to Lie theory, Cohen?Macaulay modules, quantum
groups and other algebraic structures.
Graduate students and research mathematicians interested in representation theory of algebras.
Contemporary Mathematics, Volume: 761
2021; 257 pp; Softcover
Print ISBN: 978-1-4704-5159-2
Product Code: CONM/761
MAA Press: An Imprint of the American Mathematical Society
Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them?common sense and common knowledge?not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world?this text helps students use it thoughtfully and wisely.
This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully?and critically?about numerical information in everyday contexts.
Undergraduate students interested in taking a Quantitative Literacy course.
AMS/MAA Textbooks, Volume: 63
2021; 342 pp; Softcover
Print ISBN: 978-1-4704-6134-8
Product Code: TEXT/63
Not yet published
Expected publication date March 27, 2021
MAA Press: An Imprint of the American Mathematical Society
Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout.
The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course.
Undergraduate students interested in abstract algebra.
AMS/MAA Textbooks, Volume: 65
2021; 592 pp; Softcover
Print ISBN: 978-1-4704-6030-3
Product Code: TEXT/65
Not yet published
Expected publication date April 4, 2021
Not yet published - available from January 2021
FORMAT: Hardback
ISBN: 9780521197427
This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey?Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapters cover orthogonal polynomials on the unit circle, zeros of orthogonal polynomials and matrix orthogonal polynomials, with detailed results about matrix-valued Jacobi polynomials. A chapter on moment problems provides many examples of indeterminate moment problems. A thorough bibliography rounds off what will be an essential reference.
A necessary update of the Bateman Manuscript Project for the twenty-first century
Offers an encyclopedic source of various properties and formulas for special functions
Now includes special functions not treated elsewhere
ISBN : 9780198871378
608 Pages
Format Hardcover
Size 156 x 234 mm
Pub date Jan 2021
Softcover 9780198871385
Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac Lane. It describes relationships between mathematical structures. Outside of pure mathematics, category theory is an important tool in physics, computer science, linguistics, and a quickly-growing list of other sciences. This book is about 2-dimensional categories, which add an extra dimension of richness and complexity to category theory. 2-Dimensional Categories is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax functors, 2-/bilimits, the Duskin nerve, 2-nerve, internal adjunctions, monads in bicategories, 2-monads, biequivalences, the Bicategorical Yoneda Lemma, and the Coherence Theorem for bicategories. Grothendieck fibrations and the Grothendieck construction are discussed next, followed by tricategories, monoidal bicategories, the Gray tensor product, and double categories. Completely detailed proofs of several fundamental but hard-to-find results are presented for the first time. With exercises and plenty of motivation and explanation, this book is useful for both beginners and experts.