Quantum Scientific Publishing (QSP) is committed to providing publisher-quality, low-cost Science, Technology, Engineering, and Math (STEM) content to teachers, students, and parents around the world. This book is the third of four volumes in Algebra 2, containing lessons 91 - 135. Volume I: Lessons 1 - 45 Volume II: Lessons 46 - 90 Volume III: Lessons 91 - 135 Volume IV: Lessons 136 - 180 This title is part of the QSP Science, Technology, Engineering, and Math Textbook Series.

Quantum Scientific Publishing (QSP) is committed to providing publisher-quality, low-cost Science, Technology, Engineering, and Math (STEM) content to teachers, students, and parents around the world. This book is the third of four volumes in General Math, containing lessons 91 - 135. Volume I: Lessons 1 - 45 Volume II: Lessons 46 - 90 Volume III: Lessons 91 - 135 Volume IV: Lessons 136 - 180 This title is part of the QSP Science, Technology, Engineering, and Math Textbook Series.

Quantum Scientific Publishing (QSP) is committed to providing publisher-quality, low-cost Science, Technology, Engineering, and Math (STEM) content to teachers, students, and parents around the world. This book is the third of four volumes in Pre-Algebra, containing lessons 91 - 135. Volume I: Lessons 1 - 45 Volume II: Lessons 46 - 90 Volume III: Lessons 91 - 135 Volume IV: Lessons 136 - 180 This title is part of the QSP Science, Technology, Engineering, and Math Textbook Series.

Prodigy Books is committed to providing publisher-quality, low-cost, outstanding educational content to teachers, students, and parents around the world. This book is the third of four volumes in Spanish 1, containing lessons 91 - 135. Volume I: Lessons 1 - 45 Volume II: Lessons 46 - 90 Volume III: Lessons 91 - 135 Volume IV: Lessons 136 - 180 This title is part of the Prodigy Books Textbook Series.

The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such areas as functional and real analysis, group theory, measure and set theory, probability, and topology. Finding solutions to the problems they proposed has been ongoing since World War II, with prizes offered in many cases to those who are successful. In the 35 years since the first edition published, several more problems have been fully or partially solved, but even today many still remain unsolved and several prizes remain unclaimed. In view of this, the editor has gathered new and updated commentaries on the original 193 problems. Some problems are solved for the first time in this edition. Included again in full are transcripts of lectures given by Stanislaw Ulam, Mark Kac, Antoni Zygmund, Paul Erdös, and Andrzej Granas that provide amazing insights into the mathematical environment of Lwów before World War II and the development of The Scottish Book. Also new in this edition are a brief history of the University of Wrocław’s New Scottish Book, created to revive the tradition of the original, and some selected problems from it. The Scottish Book offers a unique opportunity to communicate with the people and ideas of a time and place that had an enormous influence on the development of mathematics and try their hand on the unsolved problems. Anyone in the general mathematical community with an interest in the history of modern mathematics will find this to be an insightful and fascinating read.

This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.

This book studies when a prime p can be written in the form x2+ny2. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of p=x2+ny2. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields. The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.