How Many Zeroes

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.

The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to … translate verbal discussions into analytical data.learn problem-solving methods for attacking collections of analytical questions or data.build a personal arsenal of internalized problem-solving techniques and solutions.become “armed problem solvers”, ready to do battle with a variety of puzzles in different areas of life.Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a “Challenge Problem” is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is available.

A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra. It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study. This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

This year has witness major changes in the field of academics; where CBSE’s reduced syllabus was a pleasant surprise while the introduction of 2 Term exam pattern was little uncertain for students, parents and teachers as well. Now more than ever the Sample Papers have become paramount importance of subjects with the recent changes prescribed by the board. Give final punch to preparation for CBSE Term 1 examination with the all new edition of ‘Sample Question Papers’ that is designed as per CBSE Sample Paper that are issued on 02 Sept, 2021 for 2021 – 22 academic session. Encouraging with the motto of ‘Keep Practicing, Keep Scoring’, here’s presenting Sample Question Paper – Mathematics (Basic) for Class 10th that consists of: 1. 10 Sample Papers along with OMR Sheet for quick revision of topics. 2. One Day Revision Notes to recall the concepts a day before exam 3. The Qualifiers – Chapterwise sets of MCQs to check preparation level of each chapter 4. CBSE Question Bank are given for complete practice 5. Latest CBSE Sample Paper along with detailed answers are provided for better understanding of subject. TOC One Day Revision, The Qualifiers, CBSE Qualifiers, CBSE Question Bank, Latest CBSE Sample Paper, Sample Paper (1- 10).

Emphasizes the conceptual and historical continuity of analytic function theory. This book covers canonical topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It also features chapters on majorization and on functions holomorphic in a half-plane.

Humor writer Sue Langenberg has written a weekly humor column for more than ten years in various newspapers, often winning placement in HumorPress.com contests. In her book, "Hot Flashes," she has compiled 101 timely examples that represent one goofy hag's take on life using wry and sometimes edgy humor. She never forgot anything in her Boomer life that made her laugh, but rather stored it until the time was right. The stories begin as an ordinary observation of reality and rapidly turn into a wild ride full of laughs, all within some 600 words of wit that strike a chord with young, old, teen and like-hags. There is something to laugh about for everyone in her musings.