## Gre Mathematics Subject Test Gr0568 and Gr9768 Solutions

Author: Charles Rambo
Publisher: CreateSpace
ISBN: 9781500171933
Format: PDF, Docs

Approachable solutions for two official GRE mathematics subject tests--the GR0568 and GR9768. The booklet contains 84 pages of solutions and a 12 page glossary. The purpose of this booklet is simple: To help students study. Solutions have enough detail to aid those struggling, but the design is such that it is also suitable as a reference. All major theorems are stated either within the main text, glossary, or both. In particular, great pains were taken to include theorems from Calculus and below. Everything is written from an intuitive perspective. Graphs are used extensively, and geometric arguments are frequently utilized. Constructive solutions are given whenever possible.

## GRE Mathematics Subject Test Solutions

Author: Charles Rambo
Publisher: Createspace Independent Publishing Platform
ISBN: 9781533659347
Format: PDF, ePub, Mobi

The purpose of this text is simple: It's to help students study. This booklet is intended to have enough detail to help struggling students understand key concepts. The design is such that solutions are self-contained and you can easily see what theorems are used. Major theorems are precisely formulated, either within the main text, the glossary, or both. From preface.

## Cracking the GRE Mathematics Subject Test

Author: Steven A. Leduc
Publisher: Princeton Review
ISBN: 0375429727
Format: PDF, ePub, Docs

Each test-preparation handbook is designed to help students achieve high scores on a particular exam and includes thorough reviews of the subject matter, practice questions with detailed answer explanations and helpful test-taking skills.

Author: David C. Ullrich
Publisher: American Mathematical Soc.
ISBN: 0821844792
Format: PDF, ePub

Perhaps uniquely among mathematical topics, complex analysis presents the student with the opportunity to learn a thoroughly developed subject that is rich in both theory and applications. Even in an introductory course, the theorems and techniques can have elegant formulations. But for any of these profound results, the student is often left asking: What does it really mean? Where does it come from? In Complex Made Simple, David Ullrich shows the student how to think like an analyst. In many cases, results are discovered or derived, with an explanation of how the students might have found the theorem on their own. Ullrich explains why a proof works. He will also, sometimes, explain why a tempting idea does not work. Complex Made Simple looks at the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains.Ullrich also takes considerable care to discuss the modular group, modular function, and covering maps, which become important ingredients in his modern treatment of the often-overlooked original proof of the Big Picard Theorem. This book is suitable for a first-year course in complex analysis. The exposition is aimed directly at the students, with plenty of details included. The prerequisite is a good course in advanced calculus or undergraduate analysis.

## Measure and Integral

Author: Richard L. Wheeden
Publisher: CRC Press
ISBN: 1498702902
Format: PDF, ePub, Docs

Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content. Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables Includes many new exercises not present in the first edition This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.

## All the Mathematics You Missed

Author:
Publisher: 清华大学出版社有限公司
ISBN: 9787302090854
Format: PDF, ePub, Docs

## Fermat s Last Theorem

Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780387950020
Format: PDF

This introduction to algebraic number theory via "Fermat's Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummer theory of "ideal" factorization. In treats elementary topics, new concepts and techniques; and it details the application of Kummer theory to quadratic integers, relating it to Gauss theory of binary quadratic forms, an interesting connection not explored in any other book.

## Algebraic Number Theory

Author: Edwin Weiss
Publisher: Courier Corporation
ISBN: 048615436X
Format: PDF, ePub, Docs

Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

## Problems in Abstract Algebra

Publisher: American Mathematical Soc.
ISBN: 1470435837
Format: PDF

This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.

## A Romp Tour of Trigonometry

Author: Charles Rambo
Publisher: Createspace Independent Publishing Platform
ISBN: 9781978327887
Format: PDF, ePub, Mobi

Trigonometry is a sore spot for many students. Not only are the topics hard, but STEM majors see them come up again and again in their classes. Where is a student to go for help? Most trigonometry texts are either extremely expensive, shallow, or old and not well suited for current STEM curricula. Hence, the motivation for A Romp Tour of Trigonometry. It has all the topics students need and they are presented in a modern fashion. This text is designed for students going into Calculus and physics. The trigonometric identities needed for Calculus are emphasized. There is a thorough treatment of polar coordinates. Vectors are addressed, including treatment of the dot product. There are several applications of vectors, such as work and force problems, which will be helpful in physics. A Romp Tour of Trigonometry also provides a more robust theoretical backing of ideas than most trigonometry texts. Most notably it introduces the geometric study of triangles, including a study of triangle congruence and similarity of triangles. This provides students with a richer foundation on which to analyze trigonometry. The majority of students learn more easily when first introduced to ideas within a concrete setting as opposed to introducing ideas by providing general principles. Frequently, students don't even look at their books, because their texts approach concepts from a perspective that is too abstract for someone learning the material for the first time. For most students, a general understanding of ideas must be built slowly by means of analyses of specific cases. As a result, the emphasis of this text is teaching by means of examples. Abstract ideas are covered, but new ideas are always reiterated more concretely. Furthermore, the examples provide students with an enriched sense of the mathematics, because they provide intuition and explore more ways to formulate problems. A Romp Tour of Trigonometry is also unique because it doesn't solve problems the way most books do. Instead, it solves them the way students do: based on core ideas. Formulas are used sparingly, unlike in most math books. For example, A Romp Tour of Trigonometry only uses one formulation of the Law of Cosines. Usually, two formulations are provided, one for side lengths and another for angle measures. It makes solving the problems computationally easier, but almost all students forget all but one formulation voiding the benefit. The approach of this text requires more algebra, but it teaches students to solve problems in a more realistic way. Problem-solving is a critical component of learning mathematics. More than enough exercises are included for students to obtain a thorough understanding of the material. Furthermore, the problems cover a wide range of difficulty, which means A Romp Tour of Trigonometry will be helpful to trigonometry students at many skill levels.