Gre Mathematics Subject Test Gr0568 And Gr9768 Solutions

Author: Charles Rambo
Publisher: CreateSpace
ISBN: 9781500171933
Size: 41.48 MB
Format: PDF
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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
Size: 28.57 MB
Format: PDF
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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
Size: 34.15 MB
Format: PDF, Kindle
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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.

Fermat S Last Theorem

Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780387950020
Size: 74.71 MB
Format: PDF, Docs
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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.

Advanced Calculus

Author: Patrick Fitzpatrick
Publisher: American Mathematical Soc.
ISBN: 9780821847916
Size: 68.85 MB
Format: PDF, Docs
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Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.

Complex Variables

Author: Joseph L. Taylor
Publisher: American Mathematical Soc.
ISBN: 0821869019
Size: 71.20 MB
Format: PDF, Mobi
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The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem.

Problems In Abstract Algebra

Author: A. R. Wadsworth
Publisher: American Mathematical Soc.
ISBN: 1470435837
Size: 46.45 MB
Format: PDF, ePub, Docs
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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.

Counterexamples In Analysis

Author: Bernard R. Gelbaum
Publisher: Courier Corporation
ISBN: 0486134911
Size: 35.81 MB
Format: PDF, ePub, Docs
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These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.

A Romp Tour Of Trigonometry

Author: Charles Rambo
Publisher: Createspace Independent Publishing Platform
ISBN: 9781978327887
Size: 35.42 MB
Format: PDF, ePub, Docs
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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.