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Offers suggestions and techniques to help students prepare for the Graduate Record Examination subject test in mathematics, and includes a full-length sample test with answers and explanations
Comprehensive Prep for GRE Math. Every year, students pay $1,000 and more to test prep companies to prepare for the math section of the GRE. Now you can get the same preparation in a book. Although the GRE math section is difficult, it is very learnable. GRE Math Prep Course presents a thorough analysis of GRE math and introduces numerous analytic techniques that will help you immensely, not only on the GRE but in graduate school as well. Features: * Comprehensive Review: Twenty-three chapters provide complete review of GRE math. * Practice: Includes 164 examples and more than 600 exercises! Arranged from easy to medium to hard to very hard. * Diagnostic Test: The diagnostic test measures your strengths and weaknesses and directs you to areas you need to study more. * Duals: These are pairs of similar problems in which only one property is different. They illustrate the process of creating GRE questions. * If your target is a top score, this is the book!
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
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.
This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, Lie theory, representation theory, and group theory.
Named “Best Mathematics Subject GRE Test Guide” by The Daily News! THE PRINCETON REVIEW GETS RESULTS. Getting a high score on the GRE Mathematics Subject Test isn’t about memorizing everything there is to know about math–it’s about targeting your test preparation. We teach you only the information you’ll need along with the best strategies for the test day. Within this book, you’ll find practical information on the what, when, where, and how of the exam, as well as subject reviews for all potential topics, including precalculus, calculus I and II, differential equations, linear algebra, number theory, and more. Techniques That Actually Work. • Preparation strategies and test-taking techniques to help you reach your top score • Shortcuts and strategies to speed up pacing and increase accuracy • Clear diagrams to acclimate you to three-dimensional coordinate problems Practice Your Way to Excellence. • 1 full-length practice test to familiarize you with the quirks and patterns of the GRE Mathematics Subject Test • Over 150 guided practice problems that directly demonstrate key strategies for dealing with tricky topics from trigonometric functions to double integrals, homomorphisms, and complex logarithms • Over 200 drill questions for independent practice, with thorough explanations to help provide total content mastery
Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory. A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.
Magoosh gives students everything they need to make studying a breeze. We've branched out from our online GRE prep program and free apps to bring you this GRE prep book. We know sometimes you don't have easy access to the Internet--or maybe you just like scribbling your notes in the margins of a page! Whatever your reason for picking up this book, we're thrilled to take this ride together. In these pages you'll find: --Tons of tips, FAQs, and GRE strategies to get you ready for the big test. --More than 130 verbal and quantitative practice questions with thorough explanations. --Stats for each practice question, including its difficulty rating and the percent of students who typically answer it correctly. We want you to know exactly how tough GRE questions tend to be so you'll know what to expect on test day. --A full-length practice test with an answer key and detailed explanations. --Multiple practice prompts for the analytical writing assessment section, with tips on how to grade each of your essays. If you're not already familiar with Magoosh online, here's what you need to know: --Our materials are top-notch--we've designed each of our practice questions based on careful analysis of millions of students' answers. --We really want to see you do your best. That's why we offer a score improvement guarantee to students who use the online premium Magoosh program. --20% of our students earn a top 10% score on the GRE. --Magoosh students score on average 12 points higher on the test than all other GRE takers. --We've helped more than 1.5 million students prepare for standardized tests online and with our mobile apps. So crack open this book, join us online at magoosh.com, and let's get you ready to rock the GRE!
The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.
