Advanced Mathematics
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Advanced Mathematics
Author: Stanley J. Farlow
language: en
Publisher: John Wiley & Sons
Release Date: 2019-10-02
Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared for higher-level mathematics course from their onset. Advanced Mathematics: A Transitional Reference provides a “crash course” in beginning pure mathematics, offering instruction on a blendof inductive and deductive reasoning. By avoiding outdated methods and countless pages of theorems and proofs, this innovative textbook prompts students to think about the ideas presented in an enjoyable, constructive setting. Clear and concise chapters cover all the essential topics students need to transition from the "rote-orientated" courses of calculus to the more rigorous "proof-orientated” advanced mathematics courses. Topics include sentential and predicate calculus, mathematical induction, sets and counting, complex numbers, point-set topology, and symmetries, abstract groups, rings, and fields. Each section contains numerous problems for students of various interests and abilities. Ideally suited for a one-semester course, this book: Introduces students to mathematical proofs and rigorous thinking Provides thoroughly class-tested material from the authors own course in transitioning to higher math Strengthens the mathematical thought process of the reader Includes informative sidebars, historical notes, and plentiful graphics Offers a companion website to access a supplemental solutions manual for instructors Advanced Mathematics: A Transitional Reference is a valuable guide for undergraduate students who have taken courses in calculus, differential equations, or linear algebra, but may not be prepared for the more advanced courses of real analysis, abstract algebra, and number theory that await them. This text is also useful for scientists, engineers, and others seeking to refresh their skills in advanced math.
Elements of Advanced Mathematics, Third Edition
For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. Elements of Advanced Mathematics, Third Edition retains the content and character of previous editions while making the material more up-to-date and significant. This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques. Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.
Mathemagics: A Magical Journey Through Advanced Mathematics - Connecting More Than 60 Magic Tricks To High-level Math
Author: Ricardo V Teixeira
language: en
Publisher: World Scientific
Release Date: 2020-05-29
'This delightful book connects mathematical concepts in a dozen areas to magic tricks. Expositions of the mathematics precede description and analysis of the tricks. The expositions are too short for in-depth learning; the intent is to give sophomores a taste of the content and ideas of later mathematics courses. Each chapter features exercises on the mathematics, and students can have fun practicing the tricks.'Mathematics MagazineTeixeira and Park present over 60 different magic tricks while introducing students to high-level math areas. Readers will learn really interesting ideas that will better prepare them for future courses and help them finding areas they might want to study deeper. And as a 'side effect' students will learn amazing magic tricks, century-old secrets, and details from famous magicians and mathematicians.The material was written to quickly present key concepts in several mathematical areas in direct way. Little or no proficiency in math is assumed. In fact, students do not require any Calculus knowledge. And since chapters are almost independent from each other, this book also work as introduction to several other courses.Topics covered include mathematical proofs, probability, abstract algebra, linear algebra, mathematical computing, number theory, coding theory, geometry, topology, real analysis, numerical analysis and history of math.