Principles of Mathematics

Author: Vladimir Lepetic
Publisher: John Wiley & Sons
ISBN: 1119131693
Format: PDF, Kindle
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Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.

A Primer of Real Functions

Author: Ralph P. Boas
Publisher: Cambridge University Press
ISBN: 9780883850299
Format: PDF, ePub
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Revised edition of a classic Carus monograph with a new chapter on integration and its applications.

3D Math Primer for Graphics and Game Development 2nd Edition

Author: Fletcher Dunn
Publisher: CRC Press
ISBN: 1568817231
Format: PDF
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This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.

Risk Neutral Pricing and Financial Mathematics

Author: Peter M. Knopf
Publisher: Elsevier
ISBN: 0128017279
Format: PDF, ePub, Mobi
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Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, and term structure models, along with related valuation and hedging techniques. The joint effort of two authors with a combined 70 years of academic and practitioner experience, Risk Neutral Pricing and Financial Mathematics takes a reader from learning the basics of beginning probability, with a refresher on differential calculus, all the way to Doob-Meyer, Ito, Girsanov, and SDEs. It can also serve as a useful resource for actuaries preparing for Exams FM and MFE (Society of Actuaries) and Exams 2 and 3F (Casualty Actuarial Society). Includes more subjects than other books, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, term structure models, valuation, and hedging techniques Emphasizes introductory financial engineering, financial modeling, and financial mathematics Suited for corporate training programs and professional association certification programs

A Primer for Mathematics Competitions

Author: Alexander Zawaira
Publisher: OUP Oxford
ISBN: 0191561703
Format: PDF, Mobi
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The importance of mathematics competitions has been widely recognised for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics; they constitute the most effective way of discovering and nurturing mathematical talent; and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded. Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest. An unusual feature of this book is the attention paid throughout to the history of mathematics - the origins of the ideas, the terminology and some of the problems, and the celebration of mathematics as a multicultural, cooperative human achievement. As a bonus the aspiring "mathlete" may encounter, in the most enjoyable way possible, many of the topics that form the core of the standard school curriculum.

Primer of Modern Analysis

Author: K.T. Smith
Publisher: Springer Science & Business Media
ISBN: 1461211441
Format: PDF, ePub, Mobi
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This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.

A Primer on Pontryagin s Principle in Optimal Control

Author: I. Michael Ross
ISBN: 9780984357116
Format: PDF, ePub, Mobi
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EDITORIAL REVIEW: This book provides a guided tour in introducing optimal control theory from a practitioner's point of view. As in the first edition, Ross takes the contrarian view that it is not necessary to prove Pontryagin's Principle before using it. Using the same philosophy, the second edition expands the ideas over four chapters: In Chapter 1, basic principles related to problem formulation via a structured approach are introduced: What is a state variable? What is a control variable? What is state space? And so on. In Chapter 2, Pontryagin's Principle is introduced using intuitive ideas from everyday life: Like the process of "measuring" a sandwich and how it relates to costates. A vast number of illustrations are used to explain the concepts without going into the minutia of obscure mathematics. Mnemonics are introduced to help a beginner remember the collection of conditions that constitute Pontryagin's Principle. In Chapter 3, several examples are worked out in detail to illustrate a step-by-step process in applying Pontryagin's Principle. Included in this example is Kalman's linear-quadratic optimal control problem. In Chapter 4, a large number of problems from applied mathematics to management science are solved to illustrate how Pontryagin's Principle is used across the disciplines. Included in this chapter are test problems and solutions. The style of the book is easygoing and engaging. The classical calculus of variations is an unnecessary prerequisite for understanding optimal control theory. Ross uses original references to weave an entertaining historical account of various events. Students, particularly beginners, will embark on a minimum-time trajectory to applying Pontryagin's Principle.

How to Teach Mathematics Second Edition

Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 0821813986
Format: PDF
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This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues. Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. He also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner. The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications.

Quantum Mechanics and Quantum Field Theory

Author: Jonathan Dimock
Publisher: Cambridge University Press
ISBN: 1139497480
Format: PDF, ePub
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Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.

A Primer for Teaching World History

Author: Antoinette Burton
Publisher: Duke University Press
ISBN: 0822351889
Format: PDF
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This book offers principles to consider when creating a world history syllabus; it prompts a teacher, rather than aiming for full world coverage, to pick an interpretive focus and thread it through the course. It will be used by university faculty, graduate students, and high school teachers who are teaching world history for the first time or want to rethink their approach to teaching the subject.