The Probability Lifesaver

All the Tools You Need to Understand Chance

Author: Steven J. Miller

Publisher: Princeton University Press

ISBN: 1400885388

Category: Mathematics

Page: 752

View: 5148

The essential lifesaver for students who want to master probability For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results. The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement—both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus. The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. A helpful introduction to probability or a perfect supplement for a course Numerous worked-out examples Lectures based on the chapters are available free online Intuition of problems emphasized first, then technical proofs given Appendixes review proof techniques Relaxed, conversational approach
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The Real Analysis Lifesaver

All the Tools You Need to Understand Proofs

Author: Raffi Grinberg

Publisher: Princeton University Press

ISBN: 140088313X

Category: Mathematics

Page: 200

View: 8303

Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. The essential “lifesaver” companion for any course in real analysis Clear, humorous, and easy-to-read style Teaches students not just what the proofs are, but how to do them—in more than 40 worked-out examples Every new definition is accompanied by examples and important clarifications Features more than 20 “fill in the blanks” exercises to help internalize proof techniques Tried and tested in the classroom
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The Calculus Lifesaver

All the Tools You Need to Excel at Calculus

Author: Adrian Banner

Publisher: Princeton University Press

ISBN: 9781400835782

Category: Mathematics

Page: 752

View: 4000

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory. The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus. Serves as a companion to any single-variable calculus textbook Informal, entertaining, and not intimidating Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures More than 475 examples (ranging from easy to hard) provide step-by-step reasoning Theorems and methods justified and connections made to actual practice Difficult topics such as improper integrals and infinite series covered in detail Tried and tested by students taking freshman calculus
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Calculus in Context

Background, Basics, and Applications

Author: Alexander J. Hahn

Publisher: JHU Press

ISBN: 1421422301

Category: Mathematics

Page: 712

View: 6451

Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: • the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development• a brief, introductory calculus from the works of Newton and Leibniz• a modern development of the essentials of differential and integral calculus• the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration—for students and instructors alike—of a discipline that is both rich in conceptual beauty and broad in its applied relevance.
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An Invitation to Modern Number Theory

Author: Steven J. Miller,Ramin Takloo-Bighash

Publisher: Princeton University Press

ISBN: 9780691120607

Category: Mathematics

Page: 503

View: 4081

In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
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Multivariable Calculus, Linear Algebra, and Differential Equations

Author: Stanley I. Grossman

Publisher: Academic Press

ISBN: 1483218031

Category: Mathematics

Page: 992

View: 9892

Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.
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Dr. Euler's Fabulous Formula

Cures Many Mathematical Ills

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400838479

Category: Mathematics

Page: 416

View: 8133

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.
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Data Analysis for Scientists and Engineers

Author: Edward L. Robinson

Publisher: Princeton University Press

ISBN: 1400883067

Category: Science

Page: 408

View: 1072

Data Analysis for Scientists and Engineers is a modern, graduate-level text on data analysis techniques for physical science and engineering students as well as working scientists and engineers. Edward Robinson emphasizes the principles behind various techniques so that practitioners can adapt them to their own problems, or develop new techniques when necessary. Robinson divides the book into three sections. The first section covers basic concepts in probability and includes a chapter on Monte Carlo methods with an extended discussion of Markov chain Monte Carlo sampling. The second section introduces statistics and then develops tools for fitting models to data, comparing and contrasting techniques from both frequentist and Bayesian perspectives. The final section is devoted to methods for analyzing sequences of data, such as correlation functions, periodograms, and image reconstruction. While it goes beyond elementary statistics, the text is self-contained and accessible to readers from a wide variety of backgrounds. Specialized mathematical topics are included in an appendix. Based on a graduate course on data analysis that the author has taught for many years, and couched in the looser, workaday language of scientists and engineers who wrestle directly with data, this book is ideal for courses on data analysis and a valuable resource for students, instructors, and practitioners in the physical sciences and engineering. In-depth discussion of data analysis for scientists and engineers Coverage of both frequentist and Bayesian approaches to data analysis Extensive look at analysis techniques for time-series data and images Detailed exploration of linear and nonlinear modeling of data Emphasis on error analysis Instructor's manual (available only to professors)
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Student’s Guide to Calculus by J. Marsden and A. Weinstein

Author: Frederick H. Soon

Publisher: Springer Science & Business Media

ISBN: 9780387963488

Category: Mathematics

Page: 294

View: 2669

This book is intended to help students using Marsden and Weinstein's Calculus III. It reinforces the concepts introduced there with exercises, study hints, and quizzes; and it provides detailed solutions of the odd-numbered exercises of the text.
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The Humongous Book of Statistics Problems

Author: Robert Donnelly,W. Michael Kelley

Publisher: Penguin

ISBN: 1101151390

Category: Mathematics

Page: 560

View: 4797

Following the successful, 'The Humongous Books', in calculus and algebra, bestselling author Mike Kelley takes a typical statistics workbook, full of solved problems, and writes notes in the margins, adding missing steps and simplifying concepts and solutions. By learning how to interpret and solve problems as they are presented in statistics courses, students prepare to solve those difficult problems that were never discussed in class but are always on exams. - With annotated notes and explanations of missing steps throughout, like no other statistics workbook on the market - An award-winning former math teacher whose website (calculus-help.com) reaches thousands every month, providing exposure for all his books
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The Induction Book

Author: Steven H. Weintraub

Publisher: Courier Dover Publications

ISBN: 0486821234

Category: Mathematics

Page: 128

View: 6189

Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all levels, the text is particularly suitable for courses in mathematical induction, theorem-proving, and problem-solving. The treatment begins with both intuitive and formal explanations of mathematical induction and its equivalents. The next chapter presents many problems consisting of results to be proved by induction, with solutions omitted to enable instructors to assign them to students. Problems vary in difficulty; the majority of them require little background, and the most advanced involve calculus or linear algebra. The final chapter features proofs too complicated for students to find on their own, some of which are famous theorems by well-known mathematicians. For these beautiful and important theorems, the author provides expositions and proofs. The text concludes with a helpful Appendix providing the logical equivalence of the various forms of induction.
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A Course in Differential Equations with Boundary Value Problems, Second Edition

Author: Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski

Publisher: CRC Press

ISBN: 1498736068

Category: Mathematics

Page: 788

View: 4462

A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®,?Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. ? Features MATLAB®,?Mathematica®, and MapleTM are incorporated at the end of each chapter. All three software packages have parallel code and exercises; There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages. Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book
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Maths: A Student's Survival Guide

A Self-Help Workbook for Science and Engineering Students

Author: Jenny Olive

Publisher: Cambridge University Press

ISBN: 9780521017077

Category: Mathematics

Page: 634

View: 7528

First published in 1998.
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Introduction to Abstract Algebra

From Rings, Numbers, Groups, and Fields to Polynomials and Galois Theory

Author: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger

Publisher: JHU Press

ISBN: 1421411776

Category: Mathematics

Page: 584

View: 309

Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math’s most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger’s clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include:• Rings• Integral domains• The fundamental theorem of arithmetic• Fields• Groups• Lagrange’s theorem• Isomorphism theorems for groups• Fundamental theorem of finite abelian groups• The simplicity of A n for n 5• Sylow theorems• The Jordan-Hölder theorem• Ring isomorphism theorems• Euclidean domains• Principal ideal domains• The fundamental theorem of algebra• Vector spaces• Algebras• Field extensions: algebraic and transcendental• The fundamental theorem of Galois theory• The insolvability of the quintic
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Metadata for Digital Collections

A How-to-do-it Manual

Author: Steven J. Miller

Publisher: Neal Schuman Pub

ISBN: 9781555707460

Category: Language Arts & Disciplines

Page: 343

View: 1299

Reference -- Metadata interoperability, shareability, and quality -- Interoperability -- Short- and long-term metadata viability -- Metadata sharing, harvesting, and aggregating -- OAI metadata harvesting -- Metadata mapping and crosswalks -- Metadata conversion and processing -- Example of metadata harvesting, processing, and aggregating -- Good quality and shareable metadata -- Assessing metadata quality -- Five ways to improve your metadata quality and interoperability -- Summary -- References -- Designing and documenting a metadata scheme -- Metadata scheme design and documentation -- Introduction -- Analyze context, content, and users and determine functional requirements -- Select and develop an element set -- General / Cross-collection metadata scheme design -- Collection-specific metadata scheme design -- Factors in choice of metadata element set -- Establish element and database specifications -- Establish controlled vocabularies and encoding schemes -- Develop content guidelines -- Document the scheme -- Metadata design examples -- General application profile examples -- Collaborative digitization program Dublin Core metadata documentation -- OhioLINK Dublin Core metadata documentation -- Indiana memory Dublin Core metadata documentation -- DLF/Aquifer MODS metadata documentation -- Collection-specific application profile examples -- University of Washington's architecture collection metadata documentation -- University of Washington's musical instruments collection metadata documentation -- University of Wisconsin-Milwaukee's transportation collection metadata documentation -- CONTENTdm examples -- Summary -- References -- Metadata, linked data, and the Semantic Web -- What are linked data and the semantic web and why care about them? -- Linked open data and the resource description framework -- Statements, properties, values, and RDF triples -- URIs: uniform resource identifiers -- Literals, strings, and.
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PROB, STATS & RANDOM PROC 3E

Author: VEERARAJAN

Publisher: Tata McGraw-Hill Education

ISBN: 1259083330

Category: Mathematical statistics

Page: 595

View: 7276

This book with the right blend of theory and applications is designed to provide a thorough knowledge on the basic concepts of Probability, Statistics and Random Variables offered to the undergraduate students of engineering. Addition of important topics as per the syllabi requirements is the basis of this revision. Features Detailed coverage of the topic on Statistical Measures of Central Tendency which includes Mean, Median and Mode. (Refer chapter number 4 on Statistical Averages. ) Detailed coverage of topics like Dispersion, Skewness and Kurtosis and Moments of a Random Variable. ( Refer chapter number 4 on Statistical Averages. ) Introduction of the topic on Linear Correlation and Regression has been discussed in chapter number 4. The applications of Random Variables have been dealt with in detail in chapter like Test of Hypothesis, Queueing Theory and Design of Experiments. ( Refer chapters 6, 9 and 10) Special Probability Distributions and their inter-relation has been explained with great clarity. Pedagogical Features : Solved Examples: 366 Numerical Questions: 1149 A total of 1555 questions in the book.
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Introduction to Financial Mathematics

Author: Kevin J. Hastings

Publisher: CRC Press

ISBN: 1498723918

Category: Mathematics

Page: 407

View: 9264

Introduction to Financial Mathematics is ideal for an introductory undergraduate course. Unlike most textbooks aimed at more advanced courses, the text motivates students through a discussion of personal finances and portfolio management. The author then goes on to cover valuation of financial derivatives in discrete time, using all of closed form, recursive, and simulation methods. The text covers nearly all of the syllabus topics of the Financial Mathematics Actuarial examination, providing students with the foundation they require for future studies and throughout their careers. It begins by covering standard material on the mathematics of interest, including compound interest, present value, annuities, loans, several versions of the rate of return on an investment, and interest in continuous time. The text explains how to value bonds at their issue dates, at coupon times, between coupon times, and in cases where the bonds are terminated early. Next, it supplies a rapid-fire overview of the main ideas and techniques of discrete probability, including sample spaces and probability measures, random variables and distributions, expectation, conditional probability, and independence. The author introduces the basic terminology of stocks and stock trading. He also explains how to derive the rate of return on a portfolio and how to use the idea of risk aversion to model the investor tradeoff between risk and return. The text also discusses the estimation of parameters of asset models from real data. The text closes with a detailed discussion of how to value financial derivatives using anti-arbitrage assumptions. The one-step and multi-step cases are covered, and exotic options such as barrier options are also introduced, to which simulation methods are applied. Many of the examples in the book involve numerical solution of complicated non-linear equations; others ask students to produce algorithms which beg to be implemented as programs. For maximum flexibility, the author has produced the text without adhering to any particular computational platform. A digital version of this text is also available in the form of Mathematica notebooks that contain additional content.
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Linear Algebra

Step by Step

Author: Kuldeep Singh

Publisher: Oxford University Press

ISBN: 0199654441

Category: Mathematics

Page: 608

View: 4867

Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematical tool ever developed. This dynamic and engaging book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.
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Benford's Law

Theory and Applications

Author: Steven J. Miller

Publisher: Princeton University Press

ISBN: 1400866596

Category: Mathematics

Page: 464

View: 4361

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world’s leading experts on Benford’s law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration. Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford’s law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford’s law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford’s law can serve as a productive meeting ground for researchers and practitioners in diverse fields.
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