Introduction to Advanced Mathematics: A Guide to Understanding Proofs

Author: Connie M. Campbell

Publisher: Cengage Learning

ISBN: 1133168787

Category: Mathematics

Page: 144

View: 1408

This text offers a crucial primer on proofs and the language of mathematics. Brief and to the point, it lays out the fundamental ideas of abstract mathematics and proof techniques that students will need to master for other math courses. Campbell presents these concepts in plain English, with a focus on basic terminology and a conversational tone that draws natural parallels between the language of mathematics and the language students communicate in every day. The discussion highlights how symbols and expressions are the building blocks of statements and arguments, the meanings they convey, and why they are meaningful to mathematicians. In-class activities provide opportunities to practice mathematical reasoning in a live setting, and an ample number of homework exercises are included for self-study. This text is appropriate for a course in Foundations of Advanced Mathematics taken by students who've had a semester of calculus, and is designed to be accessible to students with a wide range of mathematical proficiency. It can also be used as a self-study reference, or as a supplement in other math courses where additional proofs practice is needed. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

A Transition to Proof

An Introduction to Advanced Mathematics

Author: Neil R. Nicholson

Publisher: CRC Press

ISBN: 0429522002

Category: Mathematics

Page: 450

View: 4967

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology

Numbers and Proofs

Author: Reg Allenby

Publisher: Butterworth-Heinemann

ISBN: N.A

Category: Mathematics

Page: 274

View: 1398

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow. Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.

A TeXas Style Introduction to Proof

Author: Ron Taylor,Patrick X. Rault

Publisher: The Mathematical Association of America

ISBN: 1939512131

Category: Mathematics

Page: 176

View: 9058

A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the "bridge course") that also introduces TeX as a tool students can use to communicate their work. As befitting "textless" text, the book is, as one reviewer characterized it, "minimal." Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.

How to read and do proofs

an introduction to mathematical thought processes

Author: Daniel Solow

Publisher: Wiley

ISBN: 9780471680581

Category: Mathematics

Page: 269

View: 6240

An easy-to-use guide that shows how to read, understand, and do proofs. Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

View: 8143

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

Research in Collegiate Mathematics Education VII

Author: Fernando Hitt,Derek Allan Holton,Patrick W. Thompson

Publisher: American Mathematical Soc.

ISBN: 0821849964

Category: Mathematics

Page: 261

View: 9802

The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use.

An Introduction to Continuous-Time Stochastic Processes

Theory, Models, and Applications to Finance, Biology, and Medicine

Author: Vincenzo Capasso,David Bakstein

Publisher: Springer Science & Business Media

ISBN: 0817683461

Category: Mathematics

Page: 434

View: 634

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Student Writing in the Quantitative Disciplines

A Guide for College Faculty

Author: Patrick Bahls

Publisher: John Wiley & Sons

ISBN: 1118205820

Category: Education

Page: 192

View: 2618

Designing interesting problems and writing assignments is one ofthe chief tasks of all teachers, but it can be especiallychallenging to translate and apply learning theory, good teachingtechniques, and writing assignments into STEM and otherquantitative disciplines. Student Writing in the QuantitativeDisciplines offers instructors in math-based disciplines meaningfulapproaches to making their coursework richer and more relevant fortheir students, as well as satisfying institutional imperatives forwriting curricula. This important resource provides instructorswith the hands-on skills needed to guide their students in writingwell in quantitative courses at all levels of the collegecurriculum and to promote students' general cognitive andintellectual growth. Comprehensive in scope, the book includes: Ideas for using writing as a means of learning mathematicalconcepts Illustrative examples of effective writing activities andassignments in a number of different genres Assessment criteria and effective strategies for responding tostudents' writing Examples of ways to help students engage in peer review,revision, and resubmission of their written work "Those of us who spend our lives urging faculty in alldisciplines to integrate more writing into their courses havewished for the day when someone like Patrick Bahls would stepforward with a book like this one."—Chris M. Anson, UniversityDistinguished Professor and director, Campus Writing and SpeakingProgram, North Carolina State University "Written by a mathematician, this readable, theoretically soundbook describes practical strategies for teachers in thequantitative sciences to assign and respond to students' writing.It also describes numerous approaches to writing that engagestudents in disciplinary learning, collaborative discovery, andeffective communication."—Art Young, Campbell Professor ofEnglish emeritus, Clemson University "Loaded with practical advice, this timely, important, andengaging book will be an invaluable resource for instructorswishing to bring the benefits of writing-to-learn to thequantitative disciplines. As a mathematician thoroughly grounded inwriting-across-the-curriculum scholarship, Bahls brings humor,classroom experience, and pedagogical savvy to a mission he clearlyloves—improving the quality of student learning in math andscience."—John C. Bean, professor, Seattle University, andauthor, Engaging Ideas

Euclidean and Transformational Geometry: A Deductive Inquiry

Author: Shlomo Libeskind

Publisher: Jones & Bartlett Publishers

ISBN: 0763762229

Category: Mathematics

Page: 371

View: 9463

Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on solving challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next through numerous problem solving techniques. A large collection of problems, varying in level of difficulty, are integrated throughout the text and suggested hints for the more challenging problems appear in the instructor's solutions manual and can be used at the instructor's discretion.

Discrete Mathematics with Proof

Author: Eric Gossett

Publisher: John Wiley & Sons

ISBN: 0470457937

Category: Mathematics

Page: 904

View: 3065

"Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. - Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. - It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics."--Jacket.

A Guide to Elementary Number Theory

Author: Underwood Dudley

Publisher: MAA

ISBN: 9780883853474

Category: Mathematics

Page: 141

View: 4044

"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy."--P. [4] of cover.

A Guide to Plane Algebraic Curves

Author: Keith Kendig

Publisher: MAA

ISBN: 0883853531

Category: Mathematics

Page: 193

View: 7999

This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the subject, while at the same time keeping the exposition simple and understandable, by introducing abstract concepts with concrete examples and pictures. It can be used as the text for an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at graduate level. This book is accessible to those with a limited mathematical background. This is because for those outside mathematics there is a growing need for an entre to algebraic geometry, a need created by the ever-expanding role algebraic geometry is playing in areas ranging from biology to chemistry and robotics to cryptology.

A Concrete Approach to Abstract Algebra

From the Integers to the Insolvability of the Quintic

Author: Jeffrey Bergen

Publisher: Academic Press

ISBN: 9780080958620

Category: Mathematics

Page: 720

View: 5166

A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra. It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study. This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

An Introduction to Wavelet Analysis

Author: David F. Walnut

Publisher: Springer Science & Business Media

ISBN: 1461200016

Category: Computers

Page: 452

View: 8986

This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.

Practical Guide to Software Quality Management

Author: John W. Horch

Publisher: Artech House

ISBN: 9781580536042

Category: Computers

Page: 286

View: 6594

If you are responsible for designing, implementing, or managing a quality software program, this updated edition of the Practical Guide to Software Quality Management now identifies 10 major components that make up a solid program in line with ISO 9001 quality management precepts. Thoroughly revised and with new chapters on software safety and software risk management, this comprehensive primer provides you with the starting points for a standardized documentation system, and analyzes each individual program component separately, addressing in detail its specific role and overall importance to the system.

A Student's Guide to the Study, Practice, and Tools of Modern Mathematics

Author: Donald Bindner,Martin Erickson

Publisher: CRC Press

ISBN: 1439846073

Category: Mathematics

Page: 280

View: 5787

A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and MapleTM to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities. The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform mathematical research, and how to give mathematical presentations. The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more. The text describes how to compose a LaTeX file, give a presentation using Beamer, create mathematical diagrams, use computer algebra systems, and display ideas on a web page. The authors cover both popular commercial software programs and free and open source software, such as Linux and R. Showing how to use technology to understand mathematics, this guide supports students on their way to becoming professional mathematicians. For beginning mathematics students, it helps them study for tests and write papers. As time progresses, the book aids them in performing advanced activities, such as computer programming, typesetting, and research.

Geometry For Dummies

Author: Mark Ryan

Publisher: John Wiley & Sons

ISBN: 1119181550

Category: Mathematics

Page: 408

View: 3512

Hit the geometry wall? Get up and running with this no-nonsense guide! Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it's a subject that bewilders many students because it's so unlike the math they've done before—it requires the use of deductive logic in formal proofs. If you're having a hard time wrapping your mind around what that even means, you've come to the right place! Inside, you'll find out how a proof's chain of logic works and even discover some secrets for getting past rough spots along the way. You don't have to be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry! Find out how to decode complex geometry proofs Learn to reason deductively and inductively Make sense of angles, arcs, area, and more Improve your chances of scoring higher in your geometry class There's no reason to let your nerves get jangled over geometry—your understanding will take new shape with the help of Geometry For Dummies.