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Exploring Calculus

Author: Crista Arangala
Publisher: CRC Press
ISBN: 1498771041
Size: 26.47 MB
Format: PDF, ePub, Docs
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This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.

Mathematical Modeling

Author: Crista Arangala
Publisher: CRC Press
ISBN: 1498771033
Size: 46.11 MB
Format: PDF, Kindle
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Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study.

Exploring The Infinite

Author: Jennifer Brooks
Publisher: CRC Press
ISBN: 1498704506
Size: 46.47 MB
Format: PDF, ePub
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Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. It guides the reader through the processes of abstraction and log- ical argumentation, to make the transition from student of mathematics to practitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things. The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof" course. Part II constitutes an introduction to the basic concepts of analysis, including limits of sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. ? Features Two part text for the combined transition and analysis course New approach focuses on exploration and creative thought Emphasizes the limit and sequences Introduces programming skills to explore concepts in analysis Emphasis in on developing mathematical thought Exploration problems expand more traditional exercise sets

Exploring Geometry Second Edition

Author: Michael Hvidsten
Publisher: CRC Press
ISBN: 1498760821
Size: 13.14 MB
Format: PDF, Kindle
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This text promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.

A Bridge To Higher Mathematics

Author: Valentin Deaconu
Publisher: CRC Press
ISBN: 1498775268
Size: 28.39 MB
Format: PDF, ePub, Mobi
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A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

Learning By Discovery

Author: Anita E. Solow
Publisher: Cambridge University Press
ISBN: 9780883850831
Size: 17.66 MB
Format: PDF, Docs
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This book contains 26 laboratory modules for use in coursework or in independent projects.

Exploring Abstract Algebra With Mathematica

Author: Allen C. Hibbard
Publisher: Springer Science & Business Media
ISBN: 9780387986197
Size: 59.67 MB
Format: PDF, ePub, Mobi
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This work is intended as an upper-division laboratory supplement for courses in abstract algebra. It consists of several Mathematica packages that the authors have programmed as a foundation with two collections of labs for group theory and ring theory built on this base. Additionally, there is a "users guide" which illustrates the functionality of the underlying code. The lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and the students can look up details and reference information in the Users Guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer. Questions are designed so that they either be written into the electronic notebook, or on paper, whichever the instructor prefers. The notebooks are available for all versions of Mathematica and run across all platforms for which Mathematica exists. Exploring Abstract Algebra with Mathematica is a very timely addition to the undergraduate abstract algebra curriculum. This work is unique, filling a tremendous void in the literature. It offers an environment for studying algebraic structures using Mathematica, to write computer labs in which students can explore the ideas in abstract algebra computationally and visually, and it provides a Users Guide for the data structures and commands of this package. Flexibility of use, and the intention of the authors to make this work highly visual, e.g., with the inclusion of a fullcolor insert of significant algebraic concepts/images, make this publication pedagogically useful to both instructors and students alike. For more information on the underlying software packages, please go to the website http://www.central.edu/eaam/.

The Calculus 7

Author: Louis Leithold
Publisher: Good Year Books
ISBN: 9780673469137
Size: 15.95 MB
Format: PDF, Kindle
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A revision and renewal of this calculus textbook, now in its seventh edition. The author has sought to utlilize the technology now available for the teaching and learning of calculus. The hand-held graphics calculator is one such form of technology that has been integrated into the book. Topics in algebra, trigonometry, and analytical geometry appear in the Appendix.