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Bridge to Higher Mathematics

2010 Education
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Release : 2010
Genre : Education
Kind : eBook
Book Rating : 37X/5 ( reviews)

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Book Synopsis Bridge to Higher Mathematics by : Sam Vandervelde

Download or read book Bridge to Higher Mathematics written by Sam Vandervelde. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.

A Bridge to Higher Mathematics

2016-12-19 Mathematics
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Release : 2016-12-19
Genre : Mathematics
Kind : eBook
Book Rating : 276/5 ( reviews)

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Book Synopsis A Bridge to Higher Mathematics by : Valentin Deaconu

Download or read book A Bridge to Higher Mathematics written by Valentin Deaconu. This book was released on 2016-12-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Mathematical Bridge

2009 Education
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Release : 2009
Genre : Education
Kind : eBook
Book Rating : 079/5 ( reviews)

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Book Synopsis A Mathematical Bridge by : Stephen Fletcher Hewson

Download or read book A Mathematical Bridge written by Stephen Fletcher Hewson. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: Although higher mathematics is beautiful, natural and interconnected, to the uninitiated it can feel like an arbitrary mass of disconnected technical definitions, symbols, theorems and methods. An intellectual gulf needs to be crossed before a true, deep appreciation of mathematics can develop. This book bridges this mathematical gap. It focuses on the process of discovery as much as the content, leading the reader to a clear, intuitive understanding of how and why mathematics exists in the way it does.The narrative does not evolve along traditional subject lines: each topic develops from its simplest, intuitive starting point; complexity develops naturally via questions and extensions. Throughout, the book includes levels of explanation, discussion and passion rarely seen in traditional textbooks. The choice of material is similarly rich, ranging from number theory and the nature of mathematical thought to quantum mechanics and the history of mathematics. It rounds off with a selection of thought-provoking and stimulating exercises for the reader.

Laboratories in Mathematical Experimentation

1997-03 Mathematics
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Release : 1997-03
Genre : Mathematics
Kind : eBook
Book Rating : 222/5 ( reviews)

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Book Synopsis Laboratories in Mathematical Experimentation by : Mount Holyoke College

Download or read book Laboratories in Mathematical Experimentation written by Mount Holyoke College. This book was released on 1997-03. Available in PDF, EPUB and Kindle. Book excerpt: The text is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on, experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires completion of one year of calculus. The course provides a transition to the study of higher, abstract mathematics. The text is written independent of any software. Supplements will be available on the projects' web site.

Transition to Higher Mathematics

2007 Logic, Symbolic and mathematical
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Release : 2007
Genre : Logic, Symbolic and mathematical
Kind : eBook
Book Rating : 474/5 ( reviews)

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Book Synopsis Transition to Higher Mathematics by : Bob A. Dumas

Download or read book Transition to Higher Mathematics written by Bob A. Dumas. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: This book is written for students who have taken calculus and want to learn what "real mathematics" is.

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