Foundations of Higher Mathematics
Author: Peter Fletcher
Publisher:
Published: 1992
Total Pages: 0
ISBN-13: 9780534983864
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Foundations of Higher Mathematics
Author: Daniel M. Fendel
Publisher: Addison Wesley
Published: 1990
Total Pages: 486
ISBN-13:
DOWNLOAD EBOOK →Foundations of Higher Mathematics: Exploration and Proof is the ideal text to bridge the crucial gap between the standard calculus sequence and upper division mathematics courses. The book takes a fresh approach to the subject: it asks students to explore mathematical principles on their own and challenges them to think like mathematicians. Two unique features-an exploration approach to mathematics and an intuitive and integrated presentation of logic based on predicate calculus-distinguish the book from the competition. Both features enable students to own the mathematics they're working on. As a result, your students develop a stronger motivation to tackle upper-level courses and gain a deeper understanding of concepts presented.
Foundations for Higher Mathematics
Author: Wendell Motter
Publisher:
Published: 2019-07-19
Total Pages: 107
ISBN-13: 9781081357788
DOWNLOAD EBOOK →This textbook prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in courses called transition courses, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as the real number system, logic, set theory, mathematical induction, relations, functions, and continuity. It is also a good reference text that students can use when writing or reading proofs in their more advanced courses.
Transition to Higher Mathematics
Author: Bob A. Dumas
Publisher: McGraw-Hill Education
Published: 2007
Total Pages: 0
ISBN-13: 9780071106474
DOWNLOAD EBOOK →This book is written for students who have taken calculus and want to learn what "real mathematics" is.
Foundations of Advanced Mathematics
Author: William E. Kline
Publisher:
Published: 1975
Total Pages: 583
ISBN-13: 9780278469198
DOWNLOAD EBOOK →Practical Foundations of Mathematics
Author: Paul Taylor
Publisher: Cambridge University Press
Published: 1999-05-13
Total Pages: 590
ISBN-13: 9780521631075
DOWNLOAD EBOOK →This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.
A Foundation Course in Mathematics
Author: Ajit Kumar
Publisher:
Published: 2018-04-30
Total Pages: 148
ISBN-13: 9781783323586
DOWNLOAD EBOOK →Written in a conversational style to impart critical and analytical thinking which will be beneficial for students of any discipline. It also gives emphasis on problem solving and proof writing skills, key aspects of learning mathematics.
Foundations of Higher Mathematics
Author: Stella Fletcher
Publisher:
Published: 1992
Total Pages:
ISBN-13: 9780534930554
DOWNLOAD EBOOK →New Foundations in Mathematics
Author: Garret Sobczyk
Publisher: Springer Science & Business Media
Published: 2012-10-26
Total Pages: 373
ISBN-13: 0817683852
DOWNLOAD EBOOK →The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
The Foundations of Mathematics
Author: Kenneth Kunen
Publisher:
Published: 2009
Total Pages: 251
ISBN-13: 9781904987147
DOWNLOAD EBOOK →Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
