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Author: Bob A. Dumas
Publisher: McGraw-Hill Education
Published: 2007
Total Pages: 0
ISBN-13: 9780071106474
DOWNLOAD EBOOKThis book is written for students who have taken calculus and want to learn what "real mathematics" is.
Author: Daniel M. Fendel
Publisher: Addison Wesley
Published: 1990
Total Pages: 488
ISBN-13:
DOWNLOAD EBOOKFoundations 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.
Author: Sam Vandervelde
Publisher: Lulu.com
Published: 2010
Total Pages: 258
ISBN-13: 055750337X
DOWNLOAD EBOOKThis 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.
Author:
Publisher: Univalent Foundations
Published:
Total Pages: 484
ISBN-13:
DOWNLOAD EBOOKAuthor: Joseph L. Taylor
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 411
ISBN-13: 0821889842
DOWNLOAD EBOOKFoundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
Author: Kenneth Kunen
Publisher:
Published: 2009
Total Pages: 251
ISBN-13: 9781904987147
DOWNLOAD EBOOKMathematical 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.
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
Published: 2013-12-01
Total Pages: 434
ISBN-13: 1461221307
DOWNLOAD EBOOKThe aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
Author: Avner Friedman
Publisher: Courier Corporation
Published: 1982-01-01
Total Pages: 276
ISBN-13: 9780486640624
DOWNLOAD EBOOKMeasure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
Author: Dennis Sentilles
Publisher: Courier Corporation
Published: 2013-05-20
Total Pages: 418
ISBN-13: 0486277585
DOWNLOAD EBOOKThis helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
Author: Peter Fletcher
Publisher: Cengage Learning
Published: 1996
Total Pages: 344
ISBN-13:
DOWNLOAD EBOOKThis text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking.
