The Foundations of Higher Arithmetic
Author: Benjamin Franklin Sisk
Publisher:
Published: 1905
Total Pages: 226
ISBN-13:
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Homotopy Type Theory: Univalent Foundations of Mathematics
Author:
Publisher: Univalent Foundations
Published:
Total Pages: 484
ISBN-13:
DOWNLOAD EBOOKTransition to Higher Mathematics
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.
Foundations for Higher Mathematics
Author: Wendell Motter
Publisher:
Published: 2019-07-19
Total Pages: 107
ISBN-13: 9781081357788
DOWNLOAD EBOOKThis 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.
Foundations of Higher Mathematics
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.
Bridge to Higher Mathematics
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.
Foundations of Discrete Mathematics
Author: K. D. Joshi
Publisher: New Age International
Published: 1989
Total Pages: 768
ISBN-13: 9788122401202
DOWNLOAD EBOOKThis Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.
The Foundations of Mathematics
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.
Foundations of Computation
Author: Carol Critchlow
Publisher:
Published: 2011
Total Pages: 256
ISBN-13:
DOWNLOAD EBOOKFoundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
The Higher Arithmetic
Author: H. Davenport
Publisher: Cambridge University Press
Published: 1999-12-09
Total Pages: 248
ISBN-13: 9780521634465
DOWNLOAD EBOOKSeventh edition of a classic elementary number theory book.
