I admit that i have raised the bar perhaps higher than the average compared to other books on discrete maths. Pdf fuzzy sets, fuzzy logic, fuzzy methods with applications. This video is an updated version of the original video released over two years ago. An introduction to proofs, logic, sets, and numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the. But even more, set theory is the milieu in which mathematics takes place today. Eccles created date 10162007 20022 pm mathematical logic wikipedia, the free encyclopedia mathematical logic is a subfield of mathematics exploring. Wayne patty, 3th ed 2000, brookscole are old course textbooks for math. As a consequence, the version of chapter 1 from the. Introduction to logic and set theory202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Typical examples are functions from integers to integers or from the real numbers to real numbers functions were originally the idealization of how a varying quantity depends on another quantity. Chapman and hall crc publication date 2004 edition 3rd ed. There are three reasons one might want to read about this. Introduction to abstract mathematics math 2230 course description.
Subject mathematics subject headings mathematics isbn 1584884495. They are not guaranteed to be comprehensive of the material covered in the course. In this sense, abstract mathematics is much more of an art than a science. The problems left to solve by the reader are without solutions, hints or answers, which is. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. Introduction to mathematical reasoning numbers sets and. It is possible to skip the chapter on logic and proceed directly with sets functions, etc.
Basic set theory a set is a many that allows itself to be thought of as a one. This course provides a transition from the calculus to more abstract mathematics. Functions were originally the idealization of how a varying quantity depends on another quantity. Math an introduction to abstract mathematics uci math. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Sets, functions and logic an intro to abstract mathematics. For example six dogs, all the protons on earth, every thought youve ever had, n, z, q, r, c. Foundations of higher mathematics, peter fletcher and c.
Developing the skills necessary to read and practice abstract mathematics. A book of abstract algebra department of mathematics. However, i wanted to discuss logic and proofs together, and found that doing both. Sets, functions, and logic chapman hallcrc mathematics series. This note is an introduction to the zermelofraenkel set theory with choice zfc. The axioms of set theory, ordinal and cardinal arithmetic, the axiom of foundation, relativisation, absoluteness, and reflection, ordinal definable sets and inner models of set theory, the constructible universe l cohens method of forcing, independence. Sets, functions, and logic an introduction to abstract. The axioms of set theory, the natural numbers, the ordinal numbers, relations and orderings, cardinality, there is nothing real about the real numbers, the universe, reflection, elementary submodels and constructibility. But its only when we apply sets in different situations do they become the powerful building block of mathematics that they are. This is a systematic and wellpaced introduction to mathematical logic. Graph theory, abstract algebra, real analysis, complex analysis, linear algebra, number theory, and the list goes on. Youve read his columns in maa online, youve heard him on the radio, and youve seen his popular mathematics books.
Excellent as a course text, the book presupposes only elementary background and can be used also for selfstudy by more ambitious students. Sets, functions, and logic, third edition is an affordable little. Typical examples are functions from integers to integers or from the real numbers to real numbers. Today we introduce set theory, elements, and how to build sets. We now mention some set operations that enable us in generating new sets from existing ones. Keith devlins book is an excellent introduction to proofs, an important part of ones mathematics education, which is missing in the us educational system at high school level. The notions of set theory, and the ideas behind many of the. Free set theory books download ebooks online textbooks. In this whole course, all we will study are sets with some carefully chosen extra structure. Title an introduction to mathematical reasoning numbers, sets and functions author peter j.
In between all those activities and his own research, hes been hard at work revising sets, functions and logic, his standardsetting text that has smoothed the road to pure mathematics for legions of undergraduate students. This book has been reprinted with the cooperation of kyung moon publishers, south korea. Oct 03, 2018 an introduction to abstract mathematics, third edition. For its applications in topology, analysis, algebra, ai, databases. Use features like bookmarks, note taking and highlighting while reading sets, functions, and logic. They dont include multivariable calculus or contain any problem sets. What is most unique about set theory is that it is the perfect amalgam of the visual and the abstract. Spiral workbook for discrete mathematics open textbook. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, di erentiability, sequences and series of functions, and riemann integration. Topics include logic, sets and functions, an introduction to mathematical proof, mathematical induction, relations.
Sets functions and logic an introduction to abstract mathematics. Sets functions and logic an introduction to abstract mathematics chapman and hall mathematics. This is a text that covers the standard topics in a sophomorelevel course in discrete mathematics. During the seven years that have elapsed since publication of the first edition of a book of abstract algebra, i have received letters from many readers with comments and suggestions. My unconventional approach of starting with logic may not work for everybody, as some individuals. This alone assures the subject of a place prominent in human culture. It serves as a transition into advanced mathematics, and should be taken after the initial calculus sequence and before or concurrently with midlevel mathematics courses. The problems left to solve by the reader are without solutions, hints or answers, which is authors intention, but is somewhat controversial. Spiral workbook for discrete mathematics open textbook library. Chapter 6 functions injective, surjective, bijective function. Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. Keith devlins book is an excellent introduction to proofs, an important part of. The union of xand y, denoted by xy, is the set that consists of all elements of xand also all elements of y.
It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Sets functions and logic an introduction to abstract. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. A book of set theory, first published by dover publications, inc. Sets functions and logic an introduction to abstract mathematics chapman and hall mathematics authors keith devlin author publication data boca raton. Basic concepts of set theory, functions and relations. Simpli cation of boolean propositions and set expressions. The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe important properties of sets, and give. Important prerequisite material for a number of more advanced mathematics courses is.
Introduction to abstract mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. Uwmilwaukee department of mathematical sciences 69,194 views. Set theory for computer science university of cambridge. Many students confronting mathematics beyond elementary calculus for the rst time are stumped at the idea of proofs. An introduction to abstract mathematics, third edition. This course teaches a student how to construct logical arguments in the form of a proof to verify mathematical statements.
An accessible introduction to abstract mathematics with an emphasis on proof writing. For those of you new to abstract mathematics elementary does not mean simple though much of the material. This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. Sets, functions and logic an intro to abstract mathematics 3rd ed. This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality.
The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe. Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with. Proofs seem so contrary to how students have done mathematics so far.
Addressing the importance of constructing and understanding mathematical proofs, fundamentals of mathematics. Validity, entailment, and equivalence of boolean propositions. An introduction to abstract mathematics, third edition chapman hallcrc mathematics series book 25 kindle edition by devlin, keith. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and. However, not every rule describes a valid function. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
Dear student, as you are about to discover, the transition from high school mathematics to collegelevel pure abstract mathematics is a. Because the foundations of mathematics is relevant to philosophy. This course is an introduction to proofs and the abstract approach that characterizes upper level mathematics courses. Cantors diagonal argument to show powerset strictly increases size. Introduction to functions mctyintrofns20091 a function is a rule which operates on one number to give another number. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates or mathematically mature highschool students, or for use as a very. Sets, functions and logic an intro to abstract mathematics 3rd ed k devlin crc, 2004 ww pdf. Sets functions and logic an introduction to abstract mathematics third edition chapman hall. These are some notes on introductory real analysis. Noone measures the quality of a painting or sculpture by how useful it is, instead it is the. Starting with the basics of set theory, induction and computability, it covers. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions.
Discrete mathematics for computer science some notes. Induction is covered at the end of the chapter on sequences. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. Magnus university at albany, state university of new york preliminary version 0.