Set Theory For Beginners
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Basic Set Theory
Author: Nikolai Konstantinovich Vereshchagin
language: en
Publisher: American Mathematical Soc.
Release Date: 2002
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Set Theory for Beginners
Set Theory for BeginnersSet Theory for Beginners consists of a series of basic to intermediate lessons in set theory. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in set theory high school teachers working with advanced math students students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and mathematical logic. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Set Theory Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets Lesson 2 - Subsets Lesson 3 - Operations on Sets Lesson 4 - Relations Lesson 5 - Equivalence Relations and Partitions Lesson 6 - Functions Lesson 7 - Equinumerosity Lesson 8 - Induction and Recursion on N Lesson 9 - Propositional Logic Lesson 10 - First-order Logic Lesson 11 - Axiomatic Set Theory Lesson 12 - Ordinals Lesson 13 - Cardinals Lesson 14 - Martin's Axiom Lesson 15 - The Field of Real Numbers Lesson 16 - Clubs and Stationary Sets
Set Theory for Pre-Beginners
Set Theory for Pre-BeginnersSet Theory for Pre-Beginners consists of a series of lessons in set theory. The 8 lessons in this book cover elementary material from this subject. A "pre-beginner" is a math student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting. Set Theory for Pre-Beginners is perfect for students wishing to begin learning advanced mathematics, but that are not quite ready to start writing proofs. high school teachers that want to expose their students to the ideas of advanced mathematics without getting into mathematical rigor. professors that wish to introduce higher mathematics to non-stem majors. The material in this set theory book includes: 8 lessons in 8 subject areas. Examples and exercises throughout each lesson. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Pure Math Pre-Beginner Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets and Subsets Lesson 2 - Operations on Sets Lesson 3 - Relations Lesson 4 - Equivalence Relations and Partitions Lesson 5 - Functions Lesson 6 - Equinumerosity Lesson 7 - Logic and Axioms Lesson 8 - Ordinals and Cardinals