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1. 80.07.04: Logic And Set Theory
While in no way does the unit cover the entire fields of Set Theory and Logic, it does, I hope, offer an introduction to the basic concepts,
http://www.yale.edu/ynhti/curriculum/units/1980/7/80.07.04.x.html

Extractions: Richard Canalor The following unit is designed to offer teachers and children a chance to explore what may be to them a different area of Finite Mathematics. While in no way does the unit cover the entire fields of Set Theory and Logic, it does, I hope, offer an introduction to the basic concepts, symbols and importance of these two fields of Mathematics. As you will see, Set Theory and Logic are related and have therefore been combined for the content of this unit. The unit is approximately two weeks in length and is intended for grade 6,7, or 8 although both length and grade level may vary. We will begin with a short Pretest. The purpose of the pretest is twofold. On one hand it will give some barometer of success (there will be a posttest) and hopefully the pretest will foster discussion and motivate children to want to hear more. 1. There were 20 people at a party. Thirteen had coke, 7 had sandwiches, 5 had both. How many did not eat or drink?

An Elementary Introduction to logic and set theory. I. Overview II. Sentential Logic III. Predicate Logic and Quantifiers

3. Martin Flashman's Logic And Set Theory Web Surfing Page
MATHS 315 Mathematical Logic (University of Aukland) Handouts etc. for logic and set theory that parallel Hamilton s textbook Logic for Mathematicians.
http://www.humboldt.edu/~mef2/logicsites.html

Extractions: Please send suggestions for improvements and comments to Martin Flashman E-Mail: flashman@axe.humboldt.edu Logic: Mathematical Logic around the world Association for Symbolic Logic LogicAL: An excellent resource for links. Gateway to Logic Some excellent logic software on-line from Germany A. Selby's home page:much interesting stuff on education, logic, algebra, and more. Situation Puzzles Proofs in Mathematics (YES!!) Mathematics as a language ... Mathematical Logic. Around Goedel's Theorem. By K.Podnieks two hyper-textbooks in mathematical logic including an Introduction to Mathematical Logic. ... MATHS 315 Mathematical Logic (University of Aukland) Handouts etc. for logic and set theory that parallel Hamilton's textbook Logic for Mathematicians.

4. Logic And Set Theory Organizations
Groups and conferences.
http://www.math.ufl.edu/~jal/orgs.html

5. Math Forum - Ask Dr. Math Archives: College Logic/Set Theory
http://mathforum.org/library/drmath/sets/college_logic.html

6. Earliest Uses Of Symbols Of Set Theory And Logic
Explains the early introduction of notations used in logic and set theory as we know it today. Includes reference links to key people in this area.
http://members.aol.com/jeff570/set.html

Extractions: Earliest Uses of Symbols of Set Theory and Logic Last updated: Sept. 29, 2007 The study of logic goes back more than two thousand years and in that time many symbols and diagrams have been devised. Around 300 BC Aristotle introduced letters as term-variables, a "new and epoch-making device in logical technique." (W. & M. Kneale The Development of Logic (1962, p. 61). The modern era of mathematical notation in logic began with George Boole (1815-1864), although none of his notation survives. Set theory came into being in the late 19 th and early 20 th centuries, largely a creation of Georg Cantor (1845-1918). See MacTutor's A history of set theory or, for more detail, Set theory from the Stanford Encyclopedia of Philosophy Most of the basic symbols of logic and set theory in use today were introduced between 1880 and 1920. The main contributors were Ernst Schröder Giuseppe Peano Alfred North Whitehead (1861-1947) and Bertrand Russell (1872-1970). Peano had a strong influence on Whitehead and Russell and their joint work, Principia Mathematica (1910-1913), was itself very influential. Today

7. 03: Mathematical Logic And Foundations
From The Mathematical Atlas, a resource of mathematics maintained by David Rusin. Extensive resources related to logic and set theory.
http://www.math.niu.edu/~rusin/known-math/index/03-XX.html

Extractions: POINTERS: Texts Software Web links Selected topics here Mathematical Logic is the study of the processes used in mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosophy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to Proof Theory. Students encounter elementary (sentential) logic early in their mathematical training. This includes techniques using truth tables, symbolic logic with only "and", "or", and "not" in the language, and various equivalences among methods of proof (e.g. proof by contradiction is a proof of the contrapositive). This material includes somewhat deeper results such as the existence of disjunctive normal forms for statements. Also fairly straightforward is elementary first-order logic, which adds quantifiers ("for all" and "there exists") to the language. The corresponding normal form is prenex normal form. In second-order logic, the quantifiers are allowed to apply to relations and functions to subsets as well as elements of a set. (For example, the well-ordering axiom of the integers is a second-order statement). So how can we characterize the set of theorems for the theory? The theorems are defined in a purely procedural way, yet they should be related to those statements which are (semantically) "true", that is, statements which are valid in every model of those axioms. With a suitable (and reasonably natural) set of rules of inference, the two notions coincide for any theory in first-order logic: the Soundness Theorem assures that what is provable is true, and the Completeness Theorem assures that what is true is provable. It follows that the set of true first-order statements is effectively enumerable, and decidable: one can deduce in a finite number of steps whether or not such a statement follows from the axioms. So, for example, one could make a countable list of all statements which are true for all groups.

8. Guide Entry 80.07.04
logic and set theory is designed to offer teachers and children a chance to explore what may be to them a different area of Finite Mathematics.
http://www.yale-university.org/ynhti/curriculum/guides/1980/7/80.07.04.x.html

Extractions: Yale-New Haven Teachers Institute Home Logic and Set Theory, by Richard N. Canalori Logic and Set Theory is designed to offer teachers and children a chance to explore what may be to them a different area of Finite Mathematics. The unit offers an introduction to the basic concepts and symbols of Logic and Set Theory and provides exercises in these two areas. Problem solving in all areas of mathematics requires the ability to reason and to form valid conclusions. Logic and Set theory will aid students in proving the equivalence of statements as well as in solving problems. Some of the ideas introduced in the unit include types of statements, truth tables, and Venn Diagrams, as well as the language of Logic and Set Theory. (Recommended for 6th through 12th grade Mathematics.) Key Words

9. Packages For Logic And Set Theory -- From Wolfram Library Archive
The fundamental operations of set theory and logic can be elegantly implemented in Mathematica in terms of the associated Boolean rings.
http://library.wolfram.com/infocenter/MathSource/694/

10. Introduction To Mathematical Logic And Set Theory
18.510 Introduction to Mathematical logic and set theory. This course provides an introduction to mathematical logic. Topics include propositional and
http://www-math.mit.edu/~rosen/18.510/

Extractions: This course provides an introduction to mathematical logic. Topics include propositional and predicate logic, the compactness and completeness theorems, elementary model theory, Godel's Incompleteness Theorem, and Zermelo-Fraenkel set theory. There are no specific prerequisites, though students are expected to have a certain level of mathematical maturity. Lecture: TR 2:30 - 4:00, in Room 4-159 Instructor: Eric Rosen , rosen (at) math (dot) mit (dot) edu Office: Office hours: Tue. 4 - 5, Fri. 1 - 2, and by appointment Textbook: Mathematical Logic: A Course with Exercises, Parts I and II Requirements: Problem sets will be given every two weeks. The first assignment will be due Sept. 21. There will be a midterm, on Oct. 19, and a final exam, on Dec. 18. Grading: The course grade will be determined by the homework (40%), the midterm (20%), and the final exam (40%). Final Exam: The final exam will take place on Monday December 18, from 1:30 to 4:30, in room 2-135. Homework: Homework must be handed in by 6:00 pm, either in class or in Room 2-172, on the day that it is due. Students are permitted to work together, but must write up solutions in their own words.

11. Logic And Set Theory
DPMMS Teaching logic and set theory. logic and set theory. The Mathematics Faculty web site provides a schedule and a course summary. Example sheets
http://www.dpmms.cam.ac.uk/site2002/Teaching/II/SetTheory Logic/

12. 234293 - Logic And Set Theory, Winter2007-2008 - Announcements
WebCourse(tm) 234293, logic and set theory for Cs, Winter20072008.
http://webcourse.cs.technion.ac.il/234293

13. Logic And Set Theory
CS Technion course Introduction to Set Theory and Logic here. Math HUJI course Introduction to Set Theory - here. Math HUJI course Logic - here.
http://cs.haifa.ac.il/courses/logica/

14. Modal Deduction In Second-Order Logic And Set Theory - II - Van
In this paper, we generalize the set theoretic translation method for polymodal logic introduced in to extended modal logics. Instead of devising an ad hoc
http://citeseer.ist.psu.edu/5103.html

15. Burgess On Plural Logic And Set Theory{dagger} -- Linnebo 15 (1): 79 -- Philosop
Burgess on Plural logic and set theory {dagger}. Øystein Linnebo. Department of Philosophy, University of Bristol, Bristol BS8 1TB United Kingdom
http://philmat.oxfordjournals.org/cgi/content/abstract/15/1/79

16. Notes On Logic And Set Theory
http://portal.acm.org/citation.cfm?id=39284

Someone new to logic and set theory, who is still developing the mathematical maturity needed to follow informal textbook proofs, may find some reassurance
http://us.metamath.org/

Extractions: Mirror Site Selection Metamath Home Page This page: FAQ Downloads Download help Reviews ... Metamath Proof Explorer - Constructs mathematics from scratch, starting from ZFC set theory axioms. Over 7,000 proofs. Updated 2-Mar-2008. News and most recent proofs: updated daily this mirror Hilbert Space Explorer Extends ZFC set theory into Hilbert space, which is the foundation for quantum mechanics. Includes over 1,000 complete formal proofs. Updated 24-Dec-2007. Quantum Logic Explorer - Starts from the orthomodular lattice properties proved in the Hilbert Space Explorer and takes you into quantum logic with around 1,000 proofs. Updated 9-Oct-2006. Metamath Solitaire - A Java applet that demonstrates simple proofs. Built-in axiom systems include ZFC; modal, intuitionistic, and quantum logics; and Tarski's plane geometry. Updated 24-Feb-2007. GIF and PNG Images for Math Symbols Updated 24-Jan-2008. Metamath Music Page - Strictly for fun. You can listen to what mathematical proofs "sound" like! Updated 29-May-2006. 21-May-2007 Some advanced and difficult miscellaneous open problems related to Metamath and other topics on this site.

18. Logic And Set Theory
INTRODUCTION TO logic and set theory Sets, Set operations, relations, equivalence relations and partitions, functions, induction principles,
http://www.math.bgu.ac.il/~efrat/logic2000.html

Extractions: Dr. Ivgenya Ackermann Prof. Ido Efrat Dr. Rubim Lipyanski Yona Maisel Hen Dubi Victoria Lubitch Sets, Set operations, relations, equivalence relations and partitions, functions, induction principles, partial and total orderings Truth tables, truth values, logical equivalence, disjunctive normal forms, complete connector systems Its language, formulas, structures, satisfaction, normal forms, definability, isomorphisms of structures

19. McGraw-Hill's AccessScience
Probability, statistics, combinatorial theory Topology Trigonometry. logic and set theory Boolean algebra - Lattice (mathematics) - Logic
http://www.accessscience.com/browseTOC.aspx?main=12&sub=511000

20. Chapters.indigo.ca: Notes On Logic And Set Theory: P. T. Johnstone: Books
Suitable for all introductory mathematics undergraduates, this text covers the basic concept of logic firstorder logic, consistency, and the completeness
http://www.chapters.indigo.ca/books/Notes-Logic-Set-Theory-P-T-Johnstone/9780521

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