Jordan University of Science and Technology
Faculty of Science and Arts
Department of Mathematics and Statistics
Second Semester 2012/2013
Course Information
Course Title
Set Theory and Logic
Course Number
Math 245
Prerequisites
Math 102
Office Location
Instructor
Office Hours
Course Description
In this course we mainly study the following subjects Logic and Proofs, Set Theory, Relations, Functions, Cardinality of Sets and
Cardinal Numbers
Textbook
References
Shwu-Yeng T. Lin and You-Feng Lin “Set Theory: An Intuitive Approach”, First Edition, Houghton
Mifflin Comp., Boston.
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Transition to Advanced Mathematics, D. Smith, M. Eggen and R. St. Andre
Introduction to Set Theory, Monk J. Donald, McGraw-Hill Inc. New York.
Set Theory and Logic, Fraenkel Abraham A., Addison-Weseley, Reading Mass.
Set Theory and Related Topics, Schaum’s Outline Series, McGraw-Hill Book Company.
The Logic Book, M. Bergmann, J. Moore and J. Nelson, McGraw-Hill Book Company.
Grading policy
First Exam 30%
Second Exam 30%
Final Exam 40%
Course Objectives
1.
2.
3.
4.
5.
6.
7.
To know the logical statements, connectives and the quantifiers.
To be familiar of all types of mathematical proofs: direct, indirect and proof by contradiction. Also to prove statements
using mathematical induction
To study the sets: their notations, and operations. Also to study the indexed family of sets, and to know how to work
with arbitrary union and arbitrary intersection of sets.
To study relations: equivalence relations and its classes and partial order relations, then to solve variety of problems
concerning such relations.To define partitions, and to see how it is connected with equivalence classes.
To study functions, its notations, and to define injective, surjective and bijective functions; main properties and results.
To know the induced sets functions: the image and the inverse image of sets under a certain function.
To study the cardinality of sets, denumerable sets, Infinite set and finite set,
Week#
1
2
3
4+5
Sections and Suggested Exercises
1.1 Statements and their connective 12-19,22-25
1.2 There more connective 1-14
1.3 Tautology, implication, and Equivalence 1-7,9,11.
1.4 Contradiction1-5
1.5 Deductive Reasoning 1-13
*Mathematical proofs: direct, indirect and proof by contradictions
1.6 Quantification rules
1.8 Mathematical induction 3-8
6
2.1 Sets and subsets 5-8
2.2 Specification of sets 1-3
7
2.3 Unions and intersections 1,2,6-11
2.4 complements 1-11
8
2.6 Indexed Families of Sets 1,3-7
3.1 Cartesian Product of two sets 2-6,8,9
9
3.2 Relations 1-8
3.3 Partitions and Equivalence Relations 1,3,5
3.4 functions 1,2,4-5,8,12,14
3.5 Images and inverse images of sets 1,4-5,7-11
3.6 Injective , Surjective and Bijective functions 3,7,8,12,13,14
3.7 Composition of Functions 4-7
10
11
12
14
4.1 Finite and infinite sets 2,3,5,7,8
4.2 Equipotence of sets 3,4,6-8
4.3 Examples and properties of Denumerables Sets 2, 3,4,7
4.4 Nondenumerable sets 1,2
15
5.1 The concept of Cardinal numbers
13
‫ كل من يتغيب عن امتحان يجب ان يقدم عذر خالل اسبوع (كحد اقصى من عقد االمتحان ) واال يفقد حقه بتقديم‬.1
‫االمتحان التكميلي‬
‫ اي محاولة غش يقوم بها الطالب يطبق عليه نظام تاديب الطلبة وفي حالة ضبط الطالب متلبسا بالغش اثناء تادية‬.2
‫) من نظام تاديب الطلبة‬6( ‫االمتحان تطبق عليه المادة‬
‫ بدون عذر فانه يفصل من ذلك المساق حسب تعليمات منح درجة‬%10 ‫ اذا تغيب الطالب عن اي مساق اكثر من‬.3
‫البكالوريوس‬