Department of Mathematics
Islamic University of Gaza
Course Description and Syllabus
Principles of Mathematics: Math 2450 / First Semester 2015
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Instructor: Dr. Ahmed EL Mabhouh
Office: C 427
Telephone: 286-0700 ext: 2620.
E-mail: mabhouh@iugaza.edu.ps
Office Hours:
Sunday and Tuesday: 11:00 - 12:30
Monday: 11:00 - 13:00
Prerequisite: Calculus A and Calculus B.
Textbook: A Transition to Advanced Mathematics, by Douglas Smith, Seventh
Edition.
Evaluation and Grading Policy: The grade for this course will be based on the
following:
Homework and Quizzes: 10% (There will be weakly homeworks or
quizzes consisting of textbook exercises.)
Midterm Exams: 2 x 20% = 40% (the dates of each exam will be
determined later.)
Final Exam: 50%
Course Description: The course deals with the following topics: Logic and
Proofs, The Theory of Sets, Relations and Functions, Finite and Infinite Sets,
Countable and Uncountable Sets, Denumerable and Non denumerable Sets, and
Cardinal Numbers and Their Arithmetic.
Course Aims:
o To introduce Logic and Methods of Proof.
o To introduce Basic Definitions and Theorems about Set Theory.
o To introduce Relations, Equivalence Relations, and Ordered
Relations.
o To introduce Functions and Their Properties.
o To introduce Finite and Infinite Sets, Countable and Uncountable Sets, and
Denumerable and Non denumerable Sets.
o To introduce Cardinal Numbers and Their Arithmetic.
Course Intended Learning Outcomes:
 Perform basic logical operations and generalize the rules of logic to set
theory, relations and functions.
 Implement various methods of proof including direct and indirect proofs,
and proofs by induction, in proving a large selection of mathematical
statements.
 Determine whether a relation is a function, and identify the function’s
properties.
 Verify that a given relation is an equivalence relation, and find all
equivalence classes. Verify that a given relation is an ordered Relation.
 Determine whether a a function is one-to-one or onto.
 Perform basic set operations and determine set equivalence and the
cardinality of sets.
 Determine whether a given set is finite or infinite, countable or uncountable,
denumerable or non denumerable.
 Perform basic arithmetic operations on cardinal numbers.
Homework: It has been said that the best way to learn mathematics is to practice it.
You simply can’t be a good mathematician by just sitting in the classroom and
reading through-out the textbook or your notebook. You have to be a participant;
that is, beside reading throughout the textbook and class notes, you need to pick up
a pencil and a few sheets of paper and work out a lot of the exercises that are listed
at the end of each section. The more you solve problems, the more you understand
the material. Therefore, I will ask you to work out a number of problems listed at
the end of each section, and you might be asked to turn in some of these problems.
I will be glad to answer your questions about the homework problems during the
class meetings or during the office hours.
References: It is a very good idea that you try to look at other references (or
textbooks) in Set Theory and Logic. This will widen your knowledge, enhance
your understanding, and help you in solving the homework problems. The Islamic
University Library may have some references that are related to set theory and
principles of mathematics and you may borrow some. Among the good references
are:
 Lin, Shwu-Yeng T., and Lin, You-Feng, Set Theory with Applications, 2nd
edition, Mariner Publishing Company, Inc., 1981.
 Apostol, T. M., Mathematical Analysis, 2nd edition, Addison Wesley,
Reading, Mass., 1974.
 Kleene, Stephen C., Mathematical Logic, John Wiley & Sons, Inc., New
York, 1967. Frankel, Abraham A., Set Theory and Logic, Addison Wesley,
Reading, Mass., , 1966. Halmos, Paul R., Naive Set Theory, D. Van
Nostrand, Inc., Princeton, N.J., , 1960.
Distribution of Course on Weeks: We shall cover in this course as many of the
following topics as time allows.
1. Logic and Proofs: 4 weeks.
2. Theory of Sets: 3 weeks.
3. Relations : 2 weeks. .
4. Functions :3 weeks
5. Cardinal Numbers : 2 weeks.
6. Review: 1 week.