NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Foundations of Mathematics
Course code:Mth 102 FM
Unit Coordinator
Shima Adnan
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 1
Education Aims:
Foundations of mathematics is a part of mathematics which deals with the study of fundamental concepts in each of mathematical logic, theory of sets, functions and theory of numbers, in order to provide an information base for gateway the other parts of mathematics.
Course outline and objectives
There are several important reasons for studying foundations of
mathematics:
1- Through this course you can develop your mathematical maturity: that is
you able to understand and create mathematical arguments, be sure you will
not get very far in their studies in the mathematical sciences without these
skills.
2- It is the gateway to more advanced courses in all parts of the mathematical
sciences.
The course will cover: -
1- Basic ideas in mathematical logic studies, particularly some ideas in
philosophical logic-logic motivated largely by philosophical issues.
2- Theory of sets which is all other concepts in mathematics depends on it.
3- The concepts of relations and functions which they have important role in
each area of mathematics.
4- Equipotent of sets.
5- Binary operations and mathematical systems.
6- Construction of natural numbers, integer numbers, rational numbers and
real numbers.
Communications with Academic Staff
This handbook gives information on how to contact and communicate with staff.
We provide room numbers and email addresses of staff to you. The staffs in this department want to help you as much as possible so that you will be successful in your programme. We also want to encourage you to take responsibility for yourselves and for your learning so it will help you in your future careers.
Staff associated with the unit:
Staff
Room Number
Email
Shima Adnan
Head of Mathematic Dep. Room
Shima.adnan@yahoo.com
Soran University
Department of Mathematics
Unit: Calculus
Credit 4 for one semester
Method of Assessment:
2x 2 h lectures and 1 x 1 h Tutorial per week.
Examination and grading
Month’s exam: 30%
Classroom participation and assignments and homework 10%
Final exam: 60%
Marking System
The grades for each piece of assessed work are as follows:
* 90-100 % is excellent
* 80-89% is very good
* 70-79% is good
* 60-69% is a moderate pass
* 50-59% is a pass
* <49% is a fail
Unit Timetable/Content
University Academic Week
Lecture Title & Content
Assessments1Introduction to mathematical logic: statements, logical operators.2logical equivalence, tautologies, contradiction and arguments.3,4Mathematical proof.5Problem solving sessions6,7 Set theory: set operators, family of sets, power of sets, n-tuples and cartesian product
First examination8,9Relations: types of relations, (domain and range) of relations, operation on relations and composition of relations10,11,12Equivalence relations, equivalence classes and partitions.
Second examination13,14,15Partially ordered sets, (first, last, minimal and maximal) elements in partially ordered sets, bounded sets (supremum and infimum concepts), totally ordered sets and well ordered sets16,17Functions: (domain, range and graph) of functions, composition of functions, type of functions, operation on functions.
18,19Direct image and inverse image under functions, similarity between sets.
20,21Cardinality and ordinality.
22,23 Problem solving sessions,
Binary operations and mathematical systems.24,25Construction of natural numbers (N): Peano axiom’s, recursion theorem, operation on N and order on N.
26Construction of the set of integer numbers (z): operation on z and order on z.27,28Construction of the set of rational numbers (q): operation on q
and order on q.
29,30Construction of real numbers. Problem solving session
Third examination
* Note that, Tutorials will be arranged by your lecturer during the class.
Tutorials & Assessments
Attendance at tutorials & Assessments is necessary in order to gain marks for the given exercise.
Recommendation
Keeping a wall diary is recommended to enter all deadline dates so you can see what assignments are due in. It is also essential to leave yourself sufficient time to complete the work.
Recommended Reading &References:
Any reference with the following titles is useful for you:
1- Foundations of Discrete Mathematics.
2- Discrete Mathematics.
3-Logic and Theory of Sets.
4- Elements in Set Theory.
5- Set Theory. 6- Introduction of Set Theory.