## Foundations of mathematics(MAT115)

Course Code Course Name Semester Theory Practice Lab Credit ECTS
MAT115 Foundations of mathematics 1 4 0 0 4 6
 Language of Instruction French Course Type Compulsory Course Level Bachelor Degree Course Instructor(s) Serap GÜRER serapgurer@gmail.com (Email) Assistant Objective To introduce the subjects and technics of pure mathematics Content Logic, Proof methods, Notion of set, Family of sets, Product of sets,Relations, Functions, One to one, surjective functions, composition of functions, equivalence relation, equivalence classes, quotient sets, Order relations Course Learning Outcomes 1. Knowledge of proof methods2. Set notion3. Define notions of relation and function 4. Composing functions5. Define equivalence relation, order relation6. Explain notions of partial ordering, well ordering Teaching and Learning Methods References Deschamps et Warusfel , Mathématiques 1ère année, Cours et exercices.Gary Chartrand, Albert D. Polimeni, Ping Zhang, Mathematical Proofs: A Transition to Advanced Mathematics
###### Theory Topics
Week Weekly Contents
1 Introduction to logic
2 Introduction to logic
3 Set theory
4 Set theory
5 Relations
6 Relations
7 Mid-term examination
8 Functions
9 Functions
10 Cardinalities of sets
11 Cardinalities of sets
12 Mid-term examination
13 Proof in group theory
14 Proof in group theory
###### Practice Topics
Week Weekly Contents
Number Contribution
Contribution of in-term studies to overall grade 2 60
Contribution of final exam to overall grade 1 40
Toplam 3 100
###### In-Term Studies
Number Contribution
Assignments 0 0
Presentation 0 0
Midterm Examinations (including preparation) 2 50
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 4 50
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
Toplam 6 100
No Program Learning Outcomes Contribution
1 2 3 4 5
1 understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; X
2 can properly state and use concepts and results of major mathematical interest; X
3 masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; X
4 is able to express one’s mathematical ideas in an organised way both in written and oral forms; X
5 understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); X
6 has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;
7 has a theoretical and practical knowledge in computer science well adapted for learning a programming language;
8 has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;
9 has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; X
10 masters French language as well as other foreign languages, to a level sufficient to study or work abroad. X
Class Hours 14 4 56
Working Hours out of Class 0 0 0
Assignments 6 3 18
Presentation 0 0 0
Midterm Examinations (including preparation) 2 25 50
Project 0 0 0
Laboratory 0 0 0
Other Applications 0 0 0
Final Examinations (including preparation) 1 25 25
Quiz 4 1 4
Term Paper/ Project 0 0 0
Portfolio Study 0 0 0
Reports 0 0 0
Learning Diary 0 0 0
Thesis/ Project 0 0 0
Seminar 0 0 0
Other 0 0 0