Single Variable Analysis I (MAT101) | GSÜ

Content

Objective

To build, with appropriate rigour, the foundations of calculus and along the way to develop the skills to enable us to continue studying mathematics

Course Content

Course syllabus : Real Numbers, Sequences, Topology of R, Continuity, Limits

Course Learning Outcomes

The student is expected to learn the main notions ( Real Numbers, Sequences, Topology of R, Continuity, Limits).

Teaching and Learning Methods

Course and the problem solving

References

Course book : First Course in Real Analysis, Sterling K.Berberian, Springer

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Properties of reel numbers
2	Properties of reel numbers
3	İnfimum- Supremum
4	İnfimum- Supremum
5	Midterm Exam
6	Sequences : Definitions and examples
7	Sequences : Limits
8	Sequences : Convergence theorem
9	Sequences : Convergence theorem
10	Midterm Exam- Notions of function
11	Limits and continuous functions : Limits
12	Limits and continuous functions : Continuity in one point
13	Limits and continuous functions : Continuity on an interval
14	Limits and continuous functions : Elemamtary functions

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	3	60
Contribution of final exam to overall grade	1	40
Total	4	100

In-Term Studies
Activities	Number	Contribution
Assignments	2	5
Presentation	1	10
Midterm Examinations (including preparation)	2	50
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	1	10
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
Total	6	75

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	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;			X
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;			X
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;	X
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

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	5	70
Working Hours out of Class	14	3	42
Assignments	2	3	6
Presentation	4	6	24
Midterm Examinations (including preparation)	2	12	24
Final Examinations (including preparation)	1	15	15
Term Paper/ Project	1	3	3
Total Workload			184
Total Workload / 25			7.36
Credits ECTS			7