Selected Topics I (MAT371) | GSÜ - ECTS Information Guide

Content

Objective

The objective of this course is to study selected topics from five fundamental theories of Applied Mathematics: optimization theory, fixed point theory, approximation theory, game theory, and social choice theory.

Course Content

Within the framework of this course, the selected topics will first be studied through the fundamental concepts and results of the corresponding theories. Their historical development will then be discussed, followed by a presentation of the necessary mathematical tools and prerequisites. Finally, the methods and concepts studied will be applied to problems arising in fields such as data science, economics, physics, and numerical analysis.

Course Learning Outcomes

Upon successful completion of this course, students will be able to explain the fundamental concepts and main results of optimization theory, fixed point theory, approximation theory, game theory, and social choice theory. They will also be able to assess the historical development of these theories and their importance in various fields of application of mathematics, use fundamental mathematical methods and techniques related to the theories studied, construct mathematical models and apply them to different types of problems, and identify and apply appropriate mathematical methods to selected problems in data science, economics, physics, and numerical analysis.

Teaching and Learning Methods

Study and discussion of the topics covered in class, sample questions (quizzes) during the lectures, more comprehensive assignments, and reading topics.

References

Introduction to Global Optimization , R. Horst , P. M.Pardolas &N. V. Thoai , Kluwer Academic
Publishers ,

The Princeton Companion to Applied Mathematics , Edited by Nicholas J. Higham ,
Princeton University Press , 2015

https://nhigham.com/2016/03/29/the top 10 algorithms in applied mathematics

A gentle introduction to optimization / B. Guenin , J. Könemann , L. Tunçel Cambridge
University Press

Introductory Functional Analysis with Applications, E. Kreyszig, Wiley
An Introduction to Real Analysis, T. Terzioğlu, ODTÜ
Fonksiyonel Analizin Yöntemleri, T. Terzioğlu, Matematik Vakfı
Fonksiyonel Analiz, E. Şuhubi, İTÜ Vakfı
Bir Analizcinin Defeterinden Seçtikleri, T.Terzioğlu, Nesin Matematik Köyü
Real Analysis with Economic Applications, Efe A. Ök, Princeton University Press
Numerical Optimization , J. Nocedal & S. J. Wright, Springer , 1999. ve 2. basım

Mutiagent Systems,
by Yoav Shoham & Kevin Leyton-Brown,
Cambridege, 2010

You can download from:
http://www.masfoundations.org/download.html

Weekly Contents

Theory Topics
Week	Weekly Contents
1
2
3
4
5
6
7
8
9
10
11
12
13
14

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	2	50
Contribution of final exam to overall grade	1	50
Total	3	100

In-Term Studies
Activities	Number	Contribution
Assignments	1	25
Presentation	1	25
Midterm Examinations (including preparation)	0	0
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
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
Make-up	0	0
Total	2	50

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;
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	3	42
Working Hours out of Class	2	5	10
Assignments	1	25	25
Presentation	1	20	20
Midterm Examinations (including preparation)	0	0	0
Project	0	0	0
Laboratory	0	0	0
Other Applications	0	0	0
Final Examinations (including preparation)	1	20	20
Quiz	0	0	0
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
Make-up	0	0	0
Yıl Sonu	0	0	0
Hazırlık Yıl Sonu	0	0	0
Hazırlık Bütünleme	0	0	0
Total Workload			117
Total Workload / 25			4.68
Credits ECTS			5