• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Prove basic mathematical statements using direct proof, method by contradiction, proof by contrapositive.

   Contribution to Program Outcomes

   1. Acquire scientific knowledge
   2. Work effectively in multi-disciplinary research teams
   3. Find out new methods to improve his/her knowledge.

   Method of assessment

   1. Written exam
   2. Homework assignment
2. Analyze the properties of sets, functions (injective, surjective, bijective), sequences (in real line) and argue on countability of sets.

   Contribution to Program Outcomes

   1. Propose alternative point of views by analyzing complex industrial problems methodically
   2. Acquire scientific knowledge
   3. Find out new methods to improve his/her knowledge.

   Method of assessment

   1. Written exam
   2. Homework assignment
3. Analyze real line, its subsets and their properties

   Contribution to Program Outcomes

   1. Acquire scientific knowledge

   Method of assessment

   1. Written exam
   2. Homework assignment
4. Define metric spaces and generalize the definitions/ properties in real numbers to general metric spaces.

   Contribution to Program Outcomes

   1. Acquire scientific knowledge

   Method of assessment

   1. Written exam
   2. Homework assignment
5. Demonstrate a general understanding on the fundementals of Linear algebra.

   Contribution to Program Outcomes

   1. Propose alternative point of views by analyzing complex industrial problems methodically
   2. Become an authority in modeling, simulation, process management and related subjects.
   3. Acquire scientific knowledge

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Logic and proof methods
Week 2:	Review of linear algebra, LU decomposition
Week 3:	Fields, vector spaces, subspaces. Homework assignment 1
Week 4:	Linear, conic, convex, affine combinations, linear dependence, span and basis
Week 5:	Change of basis and linear transformations. Row, column, null and left null spaces
Week 6:	Orthogonality
Week 7:	Projection, pseudo inverse. Homework assignment 2
Week 8:	Eigen values, eigen vectors, diagonalizatio, the minimal polynomial. Midterm exam
Week 9:	Positive definiteness, generalized eigen spaces
Week 10:	Sets, countability, the set of real numbers and its properties, extended real numbers system. Homework Assignment 3
Week 11:	Sequences, convergence, series, test of convergence in series, absolute convergence
Week 12:	Metric spaces, inner product spaces, normed spaces
Week 13:	Open and closed sets, interior, closure and boundary of a set
Week 14:	Convergence, subsequences, accumulation points, bounded sets and completeness in metric spaces. Homework Assignment 4
Week 15*:	-
Week 16*:	Final exam
Textbooks and materials:
Recommended readings:	Principles of Mathematics in Operations Research , Levent Kandiller Mathematical Methods of Engineering Analysis, Erhan Çınlar, Robert J. Vanderbei Principles of Mathematical Analysis, Rudin, McGraw-Hill
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	30
Other in-term studies:		0
Project:		0
Homework:	3,7,10,14	30
Quiz:		0
Final exam:	16	40
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	6	14
Practice, Recitation:	0	0
Homework:	6	4
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	12	1
Mid-term:	2	1
Personal studies for final exam:	2	12
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)