M.SC. in Computer Engineering (Without Thesis)

MATH 554 | Course Introduction and Application Information

Course Name

Basic Topics in Mathematics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 554	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	-
National Occupation Classification	-
Course Coordinator	-
Course Lecturer(s)	Dr. Öğr. Üyesi Halis Can KOYUNCUOĞLU
Assistant(s)	-

Course Objectives

To introduce basic topics in Mathematics at masters level. To prepare students for advance courses in Mathematics.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to understand linear algebra.
2	will be able to learn the applications of linear algebra.
3	will be able to solve differential equations.
4	will be able to understand the applications of differential equations and their quantitative analyses

Course Description

This course will both review and extend a number of basic mathematical tools which are generally useful in applications and are typically assumed as prerequisites for many of the current courses.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Related Preparation	Learning Outcome
1	Linear systems and their graphs, Gauss elimination, determinant, the inverse of a matrix.	David C. Lay, Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications"
2	Linear independence, span of a set, basis and dimension, eigenvalue and eigenvectors, similar matrices, diagonalization.	David C. Lay, Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications"
3	İnner product space, Hilbert space, orthogonality and orthonormality.	Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
4	Applications in linear algebra.	David C. Lay, Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications", Fuad Aleskerov, Hasan Ersel, Dmitri Piontkovski," Linear Algebra for Economists"
5	Introduction to differential equations, classification of differential equations, autonomous equations and stability.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
6	First Order differential equations: Separable, homogeneous, linear, exact and Bernoulli equations.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
7	Systems of first order differential equations.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
8	System of first order differential equations.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
9	Rewiev Midterm.
10	Laplace transforms.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
11	Applications of differential equations.	R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations"
12	Introduction to difference equations, linear difference equations.	Saber N Elaydi, "An Introduction to Difference Equations "
13	Discrete dynamic systems and their fundamental properties.	Saber N Elaydi, "An Introduction to Difference Equations ", Saber N Elaydi, "Discrete Chaos"
14	Student presentation.
15	Student presentation.
16	Review.

Course Notes/Textbooks

David C. Lay, Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications", Pearson Education Limited; 5th edition.

R. Kent Nagle, Edward B. Saff, Arthur David Snider, "Fundamentals of Differential Equations", Pearson; 9th edition.

Suggested Readings/Materials

An Introduction to Difference Equations (Saber N Elaydi)

Saber N Elaydi, "Discrete Chaos ", Chapmand and Hall/CRC (2000)

Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.

Fuad Aleskerov, Hasan Ersel, Dmitri Piontkovski," Linear Algebra for Economists", Springer

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	-	-
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	50
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	1	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	15	6	90
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	-	-	0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	40	40
Final Exam	1	47	47
		Total	225

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.		-	-	-	X	-
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	X	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.		-	-	-	X	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	-	X
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	X	-
7	Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.		-	-	-	X	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.		-	-	X	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	X	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.		-	-	X	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	X	-	-	-