COURSE INFORMATION Course Title: ADVANCED MATHEMATICS FOR COMPUTER SCIENCE

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
CEN 535	B	3	3	2	0	4	7.5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Assoc.Prof.Dr. Arban Uka auka@epoka.edu.al , Wed 10:00-12:00
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Elective
Study program: (the study for which this course is offered)	Master of Science in Computer Engineering (2 years)
Classroom and Meeting Time:
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	N/A
Course Description:	Development of theories and methods for computer and information sciences, the design, implementation, and analysis of algorithms and software tools for mathematical computation and reasoning, and the integration of mathematics and computer science for scientific and engineering applications.
Course Objectives:	To equip the students with the mathematical tools and skills that are needed in different areas of Computer Engineering. Introduction to complexity theory. Statistical analysis of data, moments of data distribution. Fourier series, Fourier Transforms and its application in data analysis. Wavelet Theory. Application of Fourier Transforms in Image Processing. Eigenvalue and eigenvector problems. Diagonalization by Eigenvector Matrix, Diagonalization by Singular Value Decomposition. Introduction to Principal Component Analysis (PCA) and to Independent Component Analysis (ICA).

BASIC CONCEPTS OF THE COURSE

1	Understanding the use of Fourier and wavelet transforms in data (images)
2	Understanding the advanced Linear Algebra principles in data analysis

COURSE OUTLINE

Week	Topics
1	Complexity in Sciences, Complexity theory
2	P vs NP problem, Algorithms
3	Fourier series
4	Fourier Transform application in Signal (data, image) Processing
5	Gabor Transform, Wavelet Theory Transform
6	Image de-noising using Diffusion and Filters in k-space
7	Data processing in real and transform domains, x- & k-domain, t- & w-domain, Uncertainty Principle
8	Review
9	Linear Algebra, Eigenvalues, Eigenvectors of a matrix
10	Diagonalization of covariance matrix by Eigenvector matrix, diagonalization by SVD (Singular Value Decomposition)
11	Applications of Singular Value Decomposition
12	Introduction of Principal Component Analysis and Independent Component Analysis
13	Independent Component Analysis (ICA) application on images
14	Review

Prerequisite(s):
Textbook(s):	Data-Driven Modeling and Scientific Computation J. N. Kutz.
Additional Literature:	Numerical Recipes - The Art of Scientific Computing (3rd Edition) by W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery
Laboratory Work:	2 hours per week
Computer Usage:	Yes
Others:	No

COURSE LEARNING OUTCOMES

1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence
8	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology
9	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Master of Science in Computer Engineering (2 years) Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	4
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	5
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	5
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	5
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	4
8	Ability for effective oral and official communication skills in foreign language.	5
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	5
10	Engineering graduates with well-structured responsibilities in profession and ethics.	5
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	5
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	5

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Midterm Exam(s)	1	20
Project	1	20
Final Exam	1	50
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	5	80
Hours for off-the-classroom study (Pre-study, practice)	16	2	32
Mid-terms	1	15	15
Assignments	3	12	36
Final examination	1	24.5	24.5
Other			0
Total Work Load:			187.5
Total Work Load/25(h):			7.5
ECTS Credit of the Course:			7.5

CONCLUDING REMARKS BY THE COURSE LECTURER