MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
CMP3005	Analysis of Algorithms	Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Dr. Öğr. Üyesi CEMAL OKAN ŞAKAR
Course Lecturer(s):	Dr. Öğr. Üyesi TEVFİK AYTEKİN Prof. Dr. NAFİZ ARICA Dr. Öğr. Üyesi CEMAL OKAN ŞAKAR
Recommended Optional Program Components:	None
Course Objectives:	The objective of the course is to introduce the fundamental mathematical tools needed to analyze algorithms, basic algorithm design techniques, advanced data structures, and important algorithms from different problem domains.

Learning Outcomes

The students who have succeeded in this course;
I. Become familiar with some major advanced data structures and algorithms.
II. Become familiar with mathematical tools used in analyzing algorithms.
III. Be able to analyze the asymptotic running time of an (iterative/recursive) algorithm.
IV. Be able to make best/worst/average case analysis of algorithms.
V. Become familiar with important algorithm design paradigms.
VI. Be able to decide which data structure/algorithm among a set of possible choices is best for a particular application.
VII. Be able to recognize and distinguish efficient and inefficient algorithms.
VIII. Be able to design efficient algorithms for new problems using the techniques learned and apply/report these solutions in an intra-discipline project group.

Course Content

Introduction, asymptotic notation, empirical analysis of algorithms, designing algorithms, amortized analysis, brute force algorithms, divide and conquer algorithms, transform and conquer algorithms, space and time trade-offs, dynamic programming, greedy algorithms, advanced data structures, B-trees, Insertion and Deletion from B-trees, graphs and graph algorithms, P, NP, and NP-complete problems.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Introduction, asymptotic notation.
2)	Empirical analysis of algorithms, analysis of algorithms, amortized analysis
3)	Recurrences, substitution method, recursion-tree method, master method.
4)	Brute Force Algorithms
5)	Divide and Conquer Algorithms
6)	Merge sort, quicksort, randomized quicksort, binary search
7)	Transform and Conquer Algorithms: Solving systems of linear equations with Gaussian ination elimination, Balanced Search Trees, Heaps and Heapsort, Horner's Rule and Binary Exponentiation
8)	Space and Time Trade-offs: Input Enhancement (Counting based sorting, string matching), Prestructuring (Hashing, Hash functions, open addressing).
9)	Midterm
10)	Dynamic Programming: Coin-row problem, Knapsack problem, Longest common subsequence.
11)	Dynamic Programming: Knapsack problem, Longest common subsequence.
12)	Greedy Algorithms: Activity selection, Huffman codes, Prim’s algorithm, Kruskal’s Algorithm
13)	Single-source shortest paths: The Bellman-Ford algorithm, Dijkstra's algorithm.
14)	P, NP, and NP-complete problems

Sources

Course Notes / Textbooks:	Anany Levitin, The Design and Analysis of Algorithms, Pearson International Third Edition. Cormen, T. H., Leiserson, C. E., Rivest, R. L. and Stein, C., Introduction to Algorithms (3rd Edition), MIT Press, 2009. Sanjoy Dasgupta , Christos Papadimitriou, Umesh Vazirani, Algorithms, McGraw-Hill Education.
References:	Yok - None

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	2	% 10
Project	1	% 20
Midterms	1	% 30
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Workload
Course Hours	14	42
Project	7	21
Quizzes	6	12
Midterms	5	28
Final	5	35
Total Workload		138

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics
2)	To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods,
3)	To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials,
4)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,	4
5)	To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way,
6)	To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
7)	To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,
8)	To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,	4
9)	By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,
10)	To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning,
11)	To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school,
12)	To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.