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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS BIL 3126 COMPUTER ALGEBRA ELECTIVE 3 0 0 5

Offered By

Computer Science

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR FIDAN NURIYEVA

Offered to

Computer Science

Course Objective

The goal of this course is to gain the students the knowledge of the application of arithmetic on different algebraic fields.

Learning Outcomes of the Course Unit

1   Be able to use arithmetic operations on different algebraic fields. 2   Be able to run algorithms of algebraic problems. 3   Adopting modular arithmetic theory

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Analysis of Algorithms (Algorithmic Complexity. Bit-Operation Complexity). 2 Number Systems. Integer Computation Algorithms (Addition, Subtraction, Multiplication) and complexity. 3 Divisibility and Division Algorithm. Prime Numbers. Greatest Common Divisor (gcd). Euclid Algorithm and Complexity. 4 The Extended Euclidean algorithm and complexity. 5 Modular arithmetic (Congruences). 6 Solution Algorithms and Complexity of Modular Linear Equations. 7 Chinese remainder theorem and the usage of this theorem to speed up the computations. 8 Primitive Roots. Discrete Logarithm. 9 Comlete and Reduced Residue Systems. Fermat's Little Theorem. Euler's Theorem. Wilson Theorem. 10 Calculation Algorithm of (a^b mod n) and its Complexity. 11 Cryptology. Symmetric Cryptosystems. RSA Algorithm and Analysis. 12 Factorization Algorithms and their complexity 13 Methods of finding prime numbers and the comparison between these methods, primality tests, primality tests with probability 14 Recap.

Recomended or Required Reading

Textbook(s): 1. Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Third Edition, MIT Press, (2009). 2. Modern Computer Algebra, Joachim Von Zur Gathen and Jürgen Gerhard,Cambridge University Press, (1999). Supplemantory Book:

Planned Learning Activities and Teaching Methods

The course is taught in a lecture and discussion format. In some weeks of the course, results of the homework given previously are discussed. Lecture format, built around the textbook readings with numerous examples chosen to illustrate theoretical concepts.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

fidan.nuriyeva@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparations before/after weekly lectures 14 3 42 Preparation for midterm exam 1 18 18 Preparation for final exam 1 20 20 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 126

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 3 3 4 5 5 3 4 LO.2 5 4 5 5 4 4 4 5 5 LO.3