Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
YMB0021		Computer Algebra	3/0/0	DE	Turkish	7

Course Goals	Introducing the algorithms for the part of the commutative algebra which is suitable for computer calculations and encouraging students to implement them on their own using a computer algebra system (ApCoCoA).
Prerequisite(s)	. Linear Algebra I . Algebra I
Corequisite(s)	-
Special Requisite(s)	The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)	Assist. Prof. Dr. Levent Çuhacı
Course Assistant(s)
Schedule	Day, hours, XXX Campus, classroom number.
Office Hour(s)	Instructor name, day, hours, XXX Campus, office number.
Teaching Methods and Techniques	Explaining the theoretical background  in class with computation methods in an algorithmic way then  encouraging the students to  implement them  (see Worksheet)
Principle Sources	Computational Commutative Algebra 1 –Martin Kreuzer, Lorenzo Robbiano
Other Sources	Computer, ApCoCoA (free computer algebra software)

Course Schedules
Week	Contents	Learning Methods
1. Week	Polynomial rings and extended Euclidean algorithm	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
2. Week	Monomial ideals and term orderings	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
3. Week	Macaulay’s basis theorem and Dickson’s Lemma	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
4. Week	Grading of rings and homogenous ideals	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
5. Week	Syzygy computations and lifting of syzygies	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
6. Week	Buchberger Algorithm and computing Gröbner bases of ideals	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
7. Week	Computation of syzygy modules by the help of Gröbner bases	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
8. Week	Computation of the kern and images of homomorphims of modules and lifting of linear maps	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
9. Week	Computation of elimination, localization and saturation	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
10. Week	Systems of polynomial equations	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
11. Week	Some applications of Gröbner Bases	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
12. Week	Some examples	Explaining the theoretical background in class with computation methods in an algorithmic way then encouraging the students to implement them (see Worksheet)
13. Week	Reviewing some topics for the Exam	Worksheet
14. Week	Reviewing some topics for the Exam	Worksheet
15. Week
16. Week
17. Week

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	1	30
Homework / Term Projects / Presentations	13	30
Final Exam	1	40

Program Outcomes PO-1 Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge. PO-2 On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods PO-3 Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution. PO-4 Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides. PO-5 Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way. PO-6 Use information and communication technologies with computer software in advanced level. PO-7 Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages. PO-8 Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation. PO-9 To solve problems related to the field, establish functional interacts by using strategic decision making processes. PO-10 Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.

Learning Outcomes LO-1 I. Understand polynomial rings and monomial ideals. LO-2 II. Undestand the theoritical background and they can compute Gröbner basis and the reduced Gröbner basis of an ideal. LO-3 III. Understand the theoretical background of syzygies, colon ideals, localization and saturation and they can compute them. LO-4 IV. Apply these techniques to solve polynomial equation systems. LO-5 V. Implement these techniques by using a computer algebra program, for example ApCoCoA.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10