• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Formulate and solve problems related to linear algebra in an abstract, geometric setting.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Written exam
2. Transfer the solution procedures obtained in abstract setting into a PC by using MATLAB software in order to solve real life problems.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Develop mathematical, communicative, problem-solving, brainstorming skills.

   Method of assessment

   1. Homework assignment
3. Develop the skills to analyze various aspects in linear algebra.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Algebraic preliminaries : Semi-groups, monoids, groups , rings, structure of rings, ideals, fields.
Week 2:	Algebraic preliminaries : Vector spaces, modules and algebras.Linear independence,basis,subspaces and subspace operations, modular distributive rule,linear transformations and their representations. (HOMEWORK 1)
Week 3:	Vector spaces : Matrices, geometry induced by linear transformations, norms in vector spaces. Permutations, elementary operations and determinants, minors and cofactors, inverse transformations.
Week 4:	Vector spaces : Projections, insertion maps, factor spaces, invariant subspaces and induced maps, calculation of supremal and infimal invariant subspaces. (HOMEWORK 2)
Week 5:	Generalized eigenspaces and their calculations. Jordan form for real eigenvalues and its calculation.
Week 6:	Jordan form for complex eigenvalues and its calculation. (HOMEWORK 3)
Week 7:	Minimal polynomial, cyclic transformations and subspaces. Calculation of maximally cyclic subspaces and companion form.
Week 8:	Cyclic index, invariant factors and the Rational Canonical form and its relation to Jordan Form. Midterm Exam.
Week 9:	Linear functionals and dual spaces. Annihilators and the geometry of the dual spaces. Dual maps.
Week 10:	Inner product spaces,Bessel and Schwartz inequalities, representation of linear functionals,singular value decomposition, Hermitian operators, quadratic forms. (HOMEWORK 4)
Week 11:	Convex Analysis : Convex sets, convex and affine combinations, convex cones, dual cones.
Week 12:	Convex Analysis: Separation, Farkas Lemma. (HOMEWORK 5)
Week 13:	Convex analysis: Extreme points and directions. Linear Programming problem. Representation. Duality.
Week 14:	Factorization of matrices. LU-factorization. Cholesky factorization. Householder transformation and QR-factorization. (HOMEWORK 6)
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Advanced Linear Algebra, S. Roman Finite Dimensional Vector Spaces, P. Halmos
Recommended readings:	An In troduction To Linear Algebra, L. Mirsky Matrix Analysis, R.A. Horn ve C.R.Johnson Matrix Computations, G.H. Golub ve C.F. Van Loan.
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	30
Other in-term studies:		0
Project:		0
Homework:	2,4,6,10,12,14	10
Quiz:		0
Final exam:	16	60
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	3	14
Practice, Recitation:	0	0
Homework:	10	6
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	15	1
Mid-term:	1	1
Personal studies for final exam:	20	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)