LINEAR ALGEBRA II

Course Code:

MATH 232

Semester:

Spring

Course Type:

Core

P:

3

Lab:

2

Laboratuvar Saati:

0

Credits:

4

ECTS:

7

Course Language:

English

Course Objectives:

To provide tools for dealing with problems in many fields from a variety of disciplines and to serve as a bridge from the typical intuitive treatment of calculus to more rigorous courses such as abstract algebra and analysis.

Course Content:

Characteristic and minimal polynomials of an operator, eigenvalues, diagonalizability, canonical forms, Smith normal form, Jordan and rational forms of matrices. Inner product spaces, norm and orthogonality, projections. Linear operators on inner product spaces, adjoint of an operator, normal, self adjoint, unitary and positive operators. Bilinear and quadratic forms.

Course Methodology:

1: Lecture, 2: Problem solving, 3: Question – Answer, 4: Homework

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Determines if a given set is independent and/or spanning set.	1,2,3,4	A
2) Constructs an orthonormal basis for a given vector space.	1,2,3,4	A
3) Determines if a given linear transformation is injective, surjective or invertible.	1,2,3,4	A
4) Represents a linear transformation by matrices and obtains information about transformation by using these representations.	1,2,3,4	A
5) Determines if a matrix is diagonalizable and if it is, diagonalizes the matrix.	1,2,3,4	A
6) Computes the Jordan canonical form of a matrix.	1,2,3,4	A

Course Flow

1	Vector spaces, subspaces	Textbook
2	Bases, dimension and coordinates.	Textbook
3	Linear transformations, the algebra of linear transformations	Textbook
4	Isomorphism, the representation of linear transformations by matrices	Textbook
5	Linear functionals, the double dual, the transpose of a linear transformation	Textbook
6	Determinant functions, permutations and uniqueness of determinants,	Textbook
7	Additional properties of determinants	Textbook
8	Elementary canonical forms, characteristic values, annihilating polynomials, invariant subspaces,	Textbook
9	Direct sum decompositions, invariant direct sums,	Textbook
10	Primary decomposition theorem	Textbook
11	Cyclic subspaces and annihilators,	Textbook
12	Cyclic decompositions and the rational form	Textbook
13	The Jordan form	Textbook
14	Computation of invariant factors	Textbook

Recommended Sources

RECOMMENDED SOURCES
Textbook	Kenneth M Hoffman, Ray Kunze - Linear Algebra Second Edition -Prentice Hall (1971)
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes	-	-
Assignments	-	-
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		40
Total		100

COURSE CATEGORY

Core Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems				x
5	Consciousness of professional ethics and responsibilty					x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest					x
8	Ability to learn, choose and use necessary information technologies					x
9	Lifelong education					x

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms (Including self study)	1	15	15
Quizzes	-	-	-
Assignments	-	-	-
Final examination (Including self study)	1	20	20
Total Work Load			175
Total Work Load / 25 (h)			7
ECTS Credit of the Course			7

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