Linear Algebra II

Course Code:

MATH 232

Course Period:

Spring

Course Type:

Core

P:

3

Lab:

2

Credits:

4

ECTS:

8

Course Language:

İngilizce

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

Week	Topics	Study Materials
1	Vector space properties, linear independence and spanning sets.	Textbook
2	Bases, orthonormal bases and coordinates.	Textbook
3	Dimension, rank and nullity of a matrix.	Textbook
4	Properties of dimension, Goldilocks’ theorem, ranks and transposes.	Textbook
5	Linear transformations, injectivity, kernel.	Textbook
6	Surjectivity and range of a linear transformation.	Textbook
7	Invertible linear transformations, isomorphisms.	Textbook
8	Matrix representations.	Textbook
9	Change of basis, similarity.	Textbook
10	Eigenvalues and eigenvectors of linear transformations.	Textbook
11	Similarity and diagonalization.	Textbook
12	Orthonormal diagonalization, nilpotent linear transformations.	Textbook
13	Canonical form for nilpotent linear transformations	Textbook
14	Jordan canonical form, Cayley-Hamilton theorem	Textbook

Recommended Sources

Textbook	A First Course in Linear Algebra, Robert A Breezer. Linear Algebra with Applications, Steven Leon.
Additional Resources	Abstract Linear Algebra, Curtis Morton.

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

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	6	84
Mid-terms (Including self study)	1	20	20
Quizzes	-	-	-
Assignments	-	-	-
Final examination (Including self study)	1	22	22
Total Work Load			196
Total Work Load / 25 (h)			7.84
ECTS Credit of the Course			8

Search form