Course Code:
MATH 232
Semester:
Spring
Course Type:
Core
P:
3
Lab:
2
Laboratuvar Saati:
0
Credits:
4
ECTS:
8
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

 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 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