Course Code:
MATH 231
Semester:
Fall
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:

Matrices and systems of linear equations. Vector spaces; subspaces, sums and direct sums of subspaces. Linear dependence, bases, dimension, quotient spaces. Linear transformations, kernel, range, isomorphism. Spaces of linear transformations. Representations of linear transformations by matrices. Determinants.

Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Solves the systems of linear equations using matrices. 1,2 A 2) Determines spanning sets for a given vector space. 1,2 A 3) Applies Gram-Schmidt Process to an independent set of vectors to obtain an orthogonal set. 1,2 A 4) Determines if a given matrix is nonsingular. 1,2 A 5) Uses elementary matrices to compute the inverse of a matrix. 1,2 A 6) Uses determinant and adjoint to compute the inverse of a matrix. 1,2 A

### Course Flow

 Week Topics Study Materials 1 Systems of linear equations Textbook 2 Solutions of Homogeneous systems, null space of a matrix Textbook 3 Vector space properties, linear combinations Textbook 4 Spanning sets Textbook 5 Linear independence and nonsingular matrices Textbook 6 Linear dependence and spans Textbook 7 Orthogonality, inner products Textbook 8 Orthogonal vectors, Gram-Schmidt Process Textbook 9 Matrix operations, transposes and symmetric matrices Textbook 10 Adjoint of a matrix Textbook 11 Hermitian matrices Textbook 12 Elementary matrices, inverse of a matrix Textbook 13 Column space, row space, null space of a matrix Textbook 14 Determinants 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 5 70 Mid-terms (Including self study) 1 20 20 Quizzes - - - Assignments - - - Final examination (Including self study) 1 16 16 Total Work Load 176 Total Work Load / 25 (h) 7.04 ECTS Credit of the Course 7