ISHIK UNIVERSITY
FACULTY OF EDUCATION
Department of MATHEMATICS EDUCATION,
2018-2019 Spring
Course Information for MATH 204 LINEAR ALGEBRA II | | Course Name: | LINEAR ALGEBRA II |
| Code | Course type | Regular Semester | Theoretical | Practical | Credits | ECTS |
| MATH 204 | 2 | 4 | 3 | - | 3 | 4 |
| | Name of Lecturer(s)-Academic Title: | Sanhan Khasraw - | | Teaching Assistant: | - | | Course Language: | English | | Course Type: | Main | | Office Hours | 13:30-14:30, Wednesday | | Contact Email: | [email protected]
Tel:xxx
| | Teacher's academic profile: | PhD in Mathematics, 2015, University of Birmingham, United Kingdom.
| | Course Objectives: | Students will be able to show functions are linear transformations under the certain conditions, apply the basic arithmetic operations on linear transformations, using technology where appropriate and gain the basic terminology of linear algebra in Euclidean spaces, including linear independence, spanning, basis, rank, nullity, subspace. They become computationally proficient at procedures in Linear Algebra. They will be able to find eigenvalues and eigenvectors for given linear transformations and matrices. | | Course Description (Course overview): | Vectors in R^2 and R^3 , vector spaces , linear dependence and independence, basis and dimension, Eigen values and eigenvectors, Characteristic polynomial, diagonalization, Cayley-Hamilton theorem. Matrix representation of linear transformations, kernel and image of Linear transformations, | COURSE CONTENT| Week | Hour | Date | Topic | | 1 |
3 |
3-7/2/2019 |
Fields and Vector spaces | | 2 |
3 |
10-14/2/2019 |
Subspaces, Sum and Intersection of Subspaces |
| | 3 |
3 |
17-21/2/2019 |
Linear independence, Linear dependence, Linear combinations and Bases | | 4 |
3 |
24-28/2/2019 |
Dimensions, examples and theorems |
| | 5 |
3 |
3-7/3/2019 |
Vector coordinates and transition matrix | | 6 |
3 |
26-28/3/2019 |
Linear Transformations, examples |
| | 7 |
3 |
31/3-4/4/2019 |
Basic properties of linear transformations | | 8 |
3 |
7-11/4/2019 |
Sum and scalar multiplication of linear transformations |
| | 9 |
3 |
14-18/4/2019 |
Midterm Exam | | 10 |
3 |
21-25/4/2019 |
Kernel and image of Linear transformations, rank and nullity of Linear transformations. |
| | 11 |
3 |
28/4-2/5/2019 |
The Matrix Representation of a Linear Transformation | | 12 |
3 |
5-9/5/2019 |
Composition of linear transformations, inverse of linear transformations and isomorphic spaces. |
| | 13 |
3 |
12-16/5/2019 |
Eigenvalues and eigenvectors of linear transformations, characteristic polynomial and characteristic equations. | | 14 |
3 |
19-23/5/2019 |
Diagonalizability |
| | 15 |
3 |
26-30/5/2019 |
Inner Products and Norms | | 16 |
3 |
9-13/6/2019 |
Final Exam |
| | 17 |
3 |
16-20/6/2019 |
Final Exam |
| COURSE/STUDENT LEARNING OUTCOMES | | | 1 | Prove algebraic statements about vector addition, scalar multiplication, inner products, projections, norms, orthogonal vectors, linear independence, spanning sets, subspaces, bases, dimension and rank | | 2 | Find the kernel, rank, range and nullity of a linear transformation | | 3 | Calculate eigenvalues, eigenvectors and eigenspaces | | 4 | Determine if a linear transformation is diagonalizable, and if it is, diagonalize it. |
| COURSE'S CONTRIBUTION TO PROGRAM OUTCOMES
(Blank : no contribution, I: Introduction, P: Profecient, A: Advanced ) | Program Learning Outcomes |
Cont. | | 1 | Demonstrate an understanding of the common body of knowledge in mathematics. | P | | 2 | Demonstrates an understanding of pedagogical content knowledge, technology and perfectible assessment. | | | 3 | Demonstrate the ability to think critically, research scientifically, and become modern and up-to-date. | A | | 4 | Understands the interrelationship of human development, cognition, and culture and their impact on learning. | | | 5 | Demonstrate the ability to apply analytical and theoretical skills to model and solve mathematical problems. | P | | 6 | Demonstrate the ability to effectively use a variety of teaching technologies and techniques and classroom strategies to positively influence student learning. | | | 7 | Understands how to form connections among educators, families, and the larger community to promote equity and access to education for his/her students. | | | 8 | Understands assessment and evaluation of student performance and learning and program effectiveness. | | | 9 | Communicates effectively and works collaboratively within the context of a global society. | |
| | Prerequisites (Course Reading List and References): | Elementary Linear Algebra, 2nd edition, by Bernard Kolman, 1970. | | Student's obligation (Special Requirements): | 1. Students have an obligation to arrive on time and remain in the classroom for the duration of scheduled classes and activities. 2. Students have an obligation to write, homeworks, tests and final examinations at the times scheduled by the teacher or the College. Students have an obligation to inform themselves of, and respect, College examination procedures. 3. Students have an obligation to show respectful behaviour and appropriate classroom deportment. Should a student be disruptive and/or disrespectful, the teacher has the right to exclude the disruptive student from learning activities (classes) and may refer the case to the Director of Student Services under the Student Code of Conduct. 4. Electronic/communication devices (including cell phones, mp3 players, etc.) have the effect of disturbing the teacher and other students. All these devices must be turned off and put away. Students who do not observe these rules will be asked to leave the classroom | | Course Book/Textbook: | 1. Elementary Linear Algebra, 2nd edition, by Bernard Kolman, 1970. | | Other Course Materials/References: | 1. An introduction to linear algebra by V. Krishnamurthy, V.P. Mainra and J. L. Arora; 1976.
2. Basic Linear Algebra, 2nd edition, by T. S. BIyth and E. F. Robertson, 2002. | | Teaching Methods (Forms of Teaching): | Lectures, Practical Sessions, Excersises, Presentation, Assignments | COURSE EVALUATION CRITERIA
| Method | Quantity |
Percentage (%) | | Attendance | 1 | 5 | | Participation | 1 | 5 | | Quiz | 2 | 5 | | Homework | 2 | 5 | | Midterm Exam(s) | 1 | 30 | | Final Exam | 1 | 40 |
| Total | 100 |
Examinations: Essay Questions, Multiple Choices, Short Answers |
| Extra Notes:
| ECTS (ALLOCATED BASED ON STUDENT) WORKLOAD| Activities | Quantity | Duration (Hour) | Total Work Load | | Contact Hours (Theoretical hours + Practical hours/2) x Weeks | | | 0 | | Hours for off-the-classroom study | | | 0 | | Study hours for the Midterm Exam | | | 0 | | Study hours for the Final Exam | | | 0 | | Other | | | 0 | | ECTS | | | 0 | | | | 0 | | | | 0 | | Total Workload | 0 | | ECTS Credit (Total workload/25) | 0 |
|
Peer review
| Signature: | Signature: | Signature: |
Name:
| Name:
| Name:
|
| Lecturer | Head of Department | Dean |
|