| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2003 | Linear Algebra I | Fall | 3 | 2 | 4 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Must Course |
| Course Level: | Bachelor |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor NERMINE AHMED EL SISSI |
| Course Objectives: | Linear algebra is an area of mathematics in which linear operators over vector spaces are studied. This course aims to introduce students to the concepts of linear algebra in order to enable them to: 1. use mathematically correct language and notation for Linear Algebra; 2. develop computational proficiency in problems involving Linear Algebra; 3. understand the axiomatic structure of a modern mathematical subject and learn to construct proofs; 4. explore some of the many applications of the subject; 5. communicate their knowledge of the subject. |
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The students who have succeeded in this course; Upon completion of the course students will be able to: 1. apply the Gauss-Jordan elimination method to solve a system of linear equations; 2. carry out matrix operations, including inverses and determinants; 3. Demonstrate understanding of the concepts of the n-dimensional space Rn and and its subspaces; 4. demonstrate understanding of linear independence, span, and basis; 5. Find the coordinate vector of a vector with respect to a given basis; 6. Find the change of basis matrix; 7. determine whether a map is linear; 8. represent linear transformations as matrices and vice versa; 9. compute eigenvalues and eigenspaces of matrices; 10. identify whether a matrix is diagonalizable or not; 11. use basic proof and disproof techniques, including mathematical induction, verifying that axioms are satisfied, standard "uniqueness" proofs, proof by contradiction, and disproof by counterexample. |
| Systems of linear equations; Gaussian elimination; The arithmetic and algebra of matrices; Determinants; Subspaces, linear independence, dimension, change of basis; Linear transformations; Orthogonality; Eigenvalues; Diagonalization of a matrix. |
| Week | Subject | Related Preparation | |
| 1) | |||
| 1) | The geometry and algebra of vectors, the dot product. | ||
| 1) | |||
| 1) | |||
| 2) | Lines and planes; introduction to systems of linear equations | ||
| 3) | Direct Methods for Solving Linear Systems | ||
| 4) | Spanning sets and linear independence; matrix operations | ||
| 5) | Matrix operations continued; algebraic properties of matrices | ||
| 6) | The Inverse of a matrix; the LU factorization | ||
| 7) | Subspaces, basis, dimension, and rank | ||
| 8) | Vector spaces and subspaces; linear independence, basis and dimension revisited | ||
| 9) | Change of basis; linear transformation | ||
| 10) | The kernel and range of a linear transformation; the matrix of a linear transformation | ||
| 11) | Introduction to eigenvalues and eigenvectors; determinants | ||
| 12) | Eigenvalues and eigenvectors; similarity and diagonalization | ||
| 13) | Orthogonality in n-dimensional real space; orthogonal complements | ||
| 14) | Orthogonal projections; the Gram-Schmidt Process; a brief introduction to inner product spaces | ||
| Course Notes: | Poole D., Linear Algebra: A Modern Introduction, 3rd Edition, Brooks Cole, 2011 |
| References: | G. Strang, Introduction to Linear Algebra. Fifth edition (2016) Wellesley-Cambridge Press and SIAM. Elementary Linear Algebra 6th Edition, 2009, Larson; Falvo ISBN-13: 978-0495829232, ISBN-10: 0495829234. Anton H., Rorres C., Elementary Linear Algebra with supplemental applications, Wiley International Student Version, 11th edition, 2015 Linear Algebra and Its Applications 4th Edition, 2012, David C. Lay, ISBN-13: 978-0- 321-62335-5, ISBN-10: 0-321-62335-5 |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 6 | % 10 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | 1 | % 10 |
| Seminar | % 0 | |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 14 | 2 | 28 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | 0 | 0 |
| Midterms | 2 | 15 | 30 |
| Paper Submission | 0 | 0 | 0 |
| Jury | 0 | 0 | 0 |
| Final | 1 | 25 | 25 |
| Total Workload | 195 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |