| 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 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor NERMINE AHMED EL SISSI |
| Recommended Optional Program Components: | None |
| 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 / Textbooks: | 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 |
| Quizzes | 6 | % 10 |
| Project | 1 | % 10 |
| Midterms | 2 | % 40 |
| Final | 1 | % 40 |
| 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 |
| Application | 14 | 2 | 28 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Midterms | 2 | 15 | 30 |
| Final | 1 | 25 | 25 |
| Total Workload | 195 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics | 5 |
| 2) | To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, | 5 |
| 3) | To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, | 3 |
| 4) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 4 |
| 5) | To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, | 3 |
| 6) | To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, | 4 |
| 7) | To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, | 1 |
| 8) | To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, | 3 |
| 9) | By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, | 3 |
| 10) | To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, | 3 |
| 11) | To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, | 3 |
| 12) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 2 |