Linear Algebra with Exercises A
| Numbering Code | U-LAS10 10008 LE55 | Year/Term | 2022 ・ First semester |
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| Number of Credits | 3 | Course Type | Lecture |
| Target Year | Mainly 1st year students | Target Student | For science students |
| Language | English | Day/Period | Mon.3・Tue.2 |
| Instructor name | COLLINS，Benoit Vincent Pierre (Graduate School of Science Professor) | ||
| Outline and Purpose of the Course |
Calculus and linear algebra form the essential mathematical background necessary for understanding and developing modern science and technology. In this lecture, basics of Linear Algebra required for further pursuing of studies majored in science are explained. In the Linear Algebra A class, students will learn to manipulate concretely vectors, matrices, and systems of linear equations. |
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| Course Goals |
The goal of this class is to learn to manipulate concretely vectors, matrices, and systems of linear equations. In addition to learning linear algebra, students can learn how to discuss and present mathematical topics in English through this course. |
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| Schedule and Contents |
This subject is composed of two interrelated parts: Lecture and Exercises. The exercises sessions will take place basically once in two weeks, their purpose being to deepen the students' understanding of the contents of the lecture sessions through active participation in problem solving and through regular submission of reports. In the course outline below, the order in which the given items will be presented is not fixed and depends on the background and understanding of enrollees. 1. Fundamental concepts (1 week) -numbers, sets, mappings, basic notions of mathematical logic 2. Vectors in the plane and 2x2 matrices (2 weeks) -matrix and vector calculus, matrix inverses, Cayley Hamilton theorem -linear transformations of the plane (rotation, reflections, etc) and matrices -linear systems of equations and matrices 3. Concrete vector spaces and matrices (5-7 weeks) -vectors, vector calculus, linear span -matrices, matrix calculus (addition, scalar product, product) -examples of matrices (2-3 weeks) -elementary operations on matrices, rank, invertible matrices, inverse matrix -solving linear equations, structure of solutions (3-4 weeks) 4. Determinant (4-6 weeks) -row/column substitution and signature; definition of determinant and properties (3-4 weeks) -computation of determinant, Cramer's rule, volume and determinant (1-2 weeks) Total：14 classes, 1 Feedback session |
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| Evaluation Methods and Policy |
Students will be evaluated based on their performance in both the lecture and the exercises sessions. * Lecture will be graded based mainly on the final examination. * Exercises will be evaluated based mainly on submitted reports and participation in class. The details of the evaluation system will be given by the lecturer at the first lecture. |
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| Course Requirements | None | ||
| Study outside of Class (preparation and review) | To be announced. | ||
| References, etc. |
Linear Algebra and Its Applications, Jim Hefferon
This text is Free, under either the GNU Free Documentation License or the Creative Commons License Creative Commons Attribution-ShareAlike 2.5 License. Website: http://joshua.smcvt.edu/linearalgebra/ |
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