**Linear Algebra I (G30 Program) - Fall 2019**

This page will be updated shortly before the course starts.

Linearity one of the most fundamental concepts for the handling of quantities in current natural science. Indispensable in quantum mechanics & relativity or fields like computer graphics & machine learning, its use has spread across all branches of natural science and beyond.

Linear algebra, developed in the nineteenth century, is the mathematical theory of linearity. The first half of this one-year course focuses on techniques for manipulating systems of linear equations, and the application of these techniques to analytic geometry (in arbitrary dimensions). Emphasis is placed on the ability to think abstractly.

No formal prerequisites. Some ability to manipulate systems of linear equations and understanding of elementary geometry will be useful for the understanding of the course material.

Linear systems, Gaussian elimination, matrices, vectors, linear maps, matrix multiplication, the inverse of a linear map, subspaces of Rn, image and kernel, linear independence, bases, dimension, coordinates, orthogonal bases, the Gram–Schmidt algorithm, QR factorization, orthogonal complement, orthogonal maps, least square approximations.

Otto Bretscher:

There will be two main, written exams: midterm (35%) and final (45%). Additionally, there will be homework assignments (10%) and quizzes (10%).

The final grade will be determined by the total amount of points obtained according to the following scale:

S: 90-100, A: 80-89, B: 70-79, C: 60-69, F:0-59.

Students do not need to submit a Course Withdrawal Form for course withdrawal. Anyone who does not attend the final exam will receive the grade “Absent”.

The Reference Book is available in the Main library and in the Science library (enough copies in total for all students). Additional helpful references will be presented at the beginning of the first lecture.

It is

**●****Objectives of the course**Linearity one of the most fundamental concepts for the handling of quantities in current natural science. Indispensable in quantum mechanics & relativity or fields like computer graphics & machine learning, its use has spread across all branches of natural science and beyond.

Linear algebra, developed in the nineteenth century, is the mathematical theory of linearity. The first half of this one-year course focuses on techniques for manipulating systems of linear equations, and the application of these techniques to analytic geometry (in arbitrary dimensions). Emphasis is placed on the ability to think abstractly.

**●****Course Prerequisites**No formal prerequisites. Some ability to manipulate systems of linear equations and understanding of elementary geometry will be useful for the understanding of the course material.

**●****Course Contents**Linear systems, Gaussian elimination, matrices, vectors, linear maps, matrix multiplication, the inverse of a linear map, subspaces of Rn, image and kernel, linear independence, bases, dimension, coordinates, orthogonal bases, the Gram–Schmidt algorithm, QR factorization, orthogonal complement, orthogonal maps, least square approximations.

**●Reference book**Otto Bretscher:

**, fourth edition, Pearson 2009.***Linear Algebra with Applications**ISBN: 978-0-13-600926-9.***●****Evaluation methods**There will be two main, written exams: midterm (35%) and final (45%). Additionally, there will be homework assignments (10%) and quizzes (10%).

The final grade will be determined by the total amount of points obtained according to the following scale:

S: 90-100, A: 80-89, B: 70-79, C: 60-69, F:0-59.

Students do not need to submit a Course Withdrawal Form for course withdrawal. Anyone who does not attend the final exam will receive the grade “Absent”.

**●****Notice for students**The Reference Book is available in the Main library and in the Science library (enough copies in total for all students). Additional helpful references will be presented at the beginning of the first lecture.

It is

*strongly*recommended to also follow the course Mathematics Tutorial I b.