LINEAR ALGEBRA AND GEOMETRY(LECTURE IN ENGLISH)

The two main themes throughout the course are vector geometry and linear transformations. Topics from vector geometry include vector arithmetic, dot product, cross product, and representations of lines and planes in three-space. Linear transformations covered include rotations, reflections, shears and projections. Students will study the matrix representations of linear transformations along with their derivations. The curriculum also presents Affine geometry and affine transformations along with connections to computer graphics. This course also includes a review of relevant algebra and trigonometry concepts.

We will cover the basics of linear algebra and geometry such as coordinate systems, trigonometry, vectors and vector operations, barycenters, representations of lines and planes, linear transformations, matrices, and affine transformations.

Attendance is mandatory. Please write [LAG] in the subject of any emails you send to me.

There are no specific prerequisites for this course. However, it is assumed that the student has enough knowledge of high-school level mathematics, including basic arithmetic, trigonometry, linear systems of equations with 3 unknowns, and some experience using vectors and matrices. The student is responsible to cover the lack of this knowledge in any case, but I will be happy to help you in my office hours.

Upon successful completion of this course the student will understand, in both 2D and 3D: 1. The fundamental data types of point and vector, the algebraic and geometric differences between them, and various typical applications in the context of computer graphics, 2. The geometry of the basic vector operations of dot product and cross product, and the way they are typically used in representing and manipulating geometric objects such as lines and planes, 3. The concept of barycentric combinations and barycentric coordinates, and know how to use these in representing and manipulating geometric objects such as lines and planes, 4. The geometric origin of a matrix, the way that a matrix represents a linear transformation, and know how to derive the matrix for implementing a linear map given a geometric description of its effect. 5. The geometry of standard matrices, including: scaling, projection, reflection, rotation, and shear matrices for linear and affine transformations. 6. The extra-dimension technique to express affine as linear transformations, what will simplify codes in further courses. 7. As a cross curricular discipline, the students must develop the ability to present material – and answer questions- coherently, completely and accurately, using the right concepts and no