# Course Identification

Mathematics module: Analysis for high School mathematics teachers
20206141

## Lecturers and Teaching Assistants

Prof. Sergei Yakovenko
Itamar Vigdorovich

## Course Schedule and Location

2020
First Semester
Tuesday, 09:15 - 11:00, FGS, Rm 5

Tutorials
Tuesday, 11:30 - 13:00, FGS, Rm 5
05/11/2019

## Field of Study, Course Type and Credit Points

Science Teaching (non thesis MSc Track): Lecture; Obligatory; Regular; 4.00 points

לתלמידי שני השנתונים

No

20

Hebrew

## Attendance and participation

Obligatory

Numerical (out of 100)

100%

Take-home exam

N/A
N/A
-
N/A

4

## Syllabus

The main goal of this course is to outline geometry as an area of modern mathematics, and to show that this presentation is essential, relevant and makes sense for math teachers at the high school level. Students will be accustomed to viewing concepts from more than one viewpoint.

1. Classical geometry through the modern lens.
2. Curves in the plane - parametric representations and other representations (and their significance), tangent, normal, length, curvature, conic sections and quadratic forms.
3. Topic in linear spaces.
4. The concept of a surface as represented in several ways.
5. Elementary differential geometry: first fundamental form, tensors, second fundamental form, curvature(s), Gauss map, Gauss theorem.
6. Euclidean metric (length, area, volume), Riemannian metric, geodesics, elementary calculus of variations. Spherical geometry is going to be emphasized.
7. Topics in: Euclidean geometry (metric), various non-Euclidean geometries, analytic and synthetic approaches, a new look on conic sections and quadratic forms, different representations of the same objects, the Erlangen program.

Right from the beginning, we will emphasize the need for invariant representations of objects on one hand and easily computable representations on the other hand.

## Learning Outcomes

Upon successful completion of the course students will be able to:

1. Demonstrate proficiency in the different topics in the field of Geometry.
2. Recognize the relevancy of Geometry to their everyday practice as mathematics teachers in high schools.
3. Look at geometry concepts from more than one viewpoint.