The main themes of this course will be focused on linear algebra, differential equations, and projective geometry.
This is a course designed for students who are not mathematics majors. Students of mathmatics are discouraged to take this course.
We will discuss the interplay between differential equations and linear algebra. Then we will study some basic notions of linear algebra, differential equations, and projective geometry, such as vector spaces, simplifying linear transformations, application of linear algebra in solving differential equations, collineation transformations, some classical theorems in projective geometry. We will discuss some history of mathematics in the 19-th century so that students get some ideas about the contribution of several mathematicians in this period, e.g. Jordan, Weierstrass, Frobenius, Poncelet, etc.
Projective spaces will be introduced via synthetic and analytic methods so that it will not be too abrupt for students who understand geometry only from the plane Euclidean viewpoint. Complex projective spaces will be mentioned and we will try to convince students that, even in geometry, working on the complex numbers is superior to working on the real numbers (although it is not intuitive to visualize complex figures).