Welcome to MAT 515
MAT 515 is devoted to elementary geometry. The study will focus on the features of
the subject which develop logical skills and geometric imagination of students.
For more information, please select General information link in
the menu to the left.
Announcements are listed in reverse choronological order:
most recent announcement at the top.
The final exam will be on Thursday, December 16, at 2:15 pm - 4:45 pm
in the room 4-130.
The exam will cover the whole content of the course, except the part
covered by the second midterm (vectors and analytic geometry).
It will include theoretical questions about theorems and thier proofs.
One of the questions will suggest to formulate and prove
a few theorems from the course closely related to each other.
Here is the list of topics
that are recommended for revisiting to this end.
One question will require just formulation of definitions
and statements of theorems without proof.
Here is the list
of topics recommended for revisiting in this connection.
This list is longer, it provides also a reliable skeleton for
preparation to the whole exam.
Other questions in the exam will be in the traditional shape of a problem.
On Tuesday, December 14, at 5:20 in room 4-130, we will have a review
We start studying of the similarity geometry. This is an integral part of
The main notions of the similarity geometry emerge in traditional presentations of Euclidean
Geometry (in particular in the textbook by Hadamard that we use) in a
very indirect way. A short modern introduction can be found here.
The second midterm exam will be on Thursday November 18.
It will cover vector algebra and a piece of so-called Analytic Geometry related to
lines and planes. It will consist of 4 problems.
This material is included into the course, because a teacher should be
aware about it and should be able to solve elementary geometric problems
in coordinates or using vector algebra.
The textbook does not cover this material. For vector algebra, you may
find easily everything needed on the web. For example, take a look at
Everything related to cross-product can be found on
Dot-product in wikipedia starts from a perspective which differs from what
we did in the class. Much closer to this course it is presented
survey of equations of a line on the plane you can find on a
All these sources miss vector equations, and I could not find a web site
with appropriate text. That is why I wrote a
concise text about various
equations presenting lines and planes.
The first midterm exam will be on Thursday October 28. It will consist
of 5 problems. In the homework, which is due by Tuesday, you have to
compose your own version of this exam. On the page of homework you may find
a detailed description of the kinds of problems. Below the material covered
by the exam is described.
The exam covers the book 1 of the textbook, the first two chapters
from the book 2 of the textbook and the material about isometries presented
on this web site. I recommend revisiting all these texts. Pay a special
attention to definitions and formulations of theorems.