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.
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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 session.
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 http://emweb.unl.edu/Math/mathweb/vectors/vectors.html Everything related to cross-product can be found on wikipedia. 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 here. A good survey of equations of a line on the plane you can find on a beautiful web-site www.cut-the-knot.com.
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.