Aalborg University
Basic year 2007-2008

Mathematics 2C

Regarding the Mathematics 2C Exam, June 2008

Examination Syllabus

The examination syllabus for the course is the following sections of David C. Lay, Linear Algebra and Its Applications, Third Edition, Pearson Education:

Section 1.1-1.5
Section 1.7-1.9
Section 2.1-2.3
Section 2.7

Furthermore, the mathematical aspects of the article

Elena Marchetti and Luisa Rossi Costa, The Fire Tower, Nexus Network Journal, Volume 4, Number 2, November 2002, pages 38-53

The role of the article and the animation program

In groups you are to prepare a talk covering the mathematical aspects of (parts of) the article and the mathematical aspects of the animation program. The talk is to be planned in such a way that the mathematical methods are clearly visible and in such a way that each member of the group presents a fair share of these mathematical methods.

At the exam in June, which is individual, each student must give a talk of 7-8 minutes on her/his part of the manuscript. Each person in the group is responsible for the entire manuscript and must be able to answer questions also within the parts which are presented by other group members.

Exam topics, June 2008

1. Echelon forms and row operations.
2. Systems of linear equations.
3. Linear independence.
   Explain what linear independence means in plane and space.
   Give the general definition of linear independence.
   
4. Linear transformations; standard matrix for a linear transformation.
5. Matrix multiplication.
   Explain the definition of the product of two matrices.
   Explain the relation between matrix multiplication and linear transformations.
6. Matrix algebra.
   Explain the most important rules for sums and products of matrices.
   Mention some rules, which are not true in general.
7. The inverse of a matrix.
8. Homogeneous coordinates.

Preparation of the exam topics

You are expected to have prepared talks on all eight topics and you are welcome to bring along manuscripts to the exam. You will, however, not get any credit for just reading from the manuscript or copying the manuscript to the blackboard!

You are not expected to cover every aspect of each exam topic. You are to choose some important areas for presentation so that you during the presentation of 7-8 minutes explain something important about the exam topic. Do not focus too much on being fast in order to explain as mush as possible. The most important thing is that you explain things, definitions, results or maybe examples, in such a way that the audience can feel that you yourselves understand what you are saying.

The organization of the exam

The exam is individual. You will receive a time schedule from the secretary. The examination of each student will last for 20 minutes.

The student is expected to start by giving a talk presenting her/his part of the article or the animation program lasting for 7-8 minutes. The censor and examiner may ask questions. After that the student draws one of the 8 exam questions and gives a prepared talk on this question lasting 7-8 minutes. Again, the censor and the examiner may ask questions. The student then leaves the room, and after some time you will receive the result: passed or failed.