MATH 244: Linear Algebra, Geometry and Groups
(2005/2006; Spring semester)
Lecturer: Dr. Lasse Rempe;
e-mail: lrempe @ liv...;
Office: 505
Tel.: 0151 794 4085
Lectures: Monday 12 - 1, Thursday 10 - 11, Friday 9 - 10
Tutorial Session: Friday 1-2
Venue: Proudman Lecture Theatre
General Information
(or see below).
Problem Sheets
- Problem Sheet 1.
Solutions due on February 2nd.
Solution Sheet 1
- Problem Sheet 2.
Solutions due on February 6th.
Solution Sheet 2
- Problem Sheet 3.
(There were two typos on the version handed out during the
lectures. In question 1, the last equation should have been
U=W, not V=W. In question 2, the second subspace should have been called
W, not V.)
Solutions due on February 13th.
Solution Sheet 3
-
Problem Sheet 4.
(There was a typo on the version handed out during the
lectures. In question 1, the image of the linear map should
have been a three-dimensional vector; this is
rectified by removing the first component.)
Solutions due on February 20th.
Solution Sheet 4
-
Problem Sheet 5.
Solutions due on February 27th.
Solution Sheet 5
-
Problem Sheet 6.
Comment regarding question 3:
Students who are uncomfortable with the calculation of eigenvalues and eigenvectors (which turn out to be irrational) are encouraged to do the question obtained by replacing A with
A =
( 5 2 )
( 2 2 )
and f with
f( (x_1,y_1) , (x_2, y_2) ) =
5 x_1 x_2 + 2 x_1 y_2 + 2 y_1 x_2 + 2y_1 y_2,
which will give nicer numbers.
Solutions due on Monday, March 6th.
-
Problem Sheet 7.
Solutions due on March 13th.
-
Problem Sheet 8.
Solutions due on March 20th.
-
Problem Sheet 9.
Solutions due on March 27th.
-
Problem Sheet 10.
Solutions due on April 24th.
-
Problem Sheet 11.
Solutions due on April 28th.
Lecture Notes
A list of books that
might be useful.
The final mark is 10% assessed exercises and
90% final exam. Each exercise sheet will contain 5 questions, worth
1 points each, awarded when a reasonable effort
has been made.
Exercise sheets will be handed out on Mondays, with
solutions collected a week later. (The exception to this rule is
the first sheet, for which solutions do not need to be handed in
until Thursday, February 2nd.
Your solutions must be clearly labelled with your name,
legibly written and
stapled together (no loose sheets!). Also, at
each point you should clearly state what you are proving/doing;
long uncommented calculations are not acceptable.
If your solutions do not adhere to these rules, you may receive
a mark of 0 for them!
There will be 11 exercise sheets in total; your overall exercise mark
will be the average of your 10 best marks.
Lecture Notes
Some lecture notes may be made available in electronic form on the
webpage. Otherwise, handwritten notes will be available
upon request.