Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title LINEAR ALGEBRA AND GEOMETRY
Code MATH244
Coordinator Dr V Guletskii
Mathematical Sciences
vladimir.guletskii@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 5 FHEQ First Semester 15

Aims

To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics.


Learning Outcomes

After completing the module students should be able to:

• appreciate the geometric meaning of linear algebraic ideas,

• appreciate the concept of an abstract vector space and how it is used in different mathematical

situations,

• apply a change of coordinates to simplify a linear map,

• manipulate matrix groups (in particular Gln, On and Son),

• understand bilinear forms from a geometric point of view.


Syllabus
1  1

• Review of linear algebra from MATH103.

• Real vector spaces, bases and dimension of a vector space.

• Linear maps and matrices. Change of basis.

• Endomorphisms, eigenvalues, eigenvectors and eigenspaces. Geometric interpre-tations. Diagonalisation.

• Applications to linear geometry and differential equations.

• Invertible endomorphisms and the group Gln.

• Jordan Normal Form.

• Bilinear forms and diagonalisation.

• Orthogonal matrices and isometries. Applications to the classification of conics and quadric surfaces.


Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH101; MATH102; MATH103 *MATH142 or MATH247 are alternative prerequisites for MATH343 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
MATH343*; MATH350; MATH410; MATH442; MATH444; MATH448; MATH449 

Programme(s) (including Year of Study) to which this module is available on a required basis:
Programme:G100 Year:2 (NOT XJTLU) Programme:G101 Year:2 (NOT XJTLU) Programme:G110 Year:2

Programme(s) (including Year of Study) to which this module is available on an optional basis:
Programme:G100 Year:2 (XJTLU ONLY) Programme:G101 Year:2 (XJTLU ONLY) Programme:G1N2 Year:2 Programme:G1R9 Year:2 Programme:G1X3 Year:2 Programme:GG13 Year:2 Programme:GL11 Year:2 Programme:GN11 Year:2 Programme:GR11 Year:2 Programme:GG14 Year:2 Programme:GV15 Year:2 Programme:G1F7 Year:2 Programme:BCG0 Year:2 Programme:L000 Year:2 Programme:Y001 Year:2

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Written Exam  2.5 hours  First semester  90  Standard University Policy    Assessment 2 Notes (applying to all assessments) 10 or 11 pieces of homework This work is not marked anonymously. All answers to Section A and the best THREE answers to Section B will be taken into account. The marks noted indicate the relative weight of the questions.  
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework    First semester  10  None: exemption approved November 2007  University Policy applies - see Department/School handbook for details.  Assessment 1