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 A Pratoussevitch
Mathematical Sciences
Anna.Pratoussevitch@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2020-21 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

(LO1) To understand the geometric meaning of linear algebraic ideas.

(LO2) To know the concept of an abstract vector space and how it is used in different mathematical situations.

(LO3) To be able to apply a change of coordinates to simplify a linear map.

(LO4) To be able to work with matrix groups, in particular GL(n), O(n) and SO(n),.

(LO5) To understand bilinear forms from a geometric point of view.

(S1) Problem solving skills

(S2) Numeracy

(S3) Adaptability


Syllabus

 

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 interpretations. Diagonalisation.

Applications to linear geometry and differential equations.

Invertible endomorphisms and the group GL(n).

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.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

 

Programme(s) (including Year of Study) to which this module is available on a required basis:

 

Programme(s) (including Year of Study) to which this module is available on an optional basis:

 

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final Assessment - open book and remote One hour time on task Standard UoL penalty applies for late submission.  One hour time on tas    50       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Homework 1 (12.5%) Standard UoL penalty applies for late submission. This is not an anonymous assessment.  Equivalent to 2-5 si    12       
Homework 4 (12.5%) Equivalent to 2-5 sides of A4.  Equivalent to 2-5 si    12       
Homework 3 (12.5%) Equivalent to 2-5 sides of A4.  Equivalent to 2-5 si    12       
Homework 2 (12.5%) Equivalent to 2-5 sides of A4.  Equivalent to 2-5 si    12