Module Specification

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.
1. Module Title Linear Algebra and Geometry
2. Module Code MATH244
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 5 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Professor A Pratoussevitch Mathematical Sciences Anna.Pratoussevitch@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr O Karpenkov Mathematical Sciences O.Karpenkov@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 24

  24

      48
17.

Private Study

102
18.

TOTAL HOURS

150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

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

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

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

27. Aims
 

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

 
28. 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

 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of 2 hours of active learning sessions and 2 hours of supported study/drop-in sessions.

 
30. 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.

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

Assessment

32. EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Final Assessment on campus closed book This is an anonymous assessment. 120 70
33. CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Moebius Assignment 1 Standard UoL penalty applies for late submission. This is not an anonymous assessment. 0 10
  Moebius Assignment 2 Standard UoL penalty applies for late submission. This is not an anonymous assessment 0 10
  Moebius Assignment 3 Standard UoL penalty applies for late submission. This is not an anonymous assessment 0 10