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 Introduction to Linear Algebra
2. Module Code MATH103
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 4 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Professor VV Goryunov Mathematical Sciences Victor.Goryunov@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr R Tatar Mathematical Sciences Radu.Tatar@liverpool.ac.uk
Dr SA Fairfax Mathematical Sciences Simon.Fairfax@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 develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
• To develop geometrical intuition in 2 and 3 dimensions.
• To introduce students to the concept of subspace in a concrete situation.
• To provide a foundation for the study of linear problems both within mathematics and in other subjects
 
28. Learning Outcomes
 

(LO1) Manipulate complex numbers and solve simple equations involving them, solve arbitrary systems of linear equations.
 

(LO2) Understand and use matrix arithmetic, including the computation of matrix inverses.
 

(LO3) Compute and use determinants.
 

(LO4) Understand and use vector methods in the geometry of 2 and 3 dimensions.
 

(LO5) Calculate eigenvalues and eigenvectors.
 

(S1) Numeracy
 
29. Teaching and Learning Strategies
 

Material is presented during lectures (3 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions.
 
30. Syllabus
   

Complex numbers: geometrical interpretation and algebraic manipulation. Equations involving complex numbers.

Vectors in 2 and 3 dimensions, dot and cross products, equations of lines and planes, intersections of planes, distance formulae. Linear independence.

Matrix algebra.  Solution of systems of linear equations.  Determinants: definition and basic properties. Eigenvalues and eigenvectors of matrices.

Similar matrices and diagonalisation. Further work on linear independence, basis of a subspace.
 
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/Exam 120 65
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Homework 1 0 10
  Homework 2 0 10
  Homework 3 150 15