Study-Unit Description

Study-Unit Description


TITLE Groups and Vector Spaces

LEVEL 01 - Year 1 in Modular Undergraduate Course


DEPARTMENT Mathematics

DESCRIPTION - Relations:
    - Basic properties;
    - Equivalence relations and partitions of a set;
    - Partial orders;
- Introduction to groups: symmetry, axiomatic approach;
- Lagrange's theorem;
- An introduction to number theory;
- Permutations;
- Normal subgroups;
- Quotient groups;
- First isomorphism theorem;
- Introduction to vector spaces;
- Steinitz replacement process;
- Linear transformations and matrices;
- Dimension theorem, nullity, rank;
- Change of basis;
- Transition matrices.

Study-unit Aims:

The aim of this study-unit is to introduce the basic ideas of groups and vector spaces with a good range of examples so that the student has some familiarity with the fundamental concepts of abstract algebra and a good grounding for further study. This study-unit will link with other algebra study-units students would be taking in the second, third and fourth years.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:
- Recognise the structures of groups and vector spaces as fundamental concepts in Mathematics, and be prepared for the more advanced courses they would meet in the second, third and fourth year.
- Describe a wide range of examples of vector spaces and groups.
- Analyse fundamental results in abstract algebra.

2. Skills:

By the end of the study-unit the student will be able to:
- Use the basic definitions and properties of groups and vector spaces;
- Investigate the basic properties of a good range of examples;
- Construct proofs of results in abstract algebra.

Main Text/s and any supplementary readings:

Main Texts:

- Herstein I.N., Topics in Algebra, John Wiley & Sons, 3rd Edition, 2010.
- Cameron P., Introduction to Algebra, Oxford University Press, Oxford, 2008.
- Lipschutz S. and Lipson M., Linear Algebra, Schaum’s Outline Series, McGraw-Hill, 4th Edition, 2008.
- Wallace D., Groups, Rings and Fields, Springer, 2001.

Supplementary Readings:

- Armstrong M.A., Groups and Symmetry, Springer Verlag, Heidelberg, 1997.
- Anton H., Elementary Linear Algebra, John Wiley & Sons, 10th Edition, 2010.

ADDITIONAL NOTES Pre-requisite Study-unit: MAT1100

STUDY-UNIT TYPE Lecture and Independent Study

Assessment Component/s Resit Availability Weighting
Examination (3 Hours) Yes 100%

LECTURER/S Irene Sciriha Aquilina

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2021/2. It may be subject to change in subsequent years.