| CODE | MAT1102 | ||||||
| TITLE | Groups and Vector Spaces | ||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||
| MQF LEVEL | 5 | ||||||
| ECTS CREDITS | 5 | ||||||
| DEPARTMENT | Mathematics | ||||||
| DESCRIPTION | • 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 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: 1. Understand the structures of groups and vector spaces as fundamental concepts in Mathematics, and be prepared for the more advanced study-units they would meet in the second, third and fourth year. 2. Understand a wide range of examples of vector spaces and groups. 3. Understand proofs of results in abstract algebra. 2. Skills: By the end of the study-unit the student will be able to: 1. Use the basic definitions and properties of groups and vector spaces; 2. Investigate the basic properties of a good range of examples; 3. Construct proofs of results in abstract algebra. Main Text/s and any supplementary readings: (availability at the Library or otherwise is indicated against each entry) Main Texts • Herstein I.N., Topics in Algebra, John Wiley & Sons, 3rd Edition, 2010. (Available) • Cameron P., Introduction to Algebra, Oxford University Press, Oxford, 2008. (Available) • Lipschutz S. and Lipson M., Linear Algebra, Schaum’s Outline Series, McGraw-Hill, 4th Edition, 2008. (Available) • Wallace D., Groups, Rings and Fields, Springer, 2001. (Available) Supplementary Readings • Armstrong M.A., Groups and Symmetry, Springer Verlag, Heidelberg, 1997. (Available) • Anton H., Elementary Linear Algebra, John Wiley & Sons, 10th Edition, 2010. (Available) |
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| ADDITIONAL NOTES | [Follows From: MAT1000] [Leads To: MAT2112] | ||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||
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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 2024/5. It may be subject to change in subsequent years. |
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