| CODE | MAT1115 | ||||||||
| TITLE | Introduction to Groups | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | The study-unit will cover: • Relations: Basic properties, Equivalence relations and partitions of a set, Partial orders, Hasse diagrams; • Introduction to groups: symmetry, axiomatic approach; • Lagrange's theorem: cosets; • An introduction to number theory: Fermat's Little Theorem; • Permutations; • Normal subgroups; • Quotient groups; • First isomorphism theorem: Applications of quotients groups. Study-unit Aims: The study-unit is devoted to some of the basic concepts and results of group theory. A good range of examples are given in the study-unit so that the student acquires some familiarity with the fundamental concepts of abstract algebra. This study-unit aims to introduce students to some sophisticated concepts and results of group theory as an essential part of general mathematical culture and as a basis for further study of more advanced mathematics. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: 1. Recognise the structures of groups as one of the main building blocks in Mathematics; 2. Demonstrate facility in working with various specific examples of groups; 3. Analyse fundamental results in abstract algebra; 4. Appreciate the beauty of the subject of group theory. 2. Skills By the end of the study-unit the student will be able to: 1. Apply the basic concepts, properties and results of groups presented throughout the study-unit; 2. Solve standard types of problems in introductory group theory; 3. Write clear mathematical statements and proofs of results in abstract algebra; 4. Assimilate and use novel and abstract ideas in mathematics. 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. • Wallace D., Groups, Rings and Fields, Springer, 2001. Supplementary Readings • Armstrong M.A., Groups and Symmetry, Springer Verlag, Heidelberg, 1997. |
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| ADDITIONAL NOTES | Follows from: MAT1100 | ||||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Irene Sciriha Aquilina |
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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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