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Unit of study_
MATH5310: Topics in Algebra
2024 unit information
Algebra is one of the broadest fields of mathematics, underlying most aspects of mathematics. It is sometimes considered the mathematics of symmetry or the language of mathematics. In its most general description, algebra includes number theory, algebraic geometry and the classical study of algebraic structures such as rings and groups as well as their representations. Advanced algebra intersects other fields of modern mathematics, for instance via algebraic topology, homological algebra and categorical representation theory; and modern physics, via Lie groups and Lie algebras. You will learn about fundamental concepts of a branch of advanced algebra and its role in modern mathematics and its applications. You will develop problem-solving skills using algebraic techniques applied to diverse situations. Learning an area of pure mathematics means building a mental framework of theoretical concepts, stocking that framework with plentiful examples with which to develop an intuition of what statements are likely to be true, testing the framework with specific calculations, and finally gaining the deep understanding required to create technically sophisticated proofs of general results. The selection of topics is guided by their relevance for current research. Having gained an abstract understanding of symmetry, you will discover the manifestation of algebraic structures everywhere
Unit details and rules
Managing faculty or University school:
Science
| Study level | Postgraduate |
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| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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None |
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Corequisites:
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None |
| Prohibitions:
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None |
| Assumed knowledge:
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Familiarity with abstract algebra (e.g., MATH4062 or equivalent) and commutative algebra (e.g., MATH4312 or equivalent). Please consult with the coordinator for further information |
At the completion of this unit, you should be able to:
- LO1. demonstrate a coherent and advanced understanding of key concepts in algebra
- LO2. utilise fundamental algebraic principles and results to determine solutions to given problems
- LO3. inspect and contrast the characteristics of fundamental algebraic structures and morphisms between them
- LO4. formulate mathematical problems using algebraic terminology and justify the use of select frameworks in solving them
- LO5. determine the algebraic principles inhered to complex problems, and devise strategies to solve the given problems
- LO6. compose correct proofs of unfamiliar general results in algebra
- LO7. communicate coherent mathematical arguments appropriately to student and expert audiences, both orally and through written work
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