3 1 false MATH6118 <p>This course introduces the basic concepts of modern algebra such as groups and rings. The philosophy of this course is that modern algebraic notions play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. This course emphasizes the application of techniques.<br />Topics to be covered include:</p><ul><li>Group Theory - permutation groups; abstract groups, subgroups, cyclic and dihedral groups; homomorphisms; cosets, Lagrange&#39;s Theorem, quotient groups, group actions; Sylow theory.</li><li>Ring Theory - rings and fields, polynomial rings, factorisation; homomorphisms, factor rings.</li><li>Linear algebra - unitary matrices, Hermitian matrices, canonical forms.</li></ul><p>Note: Graduate students attend joint classes with undergraduates but are required to have a deeper understanding of the material, are expected to do extra work of a more theoretical nature and are assessed separately</p> Bachelor degree; with second year Mathematics.&nbsp; 1 false 12646 <p>Assessment will be based on:</p><ul></li><li>Five assignments (10% each; LO 1-4)</li><li>Final exam (50%; LO 1-4)</li></ul> 1 1 <p>On satisfying the requirements of this course, students will have the knowledge and skills to:</p>1. Explain the fundamental concepts of advanced algebra such as groups and rings and their role in modern mathematics and applied contexts<br />2. Demonstrate accurate and efficient use of advanced algebraic techniques<br />3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from advanced algebra <br />4. Apply problem-solving using advanced algebraic techniques applied to diverse situations in physics, engineering and other mathematical contexts 2 Algebra 1: Groups, Rings and Advanced Linear Algebra 6 6 6 Second year Mathematics is required.&nbsp; Algegra 1 Band 2 NP Mathematics u8606170 2 36 lectures and ten tutorials 2010