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PMTH332 Abstract Algebra

Updated: 14 October 2011
Credit Points 6
Offering
Responsible Campus Teaching Period Mode of Study
Armidale Trimester 2 Off Campus
Armidale Trimester 2 On Campus
Intensive School(s)
Start Finish Attendance Notes
23 August 2012 25 August 2012 Non-Mandatory
Supervised Exam There is a UNE Supervised Examination held at the end of the teaching period in which you are enrolled.
Pre-requisites PMTH213 or PMTH213A or candidature in a postgraduate award in the School of Environmental and Rural Science or School of Science and Technology
Co-requisites None
Restrictions PMTH332A
Notes None
Combined Units None
Coordinator(s) Bea Bleile (bbleile@une.edu.au)
Unit Description

This unit provides an introduction to the theory of groups and rings covering basic properties, subgroups and subrings, quotient structures, products of groups and rings, isomorphism theorems, cyclic groups, the Fundamental Theorem of Finitely Generated Abelian Groups, the Sylow Theorems, polynomial rings and fields of quotients. This unit is essential for students contemplating further studies in mathematics. Three lectures and a one hour tutorial per week.
Materials Text information will be published prior to commencement of the teaching period.
Disclaimer Unit information may be subject to change prior to commencement of the teaching period.
Assessment Assessment information will be published prior to commencement of the teaching period.
Learning Outcomes (LO) Upon completion of this unit, students will be able to:
  1. demonstrate a basic understanding of the elementary topics in Abstract Algebra;
  2. demonstrate a preliminary understanding of central elementary concepts of modern algebra;
  3. continue the unification of earlier material commenced in PMTH213;
  4. develop both theoretical understanding and computing methods;
  5. prepare themselves for further studies in number theory, commutative algebra, Lie algebras, algebraic geometry, representation theory, algebraic topology, homological algebra, category theory;
  6. illustrate, demonstrate and teach modern mathematics.

Graduate Attributes (GA)
Attribute Taught Assessed Practised
1 Knowledge of a Discipline
Knowledge gained by the student in lectures will be applied in collaboration with the lecturer to problems and examples in tutorials. The student will then map this experience onto further problem-solving tasks in assignments, where the identification of central concepts in the discipline, and the student's ability to articulate them, will be assessed. 		True True True
2 Communication Skills
The student will be encouraged to participate actively in discussion during lectures and tutorials. Written communication skills, particularly with regard to construction and presentation of logical expositions and arguments, will be taught and assessed. 		True True True
3 Global Perspectives
4 Information Literacy
The student will be guided in the use of online resources, library and internet access to recommended references, particularly in conjunction with assignment tasks. 		True True True
5 Life-Long Learning
The student will discover the breadth of the discipline through this introductory unit and will become aware of its ongoing development as a field of higher degree research. 		True
6 Problem Solving
The student will encounter in this unit a field of knowledge that is intensely problem-based, and will acquire skill in connecting ideas within a network of logical relationships. A high emphasis will be placed on the development of analytical and deductive reasoning. 		True True True
7 Social Responsibility
8 Team Work
The student will be encouraged to participate in interactive discussion with other students regarding ideas and problems addressed in the unit. Written assignment submissions must be the student's own work, but may be the outcome of group discussion. 		True
   

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