MATHS512-23A (HAM)

Continuous Groups

15 Points

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Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

Staff

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Convenor(s)

Ian Hawthorn

Ian Hawthorn
9013
G.3.03
See Moodle
ian.hawthorn@waikato.ac.nz

Lecturer(s)

Administrator(s)

: maria.admiraal@waikato.ac.nz

Placement/WIL Coordinator(s)

Tutor(s)

Student Representative(s)

Lab Technician(s)

Librarian(s)

: alistair.lamb@waikato.ac.nz

You can contact staff by:

  • Calling +64 7 838 4466 select option 1, then enter the extension.
  • Extensions starting with 4, 5, 9 or 3 can also be direct dialled:
    • For extensions starting with 4: dial +64 7 838 extension.
    • For extensions starting with 5: dial +64 7 858 extension.
    • For extensions starting with 9: dial +64 7 837 extension.
    • For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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What this paper is about

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This paper is an introduction to Lie groups and Lie algebras.
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How this paper will be taught

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This paper will be taught in a series of weekly discussions. Class times will be negotiated after the start of the semester. Class participation is expected and since this is a graduate paper a certain degree of independent learning is anticipated. It it strongly recommended that you purchase a copy of the text.
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Required Readings

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The book "Lie Groups, Lie ALgebras and Representations (2nd edition)" by Brian Hall published by Springer, is the primary text and required reading for this paper. While it focuses exclusively on matrix Lie groups, it provides an excellent introduction and it is recommended that students purchase a copy.

The book "Lie Groups, beyond an Introduction" by Anthony W. Knapp published by Birkhauser is more comprehensive and advanced. Students may wish to consult it on certain advanced topics.

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Learning Outcomes

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Students who successfully complete the course should be able to:

  • To gain basic understanding of concepts in this area
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  • To have the tools needed to learn more from the literature if required
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  • To be confident and capable of applying the mathematics
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  • To learn how to construct proofs
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  • To communicate mathematical ideas in an informal context
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  • To become a better mathematician by studying and working in this area
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Assessments

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How you will be assessed

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This paper is totally internally assessed so there is no final examination. There is however a final test which is a compulsory item of assessment and which is worth 50% of the final grade. This will be held in the last week of class at a time to be announced.

Other types of assessment include:

Problems. These are assigned during the lecture to be handed in next lecture. Typically they are small exercises closely related to the work being done in class. You may be asked for example to complete a proof or apply a result in a particular case.


Class participation and presentation. Students will be expected to participate actively in class and may be called on to help complete proofs at the whiteboard. Students may also be asked to present a solved problem or give a short prepared exposition and this may be assessed as if it were an assigned problem.

Assignments. These are large more substantial items of assessment involving a number of problems and are likely to require some time and effort to complete.

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The internal assessment/exam ratio (as stated in the University Calendar) is 100:0. There is no final exam. The final exam makes up 0% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 100:0 or 0:0, whichever is more favourable for the student. The final exam makes up either 0% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Problems
10
  • Hand-in: In Lecture
2. Assignments
40
  • Hand-in: In Lecture
3. Final test
50
✔
Assessment Total:     100    
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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