MATH3031 Algebraic Structures and Symmetry
- 6 points
If this unit does not have an online alternative, then students who are presently unable to enter Western Australia and whose studies would be delayed by an inability to complete this unit, should contact the unit coordinator (details given on this page) to ascertain, on an individual case-by-case basis, if alternate arrangements can be made to support their study in this unit.
Availability Location Mode Semester 1 UWA (Perth) Face to face Predominantly face-to-face. On campus attendance required to complete this unit. May have accompanying resources online.
- Details for undergraduate courses
- Level 3 option in the Mathematics and Statistics major sequence
- Level 3 elective
- The theme of this unit is the theory of groups, and their use in measuring symmetry with special emphasis on geometric examples. Apart from the mathematical interest of groups, they are of great and increasing importance in Chemistry, Geology and Physics, and those aspects that have significance in such disciplines are strongly emphasised. The fundamental notion is that of a group action. Group actions are used to elucidate the structure of a group, culminating in the Sylow theorems, which connect finite groups and number theory. The applications of group actions extend to symmetries of the plane, three-space and higher dimensional spaces, rotation and spin, crystallographic groups and symmetries of regular figures in two and three dimensions. Other algebraic structures such as rings and fields may also be explored.
- Students are able to demonstrate skills and insights in a wide range of algebraic topics with important applications.
- Indicative assessments in this unit are as follows: (1) tests and (2) a final examination. Further information is available in the unit outline.
Supplementary assessment is not available in this unit except in the case of a bachelor's pass degree student who has obtained a mark of 45 to 49 overall and is currently enrolled in this unit, and it is the only remaining unit that the student must pass in order to complete their course.
- Unit Coordinator(s)
- Professor Gordon Royle
- Unit rules
- MATH2031 Introduction to Pure Mathematics
- Contact hours
- lectures: 3 hours per week
- The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
- All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
- Unit readings, including any essential textbooks, are listed in the unit outline for each unit, one week prior the commencement of study. The unit outline will be available via the LMS and the UWA Handbook one week prior the commencement of study. Reading lists and essential textbooks are subject to change each semester. Information on essential textbooks will also be made available on the Essential Textbooks. This website is updated regularly in the lead up to semester so content may change. It is recommended that students purchase essential textbooks for convenience due to the frequency with which they will be required during the unit. A limited number of textbooks will be made available from the Library in print and will also be made available online wherever possible. Essential textbooks can be purchased from the commercial vendors to secure the best deal. The Student Guild can provide assistance on where to purchase books if required. Books can be purchased second hand at the Guild Secondhand bookshop (second floor, Guild Village), which is located on campus.