MATH3031 Algebraic Structures and Symmetry
- 6 points
|Semester 1||UWA (Perth)||Face to face|
- Details for undergraduate courses
- Level 3 option in the Mathematics and Statistics major sequence
- The area of knowledge for this unit is Mathematical and Physical Sciences
- Category A broadening unit for Bachelor of Science students where relevant according to the broadening requirements for each student
- 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.
- Books and other material wherever listed may be subject to change. Book lists relating to 'Preliminary reading', 'Recommended reading' and 'Textbooks' are, in most cases, available via the Booktopia Textbook Finder, which has the functionality to search by course code, course, ISBN and title, and may also be posted or available at the appropriate school's administrative offices. Where texts are listed in the unit description above, an asterisk (*) indicates that the book is available in paperback.