Geometry
Subject MAST30024 (2010)
Note: This is an archived Handbook entry from 2010.
Credit Points:  12.50  

Level:  3 (Undergraduate)  
Dates & Locations:  This subject has the following teaching availabilities in 2010: Semester 2, Parkville  Taught on campus.
Lectures and practice classes. Timetable can be viewed here. For information about these dates, click here.  
Time Commitment:  Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week Total Time Commitment: Estimated total time commitment of 120 hours  
Prerequisites: 
One of
and one of  
Corequisites:  None  
Recommended Background Knowledge:  None  
Non Allowed Subjects:  None  
Core Participation Requirements:  It is University policy to take all reasonable steps to minimise the impact of disability upon academic study and reasonable steps will be made to enhance a student's participation in the University's programs. Students who feel their disability may impact upon their active and safe participation in a subject are encouraged to discuss this with the relevant subject coordinator and the Disability Liaison Unit. 
Subject Overview: 
This subject introduces three areas of geometry that play a key role in many branches of mathematics and physics. In differential geometry, calculus and the concept of curvature will be used to study the shape of curves and surfaces. In topology, geometric properties that are unchanged by continuous deformations will be studied to find a topological classification of surfaces. In algebraic geometry, curves defined by polynomial equations will be explored. Remarkable connections between these areas will be discussed. Topics include: Topological classification of surfaces, Euler characteristic, orientability. Introduction to the differential geometry of surfaces in Euclidean space: smooth surfaces, tangent planes, length of curves, Riemannian metrics, Gaussian curvature, minimal surfaces, GaussBonnet theorem. Complex algebraic curves, including conics and cubics, genus. 

Objectives: 
On completion of this subject, students should Have an understanding of:
Be able to:

Assessment: 
Two or three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3hour written examination in the examination period (80%). 
Prescribed Texts:  None 
Recommended Texts: 
N. Hitchin, Geometry of surfaces, Oxford University lecture notes, available online. M. do Carmo, Differential geometry of curves and surfaces, PrenticeHall, 1976. F. Kirwan, Complex algebraic curves, Cambridge University Press, 1992. 
Breadth Options:  This subject potentially can be taken as a breadth subject component for the following courses: You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects. 
Fees Information:  Subject EFTSL, Level, Discipline & Census Date 
Generic Skills: 
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

Notes:  This subject is available for science credit to students enrolled in the BSc (both pre2008 and new degrees), BASc or a combined BSc course. 
Related Course(s): 
Bachelor of Science 
Related Majors/Minors/Specialisations: 
Mathematics and Statistics (Mathematical Physics specialisation) Mathematics and Statistics (Pure Mathematics specialisation) Pure Mathematics 
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