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Unit of study_

Differential Geometry - MATH4068

This unit is an introduction to Differential Geometry, one of the core pillars of modern mathematics. Using ideas from calculus of several variables, we develop the mathematical theory of geometrical objects such as curves, surfaces and their higher-dimensional analogues. For students, this provides is the first taste of the investigation on the deep relation between geometry and topology of mathematical objects, highlighted in the classic Gauss-Bonnet Theorem. Differential geometry also plays an important part in both classical and modern theoretical physics. The course aims to develop geometrical ideas such as curvature in the context of curves and surfaces in space, leading to the famous Gauss-Bonnet formula relating the curvature and topology of a surface. A second aim is to remind the students about all the content covered in the mathematical units for previous years, most importantly the key ideas in vector calculus, along with some applications. It also helps to prepare the students for honours courses like Riemannian Geometry. By doing this unit you will further appreciate the beauty of mathematics which is originated from the need in solving practical problems / develop skills in understanding the geometry of the surrounding environment / prepare yourself for future study or the workplace by developing advanced critical thinking skills / gain a deep understanding of the underlying rules of the Universe.

Classes
Three 1 hour lectures and one 1 hour tutorial per week.

Assessment
The grade is determined by student works throughout the semester, including Quiz 1 (10%), Assignment 1 (15%), Assignment 2 (15%), and Exam (60%). Moreover, to provide flexibility, the final grade is taken as the maximum between the above calculated score and the score of the exam out of 100.

Assumed knowledge
(MATH2921 and MATH2922) or MATH2961

Pre-requisites

(A mark of 65 or greater in 12cp of MATH2XXX units of study) or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)]

Prohibitions

MATH3968

Details

Faculty: Science

Semester 2

05 Aug 2019

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2019
Unit of study level: Honours
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Dr Florica Cirstea
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

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