MATH3968 Differential Geometry

General Information

This page contains information on the Senior advanced Unit of Study MATH3968 Differential Geometry.

This unit is only offered in odd numbered years.

  • Taught in Semester 2.
  • Credit point value: 6.
  • Classes per week: Three lectures and one tutorial.
  • Lecturer(s): Emma Carberry.

Please refer to the Senior Mathematics and Statistics Handbook for all questions relating to Senior Mathematics and Statistics. In particular, see the MATH3968 handbook entry for further information relating to MATH3968.

You may also view the Faculty Handbook entry for MATH3968 in the central units of study database.

Important Exam Information

You may take into the exam an A4 piece of paper, with whatever you wish written on it (on both sides). No (other) formula sheet will be provided.

If you have vision problems that are not fully corrected by eyeglasses, please contact me to make equitable arrangements.

MATH3968 Class Note Corrections

Students with any suggested changes to the class notes by Nigel O'Brian (notation/definition clashes with lectures, mistakes, etc.), are asked to post their suggestions on http://geometrynotes3968.blogspot.com/. This would be greatly appreciated as it will help students who take the class in the future. Anyone who posts a legitimate recommendation will receive the school pen. The person with the most comments will win a substantial prize, and a certificate with their name in embossed calligraphy.

Pre-Exam Consultations

I will be available for consultation at the following times:
  • Friday 6 November 1pm
  • Tuesday 10 November 12pm
  • Friday 13 November 11am

Honours Scholarships

For third year students considering Honours, information on scholarships ($6000) for an Honours year is now available at http://www.usyd.edu.au/scholarships at the link "Scholarships for Current Undergraduates". The closing date is December 17. Information is also available on the same web page for the new Prime Minister’s Australia Asia Endeavour Awards (up to $41,500), for students wishing to undertake an exchange semester at a university in Asia.

Assignment

The assignment has been returned on October 29. Here are solutions. Uncollected assignments can be collected during pre-exam consultation times (see above).

Online materials

Important Information Regarding Lecture Notes

Some important changes have been made to lecture notes, including to the important definition of a manifold, as well as many other minor corrections. The files below are all the corrected versions - you are advised to redownload (especially Lectures 15,16,33,34).

Lecture Notes

Please read the course outline, linked below, for details on the syllabus and recommended reading.

Lecture Notes

Corrections 6/11/09: Minor corrections (forgotten negative signs) to Lectures 17, 25 (also updated allnotes.pdf to include these corrections)
* note this file is 12.4MB and 144 pages

Tutorials and Solutions

Solutions to Exercise Sets from Class Notes

Required Texts

  • “Differential Geometry of Curves and Surfaces”, by Manfredo do Carmo, available at the student Co-op.
  • “Lecture Notes for MATH3968”, by Nigel O'Brien, available at KopyStop.

Recommended Text: “Differential Forms and Applications”, by Manfredo do Carmo, available at the student Co-op

Office Hours: Carslaw 723 Thursdays 1-2 p.m.

Assignments: There will be one assignment, due at the beginning of class on Tuesday 20th October.

Website: http://www.maths.usyd.edu.au/u/UG/SM/MATH3968/

Lecture Notes: Notes for each lecture will be posted to the website. I will attempt to have these up by the lunchtime before each lecture, but no promises!

Expectations

Keep up to Date: Look over your lecture notes as soon as possible after class, and definitely before the next lecture.

Do the Problems: Mathematics is not a spectator sport. Doing problems is even more important than learning theory.

Ask Questions: I don't acknowledge the concept of a "stupid question". Confused? Ask!

Tutorials

Each Wednesday afternoon tutorial will cover material from the Tuesday of that week, and the Wednesday and Thursday of the previous week. Tutorials will run weeks 2-13.

You should have attempted all of the tutorial problems BEFORE coming to the tutorial. I don't expect you to have solved all of them, but attempting them is important.

Assessment

Final Exam: 70%

Assignment: 20%

There will be one assignment, worth 20%.

Participation in Tutorials: 10%

To maximise your participation grade:
  • make a solid attempt at the tutorial problems before each class,
  • contribute to to the tutorial discussion.
The participation grade is based on effort, not on brilliance.

Timetable