MMAT5021 - Differential and Algebraic Methods in Geometry - 2015/16

Announcement

• Please note that the venue of the final exam on 26/4 will be changed to WMY304.
• Thank Charles Kwok for sharing his solution to exercises.
• Final Exam will be started at 19:00 on 26/4 at WMY304

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General Information

Lecturer

• Lau Chi Hin
  • Office: LSB 208
  • Tel: 3943 7987
  • Email:

Teaching Assistant

• Zhang Yi
  • Office: AB1 505
  • Tel: 3943 4298
  • Email:

Time and Venue

• Lecture: Tuesday 18:30-21:15; WMY 303

Course Description

This course is designed for the M.Sc. Degree Programme in Mathematics. The course is intended to provide an introduction to the geometry of curves and surfaces in 3 dimensional Euclidean space. The fundamental group and its application in the classification of closed surfaces will also be discussed.

References

• O'Neill, Barrett. Elementary Differential Geometry. Academic Press.
• Pressley, Andrew. Elementary Differential Geometry. Springer Verlag.
• Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press
• Torsten Ekedahl, One semester of Elliptic Curves, European Mathematical Society
• Joseph H. Silverman and John Tate, Rational Points on Elliptic Curves, Springer Verlag.

Lecture Notes

• Curves and Surfaces
• Algebraic Methods in Geometry (14/4 revised)

Tutorial Notes

• Differential Methods in Geometry
• Exercise 0
• Exercise 1 (Revised 12/2)
• Exercise 2 (Revised 18/2)
• Exercise 3 (Revised 7/3)
• Exercise 0 Solution (by Charles Kwok)
• Exercise 1 Solution (by Charles Kwok)
• Exercise 2 Solution (by Charles Kwok)
• Lecture notes Exercise 2 Solution (by Charles Kwok)
• Lecture notes Exercise 3 Solution (by Charles Kwok)

Assignments

• Assignment 1: Exercise 1: Questions 2,3,5,7,8,11 (Due: 2 Feb (Tue)) (Revised 12/2)
• Assignment 2: Exercise 2: Questions 2,3,4,6,7,8 (Due: 23 Feb (Tue)) (Revised 18/2)
• Assignment 3: Exercise 3: Questions 1,2,3,4,7 (Due: 8 March (Tue) Not compulsory)
• Assignment 4: Exercise 2: 1(a),(c),2,4(a),(c),5(a),(c),6(b),(d),8 (Due: 5 April 2016 Tuesday) (24/3 revised)
• Assignment 5: Exercise 3: 2, 3, 4(a),(b), 5 (Due: 19 April 2016 Tuesday)

Quizzes and Exams

• solutions to midterm

Solutions

• Solutions to Exercise 1
• Solutions to Exercise 2
• Solutions to Exercise 3
• Solutions to Exercise 4
• Solutions to Exercise 5

Assessment Scheme

Assignments		20%
Mid-term exam (March 8)		35%
Final exam (April 26 19:00 WMY 304)		45%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

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Last updated: April 20, 2016 12:44:49