• Class Number 2541
  • Term Code 2930
  • Class Info
  • Unit Value 6 units
  • Mode of Delivery In Person
    • AsPr Bai-Ling Wang
    • AsPr Bai-Ling Wang
  • Class Dates
  • Class Start Date 25/02/2019
  • Class End Date 31/05/2019
  • Census Date 31/03/2019
  • Last Date to Enrol 04/03/2019
SELT Survey Results

This course introduces students to the key concepts and techniques of Differential Geometry. Possible topics include:

  • Surfaces in Euclidean space
  • General differentiable manifolds
  • Tangent spaces and vector fields
  • Differential forms
  • Riemannian manifolds
  • Gauss-Bonnet theorem

Note: Graduate students attend joint classes with undergraduates but are assessed separately.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the concepts and language of differential geometry and its role in modern mathematics
2. Analyse and solve complex problems using appropriate techniques from differential geometry
3. Apply problem-solving with differential geometry to diverse situations in physics, engineering or other mathematical contexts
4. Apply differential geometry techniques to specific research problems in mathematics or other fields

Staff Feedback

Students will be given feedback in the following forms in this course:

  • written comments
  • verbal comments
  • feedback to whole class, groups, individuals, focus group etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session Summary of Activities Assessment
1 Definition of manifolds Immersion, embeddings of submanifolds
2 Manifold construction theorem Definition of functions and maps on manifolds
3 Tangent/cotangent spaces The tangent bundle and its manifold structure
4 Vector bundles Transition functions. Examples: Tangent bundles
5 Whitney embedding theorem Applications of partitions of unity
6 Lie brackets The flow of a vector field
7 Lie derivative Frobenius theorem and applications
8 Connection 1-forms Connections and covariant derivatives
9 Riemannian metrics Levi-Civita connections
10 Gauss Lemma Exponential normal coordinates
11 Tensor bundles Curvature of a connection
12 Gauss’s Theorema Egregium Ricci curvature and scalar curvature

Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Written assignment 1 10 % 15/03/2019 25/03/2019 1,2,3,4
Written assignment 2 10 % 12/04/2019 22/04/2019 1,2,3,4
Written assignment 3 10 % 10/05/2019 20/05/2019 1,2,3,4
Workshop participation and presentation 10 % 10/03/2019 31/05/2019 1,2,3,4
Lecture participation and 10 in-class quizzes 20 % 25/02/2019 31/05/2019 1,2,3,4
Mid semester exam 20 % 01/04/2019 26/04/2019 1,2,3,4
Take home final exam 20 % 03/06/2019 10/06/2019 1,2,3,4


ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.


For high level courses like Advanced Differential Geometry, lecture attendance is very important. Lecture participation and 10 in-class (5 minute) quizzes will help students to achieve the learning outcomes. The short (5 minutes) in-class quizzes help students to clarify concepts, and to show where more work is needed. Students receive weekly feedbacks on these quizzes

Assessment Task 1

Value: 10 %
Due Date: 15/03/2019
Return of Assessment: 25/03/2019
Learning Outcomes: 1,2,3,4

Written assignment 1

A written assignment involving problem-solving, proofs of theorems and extension of theory (10%).

Assessment Task 2

Value: 10 %
Due Date: 12/04/2019
Return of Assessment: 22/04/2019
Learning Outcomes: 1,2,3,4

Written assignment 2

A written assignment involving problem-solving, proofs of theorems and extension of theory (10%).

Assessment Task 3

Value: 10 %
Due Date: 10/05/2019
Return of Assessment: 20/05/2019
Learning Outcomes: 1,2,3,4

Written assignment 3

A written assignment involving problem-solving, proofs of theorems and extension of theory (10%)

Assessment Task 4

Value: 10 %
Due Date: 10/03/2019
Return of Assessment: 31/05/2019
Learning Outcomes: 1,2,3,4

Workshop participation and presentation

Work through a list of practice questions and present the solutions.

Students are expected to contribute on an on-going basis throughout the semester. The date range for this task comprises the start of the semester and the date final results are published on ISIS.

Assessment Task 5

Value: 20 %
Due Date: 25/02/2019
Return of Assessment: 31/05/2019
Learning Outcomes: 1,2,3,4

Lecture participation and 10 in-class quizzes

Students are expected to contribute on an on-going basis throughout the semester. The date range for these tasks indicates the approximate due date for the first quiz , and the approximate return date for the last quiz. There are 10 quizzes due over the semester. Further details can be found on the Course Wattle site.

Assessment Task 6

Value: 20 %
Due Date: 01/04/2019
Return of Assessment: 26/04/2019
Learning Outcomes: 1,2,3,4

Mid semester exam

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date indicate the approximate timeframe in which the exam will be held and results returned to the student. Students should consult the course wattle site and the ANU final examination timetable to confirm the date, time and venue of the exam.

Assessment Task 7

Value: 20 %
Due Date: 03/06/2019
Return of Assessment: 10/06/2019
Learning Outcomes: 1,2,3,4

Take home final exam

Academic Integrity

Academic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Late submission permitted. Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

AsPr Bai-Ling Wang

Research Interests

Geometry, Topology and Mathematical Physics

AsPr Bai-Ling Wang

Thursday 14:00 15:30
AsPr Bai-Ling Wang

Research Interests

AsPr Bai-Ling Wang

Thursday 14:00 15:30

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