Beauty, Form & Function: An Exploration of Symmetry

Learn how to identify symmetrical forms and appreciate their importance in nature, art, architecture, crystallography and technology. Understand symmetry quantitatively, recognize its role in beauty and design, and appreciate its function in our everyday life. The level of difficulty is intermediate-to-hard depending on the Track chosen. Workload: 4-6 hrs/week for Track 1 (5 weeks - Statement of Accomplishment); 7-10 hrs/week for Track 2 (8 weeks - Statement of Accomplishment with Distinction). Students who obtain a Verified Certificate and complete Track 2 with an overall mark of more than 60% earn 3 Academic Units (AU) directed towards either an Unrestricted Elective (UE) or General Elective (GE) subject at NTU.

About The Course

Nanyang Technological University and Coursera are proud to offer Beauty, Form & Function: An Exploration of Symmetry as the first dual-track MOOC that caters to both specialists and non-specialists, and can lead to full academic credits.  Below can be found the:

Syllabus • Grading Scheme • Recommended Readings •

Required Background • Essential Resources • Student Responsibility • FAQs

Symmetry is everywhere. In the grand scheme of things it is the blueprint by which the universe operates. We see symmetry in nature, art, architecture, science and engineering. This course explores the Beauty, Form and Function of Symmetry in common objects, then progresses to investigate tiling and tessellation, gems and crystals, and finally its indispensable role in technology.  Symmetry and asymmetry are also key factors that ensure the successful reproduction of plants and animals. For example, the bilateral symmetry of orchids is widely admired and this geometry is essential for insects to pollinate these flowers.

Track 1: Overview (PARTS I and II)

Duration: 5 weeks

Time Commitment: 4-6 hours per week

Target Group: Teachers, artists, architects and anyone with a passion for symmetry

Recognition: Statement of Accomplishment

This Track gives you the means to address several fundamental questions.

  • What tags do we recognize in decorative arrangements?
  • What guidelines shape the patterns in the world around us?
  • What functions do these symmetrical patterns serve?

Track 2: Overview (PARTS I, II, III and IV)

Duration: 8 weeks

Time Commitment: 7-10 hours per week

Target Group: Scientists and Engineers (current and prospective NTU students)

Recognition: Statement of Accomplishment with Distinction

NTU Academic Units: Verified Certificate Students earn 3 Academic Units

NTU Course Type:  Unrestricted Elective or General Elective

This Track explores the impact of symmetry in technology through:

  • Describing crystals at the atomic scale to understand drug and materials design
  • Understanding how the internal arrangement of atoms is reflected by crystal faceting
  • Appreciating symmetry modification through polytypism, polymorphism and polysomatism.

To amplify these ideas, you will undertake field-exercises and be introduced to specialists - botanists, artists, geomancers, historians, scientists and engineers - that work with symmetry, and who will provide their personal insights into its ‘magic’ and impact on their disciplines.

Successful completion as a Verified Certificate student earns 3 academic units (AUs) for an Unrestricted Elective or General Elective subject at NTU.

The option of earning AUs is open to all students. It is not necessary to be already enrolled at NTU.  Once earned, the AUs remain valid for 3 years.

Frequently Asked Questions

1. Is this a hard course?
• The complete Track 2 course (Parts I, II, III, IV) is definitely challenging.  The content and assessments replicate a usual NTU undergraduate course.
• The content of Track 1 (Parts I and II) is easier and covers the fundamentals of recognizing and describing symmetry.  This Track is suitable for everyone.
• Parts III and IV contain lectures of general interest, but there is a step change in difficulty compared to Parts I and II, and the second half of the course is appropriate for science and engineering students.

2. How do I gain a Statement of Accomplishment?
• Complete Track I (Parts I and II) and obtain a score of >= 60%.

3. How do I gain a Statement of Accomplishment with Distinction?
• Complete Track 2 (Parts I, II, III and IV) and obtain a score of >= 60%.

4. How do I select to enrol in Track 1 or Track 2?
• It is not necessary to make a selection.  Simply enrol in the course as usual.
• If you meet the requirements for Track 1 – passing Part I and Part II with a score >=60% - you receive a Statement of Accomplishment.
• If you meet the requirements for Track 2 - passing Part I, Part II, Part III and Part IV with a score >=60% - you receive a Statement of Accomplishment with Distinction.

5. How do I gain NTU Academic Units (AUs)?
• Enrol in the Signature Track and earn a Verified Certificate.
• Complete Track 2 (Parts I, II, III and IV) and obtain a score of >= 60%.
• SIGNATURE TRACK AUTHENTICATION IS  NOT SUPPORTED ON MOBILE DEVICES such as iPhone and iPads. You can watch video lectures, participate in the forums, and save drafts of your quiz and assignment answers from a mobile device, but it is ESSENTIAL THAT HOMEWORK IS SUBMITTED FROM A DESKTOP OR LAPTOP COMPUTER to avoid problems with authentication.

6. When will I receive my Statement of Accomplishment?
• All Statements of Accomplishment and Verified Certificates are issued approximately 1 month after completion of the 8 week course.
• Track 1 (Parts I and II) students who complete their study after 5 weeks, must wait until the complete course ends (after 8 weeks) before being issued with their Statement of Accomplishment.

7. I am already an NTU student - why should I join this MOOC?
• You will be able to pursue this course without having to fit it into your class schedule in NTU.
• You will be guaranteed a place in the course as there is no limit to student numbers.
• You can study when you are on attachment or on overseas exchange.
• This MOOC is offered every semester and you can attempt multiple times without penalty.

8. Who is eligible to gain NTU Academic Units from this MOOC?
• Whether already an NTU student, or considering joining NTU, you can earn 3 AU by obtaining a Verified Certificate on the Signature Track.
• You will enjoy learning without worrying about your results as the MOOC is graded Pass/Fail, and there will be no impact on your cumulative grade point average (CGPA) and the classification of your degree.
• You can discontinue the course at any time.

9. I am an NTU student and unsure whether to take this course for credit - how much time do I have to decide?
• This MOOC operates in a similar way to normal face-to-face courses with an "Add" period.
• You can try out the course for up to two weeks after commencement as a normal student before converting to Signature Track to obtain a Verified Certificate.
• If you miss the two week window to enrol as a Verified Certificate student, then change your mind, you will have to re-enrol the following semester.

10. Is there a course fee?
• The course may be taken by anyone free-of-charge to earn a Statement of Accomplishment or Statement of Accomplishment with Distinction.
• Those not currently matriculated NTU students and who may wish to transfer credit for the course when they subsequently enrol at NTU must take the Signature Track for which a fee of USD39 is payable to Coursera which will issue the Verified Certificate. 
• Matriculated full-time NTU undergraduate students will be able to sign-up for the Signature Track without paying a fee and be able to transfer the credits earned if they passed the course.

11. How does an NTU student enrol to the Signature Track of the course?
• Login to Teamsites via with your network account.
• Select from the first line “Symmetry MOOC Registration” 
• For NTU students who have earlier registered for the course on the free track using their NTU email address choose Option 1
• For NTU students newly enrolling choose Option 2
• Follow the instructions to sign up for the waived-fee Signature Track and complete the online form to indicate your choice of credit transfer. 

12. How do full time NTU students transfer the credits earned?
•Wait for email from Office of Academic Services (OAS) and the Centre for IT Services (CITS).
•Follow the instructions in the email to indicate whether you are transferring credits to fulfil your GER General Elective or UE Unrestricted Elective requirement.
• A reminder will also be sent at the end of the course. 
• As long as you pass the course, earn a Verified Certificate through the Signature Track, and remain a full-time matriculated NTU undergraduate student at the point of completion, your credits will be automatically transferred towards fulfilling the requirements of your NTU degree programme.

13. How do new students transfer the credits earned?
• You should apply to your School for the credits to be transferred in the first semester of your enrolment to NTU. 
• You must produce the Verified Certificate issued by Coursera for the Signature Track, at the point of application.
•Only Verified Certificates issued within 3 years of their award by Coursera are accepted by NTU for transfer of 3 Academic Units (AUs).
• The courses transferred will be recorded in your transcript.
• Please be reminded that you must comply with the following requirements for graduation:
       - Minimum candidature period for the degree
       - Minimum AU of letter-graded courses 
       - Minimum years of study at NTU (i.e. residential period).

Recommended Background

  • Track 1: Mathematics at GCE Advanced Level or International Baccalaureate Diploma or equivalent to junior high school.

  • Track 2: In addition to the requirements for Track 1, high school or undergraduate (freshman) chemistry is very helpful.

Essential Resources Required

This is an undiluted university course and resources equivalent to an undergraduate student at NTU are essential to complete these studies.  These include:

  • Access to a Windows or Apple personal computer:  While lectures can be viewed on tablets and smartphones it is not possible to run the specialized programs on these architectures.  There can be no troubleshooting of compatibility problems.

  • Access to a smartphone with camera or a digital camera:  The field-work exercises involve photographing objects in your environment and analysing their symmetry.  Submission of these graded exercises is essential to obtain course recognition.

  • Access to Microsoft Office or Open Office: Homework must be prepared in PowerPoint or Word, converted to a pdf and uploaded.