About the Course
Nanyang Technological University
and Coursera are proud to offer Beauty, Form & Function: An Exploration of
Symmetry that caters to both non-specialists via a non-academic credit on-demand version (https://www.coursera.org/learn/symmetry) and specialists through this academic credit fixed-session version. 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
Duration: 8 weeks
Time Commitment: 7-10 hours per
Target Group: Scientists and
Engineers (current and prospective NTU students)
Recognition: Verified Certificate through Signature Track enrollment
NTU Academic Units: Verified
Certificate Students earn 3 Academic Units
NTU Course Type: Unrestricted Elective or General Elective
This course 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?
- How are drug and materials design engineered through
atomic scale symmetry?
- How is the internal
arrangement of atoms reflected by crystal faceting?
- How does symmetry manipulation create polytypes, polymorphs and polysomes?
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.
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
This is a challenging course with 65% of students rating the material
as Difficult to Very Difficult, but many find the subject matter
The course content is
released in two week blocks and consists of approximately 1 hr of
lectures and tutorials per week. There are specific windows for uploading
homework and undertaking peer-to-peer marking. These are detailed in the downloadable course timetable.
Part I: Basic Concepts of Symmetry
- Week 1: ‘A World of Symmetry’ will refresh your intuitive
appreciation of symmetry in furniture, botany and common objects and introduce
the mathematics of point symmetry.
- Week 2: ‘Tiling and the Asymmetric Unit’ begins by examining tessellations
in architecture that will illustrate key concepts in plane symmetry including
the asymmetric unit. ‘Chirality’ discusses this key concept in symmetry and its impact on drug design
Part II: Plane (2D) and Space (3D)
- Week 3: ‘Escher and Graphic Design’ introduces symmetry operations in 2 dimensions
and the difference between ‘primitive’ and ‘centered’ unit cells are illustrated
using the art of Escher. ‘Nets’ examines the role of symmetry in Islamic
architecture and history in the context of regular networks.
4: ‘Space Symmetry’ expands the symmetry operations to include 3 dimensional
motion. The methodology for reading and
using the symmetry diagrams of the 17 plane groups and 230 space groups is
Part III: Symmetry in Crystals
- Week 5: ‘Crystal Forms and the Beauty of Minerals’ looks the external shape of
mineral crystals and we learn about crystal power by visiting a geomancer. The manner in which crystal faceting
reflects the internal atomic arrangements is described. ‘Planes, Directions and Unit Cell’ introduces the mathematics
for describing perfect crystal structures.
- Week 6: ‘Platonic Solids and Atomic Bonding’
shows that regular geometrical shapes can be derived from folding plane
nets into polyhedra that often describe atomic clustering and also the appearance of defects or
asymmetry that are important aesthetically and technologically. A laboratory tour will show the experiments
used to extract crystallographic information.
Part IV: Symmetry and Technology
- Week 7: ‘Tailoring Crystals for Technology’ brings together chemistry and
crystallography, shows how they are inter-related, and how they are adapted to
engineer designer technological materials.
A clean room fabrication facility provides real world context for
exploiting chemically- and physically-driven symmetry.
- Week 8: ‘Looking for Broken Symmetry - Atomic Scale Imaging’ looks beyond 3 dimensional symmetry to higher dimensional
repetitions found in incommensurate crystal structures. ‘Deceptive Perception - Symmetry & Furniture Design’ returns to the everyday appearance of symmetry that can now be
At the conclusion of this study, you will
possess the tools and the motivation to look at symmetry with even greater
delight, wonder and appreciation!
Mathematics at GCE
Advanced Level or International Baccalaureate Diploma or equivalent to junior
high school. In addition, 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.
- 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 using the pptx and docx templates provided, converted to a
pdf and uploaded. If you have have an older version of Powerpoint and Word you can convert the pptx and docx files to doc and ppt files at http://www.convertfiles.com/convert/document/DOCX-to-DOC.html and http://www.convertfiles.com/convert/document/PPTX-to-PPT.html.
In a topic
as broad as Symmetry no single text can
do justice to the field. Therefore, the
notes and supplementary materials provided in this course strive to be
self-contained. There are also many web
resources to access.
Video book reviews are provided to get a sense of the breadth of
Quite academic treatments can be found in the research papers of the Open Access
journal Symmetry. http://www.mdpi.com/journal/symmetry
who wish to study conventionally the following texts, that are widely available in
public libraries, are recommended.
by Magdolna Hargittai and István
Symmetry is as simple or as
complicated as we are ready to absorb it in everything around us. From flowers
to bridges, buildings, coke machines, and snowflakes; from molecules to
walnuts, fences, pine cones, and sunflowers; from music to children's drawings;
from hubcaps to bank logos, propellers, wallpaper decorations, and pavements,
we recognize it if we walk around with open eyes and an open mind. This book
provides aesthetic pleasure and covert education, immersing the reader in both
the familiar and the unknown and leading always to unexpected discoveries. The authors, world-renowned
scientists, have already produced a dozen books on symmetry for professionals
as well as lay persons, for grownups as well as children, in English, Russian,
German, Hungarian, and Swedish languages. They provide this attractive account
of symmetry in few words and many, as many as 650, images in full colour from
the most diverse corners of our globe. An encounter with this book will open up
a whole new experience for the reader, who will never look at the world with
the same eyes as before.
and Crystal Structures
Richard J. D. Tilley
Crystals and Crystal Structures is an
introductory text for students and others who need to understand the subject
without necessarily becoming crystallographers. Using the book will enable
students to read scientific papers and articles describing a crystal structure
or use crystallographic databases with confidence and understanding. Reflecting the interdisciplinary nature of
the subject the book includes a variety of applications as diverse as the
relationship between physical properties and symmetry, and molecular and
protein crystallography. As well as covering the basics the book contains an
introduction to areas of crystallography, such as modulated structures and
quasicrystals, and protein crystallography, which are the subject of important
and active research.
The class is divided into 4 major Parts and will consist of:
videos about 9 - 15 minutes in length. Most lectures contain 1-2 in video quiz
questions for self-assessment. These are not graded.
- Multiple Choice Question (MCQ) Quizzes at the
end of each Part which will be graded. Model MCQ and detailed answers are available for revision.
- 3 open - ended assignments with peer-to-peer assessment. To guide you in this homework, student focus-group recordings show how undergraduates tackled these assignments.
- 2 learning logs. These logs are designed to help you reflect on what you have learned and share with fellow students.
- 4 MCQ quizzes (20% of total grade)
- 3 peer-graded assignments (72%)
- 2 peer-graded learning logs (8%)
The pass mark is >= 60% of the maximum possible score averaged across all graded assignments.
At least 8 out of the 9 assignments must be submitted and authenticated to gain
3 Academic Units (AU).Student Responsibility
It is the
responsibility of students to ensure assignments are submitted on time. Note
that times are for Singapore and we are unable to entertain late submission.
- Use the international clock
provided near the top of the navigation menu to check the time difference
with your locality.
- Download the course
timetable and print it out to ensure you do not miss homework deadlines.
- Do not leave your homework
until the last minute.
- For the graded multiple
choice question (MCQ) sets either 1 or 2 attempts are allowed. When 2 attempts are made the highest mark is
taken towards grading.
- For peer-to-peer assignments
submit 1-2 days early in case of internet failures.
- While homework submission is
not compulsory it is very difficult to pass this course without attempting
- For SIGNATURE TRACK
STUDENTS at least 8 out of the 9 assignments must be submitted and authenticated to gain
3 Academic Units (AU).
- For SIGNATURE TRACK
STUDENTS authentication through a webcam plus keystroke recognition is
always required for the assignment to be recognized. ALWAYS
USE A COMPUTER WITH WEBCAM.
- For SIGNATURE TRACK
STUDENTS a live portrait captured by webcam is compulsory for all submitted assignments.
Capturing student ID cards, passport photos, drivers licences etc is not
- All NTU MATRICULATED
SIGNATURE TRACK STUDENTS must enrol using their NTU email to avoid
paying the course fee and allow transfer of academic credits. NTU students that enrol with Coursera using a non-NTU email must change it to their university email account. Please follow the steps at https://courserahelp.zendesk.com/hc/en-us/articles/201208129-Account-Settings to change the email address.
- SIGNATURE TRACK
AUTHENTICATION IS NOT SUPPORTED ON MOBILE DEVICES such as iPhone and iPads.
Always submit your homework from a desktop or laptop computer to avoid any
problems with authentication.
- CHEATING AND UNETHICAL BEHAVIOUR ARE UNACCEPTABLE and students must comply with the Coursera Honour
and NTU Examination Policy (http://www.ntu.edu.sg/Students/Undergraduate/AcademicServices/Examination/pages/instructionstoexamcand.aspx). Failure to abide by these requirements will, at
minimum, lead to loss of Academic Units and exclusion from all NTU MOOC, with egregious
cases resulting in suspension or expulsion from NTU.
- For peer-to-peer evaluated
assignments PLAGIARISM WILL NOT BE TOLERATED and whether detected
by students or the course manager will automatically lead to a score of
zero for that assignment.
- PEER MARKERS HAVE A DUTY-OF-CARE to mark
according to the rubrics and follow all instructions. Giving marks for
obvious non-compliance with rubric instructions or clear plagiarism will
lead to an automatic loss of academic units.
- If you are sharing a
computer with other students, make sure you log out to avoid your homework
and grades being over-written on the Coursera server by another student's
uploads and answers. Once lost, your work cannot be restored.
- Matriculated NTU students
must enrol using the secure website http://teamsites.ntu.edu.sg/CITS/LearningSolutions/Symmetry/default.aspx and their NTU email account to ensure seamless transfer of Academic Units
to their degree transcript.
- Peer-to-peer marked
assignments will gain a score that is the mean taken from either 2 or 5 student
assessors. It is essential that students mark carefully against the
simple rubrics provided.
1. Is this a hard course?
- The course is definitely challenging. The content and assessments replicate a usual NTU undergraduate course.
- 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 Parts I to IV and obtain a score of >= 60%.
3. How do I gain NTU Academic Units (AUs)?
- Enrol in the Signature Track and earn a Verified Certificate.
- Complete Parts I, II, III and IV and obtain a score of >= 60%.
- All SUBMITTED ASSIGNMENTS MUST BE AUTHENTICATED using keystroke recognition and a live webcam image. Images of students IDs, passports, drivers licenses etc. are not acceptable.
- 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.
4. When will I receive my Statement of Accomplishment?
- All Statements of Accomplishment and Verified Certificates are issued approximately 4-6 weeks after completion of the 8 week course.
- Prior to issuing Verified Certificates checks for cheating, plagiarism and compliance with the Coursera Honour Code and NTU Regulations will be undertaken.
- NTU has a ZERO TOLERENCE POLICY to breaches of the honour code and students who are found not to comply will, at minimum, be denied Academic Units with more serious cases leading to suspension or expulsion from NTU.
5. 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.
6. 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 with Distinction 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.
7. 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.
8. Is there a course fee?
- The course may be taken by anyone free-of-charge to earn a Statement of Accomplishment.
- 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 USD49 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.
10. How does an NTU student enrol to the Signature Track of the course?
- Please ensure you have either one of the picture IDs (National ID card, Passport, Driver’s license) on hand before enrolling.
- Login to Teamsites via http://teamsites.ntu.edu.sg/CITS/LearningSolutions/Symmetry/default.aspx with your network account.
- Select from the line “Registration to Symmetry MOOC's Signature Track”
- For NTU students who have earlier registered for the course on the free track using their NTU email address choose Option 1a
- For NTU students newly enrolling choose Option 1b
- Follow the instructions to sign up for the waived-fee Signature Track and complete the online form to indicate your choice of credit transfer.
- Please ensure that you create your Signature Profile immediately after you have signed up for Signature Track. This is to ensure that your Signature Profile is link to your identity to each piece of graded coursework that you submit for your course. Also, when you successfully complete the course, you’ll earn a Verified Certificate.
11. 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-STS 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 with Distinction 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.
12. 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 with Distinction issued by Coursera for the Signature Track, at the point of application.
- Only Verified Certificates with Distinction 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).