Beauty, Form & Function: An Exploration of Symmetry (Coursera)

Beauty, Form & Function: An Exploration of Symmetry (Coursera)

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, with the extension of these concepts to the atomic structure of crystals. 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.

Class Deals by MOOC List - Click here and see Coursera's Active Discounts, Deals, and Promo Codes.

Syllabus

WEEK 1
Concepts in Symmetry I
These lectures will refresh your intuitive appreciation of symmetry in common objects and introduce the mathematical and symbolic descriptors of point symmetry.

WEEK 2
Concepts in Symmetry II
Some of the most beautiful examples of symmetry appear in flowers. These lectures use flowers as exemplars of the application of point symmetry to concisely describe the presence of mirror lines and rotation points.

WEEK 3
Concepts in Symmetry III
The key concepts in plane symmetry are illustrated by examining tessellations in architecture. The important concept of the asymmetric unit is also introduced. The practical importance of symmetry is illustrated through a discussion of chirality and its impact on drug design and efficacy.

WEEK 4
Concepts in Symmetry IV
The formal mathematical nomenclature of point symmetry is introduced, including the relationship between symmetrically linked objects.

WEEK 5
Plane and Space Symmetry I
Plane Groups that describe symmetry operations in 2 dimensions are illustrated using the art of Escher. The 2D Bravais Lattices that capture all tiling permutations are covered together with the difference between ‘primitive’ and ‘centred’ unit cells.

WEEK 6
Plane and Space Symmetry II
The 17 Plane Groups are formally introduced and their representation in the International Tables of Crystallography explained. By mastering the plane group diagrams and figures, all common tessellations can be deconstructed into their symmetric components.

WEEK 7
Plane and Space Symmetry III
These lectures examine the role of symmetry in Islamic architecture and history in the context of regular and irregular networks. The transition to 3D or Space Symmetry is via the five Platonic Solids. The 2D symmetry operators (rotation, reflection, glide) are expanded to include screw axes and axial glide in 3D symmetry.

WEEK 8
Plane and Space Symmetry IV
The 3D Bravais Lattices are the basis for describing the atomic relationships found in many crystalline materials. The way in which Space Symmetry determines not only the atomic locations but also the chemical composition of crystals is explained.

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Introduction to Complex Analysis (Coursera) Coursera
Wesleyan University

Introduction to Complex Analysis (Coursera)

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today.

Jun 22nd 2026
5-12 Weeks
Image and video processing: From Mars to Hollywood with a stop at the hospital (Coursera) Coursera
Duke University

Image and video processing: From Mars to Hollywood with a stop at the hospital (Coursera)

In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space.

Jun 15th 2026
5-12 Weeks
Quantum Mechanics for Scientists and Engineers 2 (edX) EdX
StanfordOnline

Quantum Mechanics for Scientists and Engineers 2 (edX)

This course covers key topics in the use of quantum mechanics in many modern applications in science and technology, introduces core advanced concepts such as spin, identical particles, the quantum mechanics of light, the basics of quantum information, and the interpretation of quantum mechanics, and covers the major ways in which quantum mechanics is written and used in modern practice.

Self Paced
Self-Paced
Introduction to Solid State Chemistry (edX) EdX
MIT,MITx

Introduction to Solid State Chemistry (edX)

Learn chemical principles by examining materials with examples from energy generation and storage to emerging technologies. This first-year University chemistry course explores the basic principles of the chemical bond by studying the properties of solids. Properties such as stiffness, electrical conductivity, thermal expansion, strength, and optical properties are the vehicle by which you can learn a great deal of practical chemistry.

Sep 6th 2023
13-24 Weeks
Aprendizaje de las matemáticas de primaria (Coursera) Coursera
Universidad de los Andes

Aprendizaje de las matemáticas de primaria (Coursera)

En este segundo curso de acceso gratuito* del programa especializado Educación Matemática para profesores de primaria, conocerás las cuestiones particulares sobre el aprendizaje de las matemáticas y las dificultades y los errores más frecuentes que tienen que enfrentar los estudiantes al aprenderlas. El curso tiene una duración aproximada de seis semanas, con una dedicación promedio de 4 horas semanales. Todas las evaluaciones tienen retroalimentación y podrás descargar la mayoría de los recursos del curso.

Jun 22nd 2026
5-12 Weeks
Introduction to Materials Science (Coursera) Coursera
Arizona State University

Introduction to Materials Science (Coursera)

Periods of our civilization have names associated with materials – stone age, bronze age, iron age and the silicon age. Materials impact all aspects of your daily life and will continue to do so in the future. The more we understand materials, the more we imagine the future with fantastic devices and advancements enabled by materials. This initial specialization introduces a limited number of material science and engineering concepts.

Jun 15th 2026
5-12 Weeks
Material Processing (Coursera) Coursera
Georgia Institute of Technology

Material Processing (Coursera)

Have you ever wondered why ceramics are hard and brittle while metals tend to be ductile? Why some materials conduct heat or electricity while others are insulators? Why adding just a small amount of carbon to iron results in an alloy that is so much stronger than the base metal? In this course, you will learn how a material’s properties are determined by the microstructure of the material, which is in turn determined by composition and the processing that the material has undergone.

Jun 22nd 2026
2 Weeks
Algebra: Elementary to Advanced - Functions & Applications (Coursera) Coursera
Johns Hopkins University

Algebra: Elementary to Advanced - Functions & Applications (Coursera)

After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition.

Jun 22nd 2026
3 Weeks
Material Behavior (Coursera) Coursera
Georgia Institute of Technology

Material Behavior (Coursera)

Have you ever wondered why ceramics are hard and brittle while metals tend to be ductile? Why some materials conduct heat or electricity while others are insulators? Why adding just a small amount of carbon to iron results in an alloy that is so much stronger than the base metal? In this course, you will learn how a material’s properties are determined by the microstructure of the material, which is in turn determined by composition and the processing that the material has undergone.

Jun 15th 2026
5-12 Weeks
Introduction to Mathematical Thinking (Coursera) Coursera
Stanford University

Introduction to Mathematical Thinking (Coursera)

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself.

Jun 15th 2026
5-12 Weeks
Matrix Algebra for Engineers (Coursera) Coursera
The Hong Kong University of Science and Technology - HKUST

Matrix Algebra for Engineers (Coursera)

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. The mathematics in this course is presented at the level of an advanced high school student, but typically students should take this course after completing a university-level single variable calculus course. There are no derivatives or integrals in this course, but students are expected to have attained a sufficient level of mathematical maturity. Nevertheless, anyone who wants to learn the basics of matrix algebra is welcome to join.

Jun 22nd 2026
4 Weeks