Exploring Groups and Symmetry: A Beginner's Guide

In summary, symmetry refers to the balanced arrangement of parts or elements around a central point or axis. It is important because it helps us understand and describe the world around us, and there are three types of symmetry: reflection, rotational, and translational. Symmetry is used in science to study physical and natural systems, and can be found in many natural and designed objects. It is also used in technology for efficient design.
  • #1
Kevin McHugh
318
164
Hi folks,

I know nothing about groups or symmetry. Could anyone recommend a good introduction that defines groups and explains their notation and operations? I am particularly interested in general, orthogonal, and unitary groups.

Thanks in advance. Kevin
 
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  • #2
I would recommend "Groups and Symmetry" by Armstrong.
 
  • #3
Being unemployed, I'd like to find a free e-book
 
  • #4
Amazon in the USA has used copies (apparently in good condition) for less than $15 including shipping. A new paperback is about twice that price. Books are always a worthy investment.
 

1. What is symmetry?

Symmetry refers to the balanced arrangement of parts or elements around a central point or axis. It is a fundamental concept in mathematics and science that describes the repeating patterns and structures found in nature and designed objects.

2. Why is symmetry important?

Symmetry is important because it helps us understand and describe the world around us. It allows us to recognize patterns, make predictions, and solve problems in various fields such as mathematics, physics, chemistry, biology, and art.

3. What are the types of symmetry?

There are three types of symmetry: reflection (or mirror) symmetry, rotational (or radial) symmetry, and translational (or glide) symmetry. Reflection symmetry refers to mirror images, rotational symmetry refers to repeating patterns around a central point, and translational symmetry refers to repeating patterns that are shifted in a particular direction.

4. How is symmetry used in science?

Symmetry is used in science to study the properties and behavior of physical and natural systems. It is used in various fields such as crystallography, molecular biology, particle physics, and cosmology to understand the structure and function of molecules, crystals, atoms, and the universe.

5. What are some real-life examples of symmetry?

Symmetry can be found in many natural and designed objects, such as snowflakes, flowers, human faces, buildings, and bridges. It can also be observed in the behavior of animals and the movement of celestial bodies. In technology, symmetry is used in the design of products and machines to ensure balance and efficiency.

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