Introductory Book on Group Theory for HS freshman?

In summary, the speaker is looking for an introductory book on group theory for their high school freshman son who has a good understanding of mathematics and is ready for calculus. They believe their son's strong understanding of symmetry and transformations may make him ready for group theory. They are seeking recommendations for a formal textbook on the topic. Another person suggests a book with short chapters and challenging problems, eventually proving the insolvability of the quintic.
  • #1
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I am looking for an introductory book on group theory for my son who is a high school freshman. He has a good grasp of the basics of mathematics and is ready to take calculus classes. He has a very strong intuitive grasp of symmetry and transformations, so I thought that he may be ready to be exposed to group theory. (I know I did when I was in high school, when I had a wonderful math teacher who was working on his PhD thesis while he was teaching and took the time to take the best kids in his class aside and teach them advanced math topics).

Are there any recommendations for good introductory group theory books? We are going through some of the online resources, but I thought a formal textbook treatment may also be useful.

Thanks in advance!
 
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  • #3
Thank you very much, I appreciate it!
 

1. What is group theory?

Group theory is a branch of mathematics that studies symmetry and the properties of objects that remain unchanged under certain transformations. It is used to understand the structure and behavior of mathematical systems, such as numbers, geometric shapes, and algebraic equations.

2. Why is group theory important?

Group theory has many applications in various fields of science, including physics, chemistry, computer science, and cryptography. It helps us understand patterns and relationships between elements in a system, and can also be used to solve complex problems and make predictions.

3. Who can benefit from learning group theory?

Anyone interested in mathematics and its applications can benefit from learning group theory. It is often taught in high school or college-level math courses, and can also be useful for scientists, engineers, and researchers in various fields.

4. What topics are typically covered in an introductory book on group theory for high school freshmen?

An introductory book on group theory for high school freshmen would typically cover concepts such as groups, subgroups, symmetry, transformations, and basic algebraic structures. It may also include examples and applications of group theory in real-life situations.

5. Do I need any prerequisites to understand group theory?

Some familiarity with algebra and basic mathematical concepts is helpful in understanding group theory. However, an introductory book on group theory for high school freshmen will typically start with the basics and build upon them, so no specific prerequisites are required.

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