Ring Theory

This page may qualify for speedy deletion because: sub-minimal content: nothing to learn from here; the only FR is to Wikipedia and Wikibooks and one link to harvard.edu (no other FR) If you disagree or intend to fix it, and you have not contributed to it before, you may remove this notice. If you have contributed before and disagree, please explain why on the discussion page, after adding {{hangon}} to the top of the . This will alert curators and custodians to your intention, and may permit you the time to write your explanation. Before deleting check the discussion page, what links here, history (last edit), the page log, and Wikiversity:Deletions.

Welcome to Ring Theory!

Ring Theory is an extension of Group Theory, vibrant, wide areas of current research in mathematics, computer science and mathematical/theoretical physics. They have many applications to the study of geometric objects, to topology and in many cases their links to other branches of algebra are quite well understood.

So, why study ring and group theory?

You might study them because you've got a research question that somehow involves symmetry --- constraint problems in computer science can be solved more efficiently when a little is known about the solution space. You might need to make some difficult calculations in a complicated topological space which become easier by passing into associated algebraic structures.

You might even want to make millions as a cryptographer --- current methods in cryptography are hard to crack, but become very easy when hacking with a quantum computer. There are good reasons to hope that rings and groups hold the key to codes that cannot be broken easily by quantum computers, just in case someone invents one and fancies stealing identities. We've just not come up with the perfect code yet.

Or perhaps simply because it's fun and not really difficult to get into. Ring theory can be understood at a moderate level by high-school level students, and in fact well enough by interested undergraduate students for them to produce original research. This is in stark contrast to the New Math introduced in American high schools in the mid-20th century, which consisted of teaching young teenagers abstract subjects like Set Theory and in certain cases Category Theory, both of which are very difficult to get an idea about without a solid grounding in undergraduate mathematics.

It's also a very beautiful subject. Many familiar mathematical objects are some sort of ring - some in more than one way. Understanding a little about rings can make it easier to understand these objects too.

Learning materials and learning projects[edit | edit source]

Wikiversity has adopted the "learning by doing" model for education. Lessons should center on learning activities for Wikiversity participants. Learning materials and learning projects can be used by multiple departments. Cooperate with other departments that use the same learning resource.

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the lesson (lessons are independent pages in the main namespace) and start writing!

Offsite Learning Materials[edit | edit source]

• Abstract Algebra - Free Harvard Courses

Active Participants[edit | edit source]

If you are an active participant, feel free to put your name down here so that students can contact you.

• MikeDoyle (discuss • contribs) 13:59, 7 June 2017 (UTC)

See also[edit | edit source]

• w: Ring Theory
• Rings at Wikibooks.