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Abstract Algebra Help and Definitions

Elvis Elvis

Abstract algebra is sometimes called algebraic structures includes studies like groups, fields, modules, rings, and vector spaces. Algebraic Structures gets deep into theory and proofs a lot more than linear algebra. When I took this course, I struggled in the proofs which caused my grade to suffer. This course is a lot like discrete mathematics and geometry because you are focusing a lot on proving theorems and applying concepts. For those majoring in mathematics or computer science, get ready for skills that will help you in your programming and analysis careers.

I would not take this course if I didn’t have too but it is a course that is needed for it uses the same skills as a programmer or compiler would need to run a program or code. Be prepared to sharpen your writing skills as this course can break you if you are not use to writing a certain way. You will find that this course is like a foreign language and will take time to notice the importance of it in the future.

There are many definitions in abstract algebra then are often used in proofs. Here are only a handful of them. You really need to do well in writing proofs for this course.

Abstract Algebra Help and Definitions

associativity – an expression containing two or more of the same associative operators in a row so that the operations are performed does not matter as long as the sequence of the operations is not changed.

binary operation – is a calculation involving two operands.

commutativity – changes the order of something without changing the end result.

cyclic group – is a group that can be generated by a single element.

finite group – is a group that has finitely many elements.

group theory – deals with the algebraic structures of groups.

identity element – is a type of element of a set with respect to a binary operation on that set usually called e for identity.