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TheBiologist
- 18
- 4
Not quite sure, could someone kindly explain the concept of the topic to me? Thanks, it really means a lot. :)
I'm still in Secondary School, so no courses, apart from school itself.Stephen Tashi said:That's asking a lot! (We should get you to explain "the concept" of biology.) Before we try this explanation, could you tell us you background in mathematics? What courses have you already taken?
Yes. I've done indices 2, nth terms, volume, surface area, sequences and we've just started loci.Stephen Tashi said:Can we assume you have done some simple algebra problems, like solving 3x + 1 = 7 ?
Thank you for the explanation.HallsofIvy said:"Abstract algebra" is essentially the study of "finite operations"- that is, operations like you do in solving simple equations (like the one Stephen Tashi gives). It includes all arithmetic operations but in a more "abstract" way- looking at general properties rather than specific numbers or operations.
"Linear algebra" is a subset of "abstract algebra" but important enough to be considered separately. It looks specifically at those operations we consider "linear". Again, the equation Stephen Tashi gives is linear. The only operations we need to consider are adding and subtracting and multiplying by numbers. That would include, say 3x+ 4y but not [itex]x^2[/itex], [itex]y^2[/itex], or [itex]xy[/itex].
Linear algebra deals with the study of linear equations and systems, while abstract algebra is concerned with algebraic structures such as groups, rings, and fields. Linear algebra uses concrete examples and real numbers to solve problems, while abstract algebra uses symbols and generalizations to study mathematical structures.
Linear algebra has various applications in fields such as physics, engineering, computer graphics, and data analysis. Abstract algebra has applications in cryptography, coding theory, and theoretical physics, to name a few.
Some key concepts in linear algebra include vector spaces, linear transformations, and matrices. In abstract algebra, important concepts include groups, rings, and fields, as well as their properties and operations.
Linear algebra is often considered a subset of abstract algebra as it deals with a specific type of algebraic structure (vector spaces). However, linear algebra also relies on concepts from abstract algebra, such as fields and matrices, to solve problems.
This is subjective and depends on individual strengths and interests. Some may find linear algebra more intuitive and straightforward, while others may prefer the abstract and general nature of abstract algebra. Both require practice and a solid understanding of foundational concepts.