Ok so i need ideas on course: Linear and Modern Algebra ... I have to create a creative piece on the course to do, as a project ...Any creative minds!?
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its an open project ..that requires creativity ...and must outline some/most of the subtopics under linear and modern Algebra...
hmm i'll think for a while lol
so why don't you talk about the general formula of solving a polynomial, and for how far we can get a one, talk about galois
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Maybe the application of modern algebra in real life?
well RV like what :P @aravindg
crypto analysis maybe?
that's interesting @amistre64
This is a delicate question and you might need to refine your question in order to get a good answer.
My Professor always taught us that Linear Algebra is the study of \(\hom_R(M,N)\) where \(M,N\) are Modules or a commutative (unitary) ring \(R\) and \(\hom\) stands for linear mappings. Things can get very easily very abstract but the underlying principle of it all is still to 'solve equations'.
So to simplify the whole thing Linear Algebra could be thought of as the study of Algorithms and Methods to solve linear equations over some algebraic structures such as \(R\)-Modules, Vectorspaces and Fields. As already mentioned by amistre, a good application of such structures can be cryptography (you can google for the underlying principle of homomorphism, also known as the universal property of homomorphisms) which provide already one fairly straight forward method of encryption.
Algebra is a whole different beast, if you found some of the informations I have given above helpful I might also write a passage about it. (Indeed, Algebra deals with solving equations too)