Perhaps this belongs better in the career guidance forum (in which case, please move it moderator) but I thought it would be more specific to this forum.(adsbygoogle = window.adsbygoogle || []).push({});

I'm planning to study physics at the university level sometime in the future. My plan is to work on the first year math credits first, to build a solid foundation. Perhaps part-time.

With that said, I'm forced to confront "Algebra I" vs "Linear Algebra I". By the names I would assume (yeah, bad idea) that Linear Algebra I is just a subset of Algebra I (but much more specific and indepth for that area).

There are a few streams of calculus at UofToronto. There is the lower Calculus I/II, then the practical Calculus!/Multivariable Calculus and finally the theoretical approach with Analysis I/Analysis II.

Analysis II requires Algebra I (the alternative streams require none). The rest of the second, third and fourth year math courses will accept either Algebra I/II or Linear Algebra I/II in the prerequisites if it is there.

So, as someone who is far removed from these, perhaps someone may enlighten me as to which I should take. Or should I aim to complete both?

Course descriptions from UofT:

Linear Algebra I

Matrix arithmetic and linear systems. Rn: subspaces, linear independence, bases, dimension; column spaces, null spaces, rank and dimension formula. Orthogonality orthonormal sets, Gram-Schmidt orthogonalization process; least square approximation. Linear transformations Rn->Rm. The determinant, classical adjoint, Cramer's Rule. Eigenvalues, eigenvectors, eigenspaces,

diagonalization. Function spaces and application to a system of linear differential equations.

Algebra I

A theoretical approach to: vector spaces over arbitrary fields including C,Zp. Subspaces, bases and dimension. Linear transformations, matrices, change of basis, similarity, determinants. Polynomials over a field (including unique factorization, resultants). Eigenvalues, eigenvectors, characteristic polynomial, diagonalization. Minimal polynomial, Cayley-Hamilton theorem.

I'm hoping someone can tell me if the Linear Algebra is inclusive in the Algebra stream, too.

Like I said above--I've no clue what most of this is and therefore don't know how pertinent it is to my future career (both academic and real world). Any help by you Master Jedis is appreciated by this young padawan :D

cheers

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# Algebra I vs Linear Algebra I

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