- #1

EmSeeSquared

- 29

- 1

So I'm going to have my first exposure to linear algebra and I've completed Calc 1 and 2.

I've seen Axler and Shilov numerous times and I'm having a hard time choosing it.

Here's my syllabus for my Linear Algebra Course.

Matrices, Gauss reduction, invertibility. Vector spaces, linear independence, spans, bases, row space, column space, null space. Linear maps. Eigenvectors and eigenvalues with applications. Inner product spaces, orthogonality.

For Linear Algebra which one would be best suited for my syllabus? Axler or Shilov. The order in which the content is represented does not matter to me since I'm planning to self learn the whole thing before the classes start in 3-4 months. :)

Now After Linear Algebra, I will have an Introductory Algebra course. The syllabus is below(Please suggest some good books on it as well):

Further linear algebra: equivalence relations, the quotient of a vector space, the homomorphism theorem for vector spaces, direct sums, projections, nilpotent linear transformations, invariant subspaces, change of basis, the minimum polynomial of a linear transformation, unique factorization for polynomials, the primary decomposition theorem, the Cayley-Hamilton theorem, diagonalization. Group theory: subgroups, cosets, Lagrange's theorem, normal subgroups, quotients, homomorphisms of groups, abelian groups, cyclic groups, symmetric groups, dihedral groups, group actions, Caley's Theorem, Sylow's Theorems. Ring theory: rings, subrings, ideals, quotients, homomorphisms of rings, commutative rings with identity, integral domains, the ring of integers modulo n, polynomial rings, Euclidean domains, unique factorization domains. Field theory: subfields, constructions, finite fields, vector spaces over finite fields.

Thanks