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How much is (upper div) linear algebra and algebra needed for an applied math?

  1. Aug 16, 2011 #1
    Hello, I'm doing a bit of course planning right now. I'm majoring in applied math, and I'm just wondering if upper division linear algebra and abstract algebra is needed to be competent as an applied mathematician (graduate school bound possibly)?

    Here are the course descriptions. Algebra is a 3 quarter sequence, while Linear Algebra is a 2 quarter sequence. Algebra I requires LA I as a prerequisite.

    110A. Algebra (4)
    Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 117. Ring of integers, integral domains, fields, polynomial domains, unique factorization. P/NP or letter grading.

    110B. Algebra (4)
    Lecture, three hours; discussion, one hour. Requisite: course 110A or 117. Groups, structure of finite groups. P/NP or letter grading

    110C. Algebra (4)
    Lecture, three hours; discussion, one hour. Requisites: courses 110A, 110B. Field extensions, Galois theory, applications to geometric constructions, and solvability by radicals.

    ---------------------------------

    115A. Linear Algebra (5)
    Lecture, three hours; discussion, two hours. Requisite: course 33A. Techniques of proof, abstract vector spaces, linear transformations, and matrices; determinants; inner product spaces; eigenvector theory. P/NP or letter grading.

    115B. Linear Algebra (4)
    Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading.

    ---------------------------------

    Note that the applied math major requires only 115A, and no algebra.

    But of course I would be willing to go over the requirements if that will help me. Any suggestions?
     
  2. jcsd
  3. Aug 16, 2011 #2
    You should at least take one semester of abstract algebra and a second semester of linear algebra (upper div LA). The abstract algebra would be good as an intro in knowing some basic things on the fundamentals of algebra (groups, homomorphisms, etc.). It's good to at least know what's out there, as well as knowing the basics for fields you aren't a specialist in. The upper div LA is quite necessary for applied math, especially if you want to delve into higher-level applied math (PDEs, ODEs, numerical methods, etc.).
     
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