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Need calculus and several books as a prerequisite for Machine Learning

  1. Jan 5, 2013 #1
    Hey!

    Happy New Year 2013 to all of you!

    I am in good mood for learning something new so I need advice.

    I'm currently watching the videos for Machine learning from Stanford University, but I'm stuck at Lagrangian multipliers and duality.

    I got solid background in Calculus I and II (I read and learned from the book by Irl Bivens and I really like it) but I've never learned about Lagrange multipliers nor Matrix Calculus, and now it's time to step my Calculus up :smile:

    Also I got solid basic background in Linear Algebra but never learned about Eigenvalues and Eigenvectors or Semidefinite Matrices.

    So I need some book for self-studying:

    Here are the topics that are new to me:

    Matrix Calculus 20
    4.1 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
    4.2 The Hessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
    4.3 Gradients and Hessians of Quadratic and Linear Functions . . . . . . . . . . 23
    4.4 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
    4.5 Gradients of the Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . 25
    4.6 Eigenvalues as Optimization

    3.10 The Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
    3.11 Quadratic Forms and Positive Semidefinite Matrices . . . . . . . . . . . . . . 17
    3.12 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 18
    3.13 Eigenvalues and Eigenvectors of Symmetric Matrices . . . . . . . . . . . . . 19

    Convex Optimization
    Convex Optimization Part 2

    Here are the materials from the course (there are documents in Section Notes).

    Thanks a lot.

    Regards.
     
  2. jcsd
  3. Jan 6, 2013 #2

    jasonRF

    User Avatar
    Science Advisor
    Gold Member

    I would first look at free books online.

    FOr calculus, including Hessians and basic optimization, one nice option is the book by Kenneth Kuttler to be found at:
    http://www.e-booksdirectory.com/listing.php?category=4

    Other books in this category may fit the bill for Hessians as well, so browse around and see what works for you. This book also covers eigenvectors and such.

    Other linear algebra references can be found:
    http://www.e-booksdirectory.com/listing.php?category=538
    I like the books by Heffron listed there (you can buy a hardcopy via amazon for <$20 US), as well as the book "linear algebra done wrong" by Treil (which is harder than Heffron).

    Again, browse around. Good luck!

    jason
     
  4. Jan 9, 2013 #3
    Thanks a lot for the help, I have never heard about e-booksdirectory.com it's pretty cool site for free e-books.

    I've found courses from Stanford on Youtube about Convex Optimization and some applied linear algebra.

    Regards.
     
  5. Jan 11, 2013 #4
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