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Help relearning mathematics.

  1. Sep 18, 2011 #1
    I am, then, to begin an undergraduate course in Mathematics (Philosophy and Mathematics, precisely) and I am in need of some help.

    It's been over two years since I last studied maths in school, and so I would like counsel as to what you consider would be sensible revising. I understand that my course touches mainly on Linear Algebra and Calculus ; what should I be looking at , any particular tips to get me on my feet , good sources for learning and studying alike , which subjects should I peruse ?

    Thank you .

  2. jcsd
  3. Sep 18, 2011 #2

    Stephen Tashi

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    You aren't making it clear whether your are taking one undergraduate course (presumably titled "Mathematics And Philosophy") or whether you are undertaking a course of study, such as double major in Mathematics And Philosophy.
  4. Sep 18, 2011 #3
    I will be studying an undergraduate course, for a Joint-Honours degree in Philosophy and Mathematics.
  5. Sep 18, 2011 #4

    Stephen Tashi

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    Do you have a specific description of the course? - a syllabus?

    I can visualize one type of course that would study the general concepts of mathematics and emphasize the history of mathematics. I can visualize another type of course that would make heavy use of symbolic logic (a topic often taught in the Philosophy department).
  6. Sep 18, 2011 #5
    Introduction to Linear Algebra (using the book 'Linear Algebra, A Modern Introduction' by David Poole):

    - Complex Numbers (Appendix C) (3)
    - Vectors and geometry (4)
    - Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence. (6)
    - Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank. (8)
    - Eigenvalues and eigenvectors. Determinants (6)
    - Orthogonality, Gram-Schmidt, orthogonal diagonalisation. (5)
    - Introduction to abstract vector spaces and subspaces. (4)
    - Selected applications (taught in sequence where appropriate) (4)


    Calculus and its applications (using 'Calculus' by James Stewart):

    1. Understanding of the ideas of limits and continuity and an ability to calculate with them and apply them.
    2. Improved facility in algebraic manipulation.
    3. Fluency in differentiation.
    4. Fluency in integration using standard methods, including the ability to find an appropriate method for a given integral.
    5. Facility in applying Calculus to problems including curve-sketching, areas and volumes.
    6. Understanding the ideas of infinite series including Taylor approximations.
    7. Understanding the ideas of differential equations and facility in solving simple standard examples.
  7. Sep 18, 2011 #6

    Stephen Tashi

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    To me, it looks like you're taking Linear Algebra and Calculus. I don't see where the Philosophy comes in. You said you studied mathematics two years ago, but you didn't say if you have previously studied Linear Algebra and Calculus. How long do you have to prepare for this course? (The syllabus could be interpreted as 3 semesters of courses.)
  8. Sep 18, 2011 #7
    Sorry , I did not give you the details on the Philosophy subjects —which are separate— because I did not need advice for those.

    Last edited: Sep 18, 2011
  9. Sep 18, 2011 #8

    Stephen Tashi

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    The topics from philosophy would be relevant if they are taught in the same course. The would not be relevant if taught in a different course.

    I suggest you study the books that are to be used in the course. Don't linger over the first chapters. Try to work a few problems from the middle chapters of the book if you have studied the material before (a fact you have not yet revealed). Get some coaching about how to write clearly.

    If you want more advice, ask your question again in the forum section:

    Physics Forums > Science Education > Academic Guidance

    and you'll get more advice than you can follow. Include the results of this cross examination in your post.
  10. Sep 18, 2011 #9


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    An alternative to this is to use the report button to request that this thread be moved there.

    If your goal is to pass the exam, you should ask your professor, not us. If your goal is to understand stuff, I suggest that you spend a lot of time studying proofs of theorems, and less time on how to calculate stuff. In linear algebra, I think one of the most important details is the relationship between linear operators and matrices (post #3 in this thread). I find it very strange that people who show up here after taking a linear algebra class don't know this, or even that the definition of matrix multiplication is [itex](AB)_{ij}=\sum_k A_{ik}B_{kj}[/itex]. In calculus, I find it more rewarding to know the proofs of e.g. the fundamental theorem of calculus, the rules for derivatives (product rule, chain rule, etc.), and the fact that the series that defines the exponential function is convergent, than to know how to do difficult integrals.
  11. Sep 18, 2011 #10
    I teach Calculus and I can tell you that you will need a good foundation in Algebra and Trigonometry to succeed in Calculus as most of the problems are only half Calculus. The rest is Math from previous years. Scan the internet and find "cheat sheets" for Algebra and Trig that summarize what you should know and then go to www.purplemath.com to the lesson index and learn what you need to know.

    As for Linear Algebra, you need to brush up on vectors and matrices. Check out my website for my Summary Sheets on Vectors and Matrices at www.scribd.com/pfreda. To download you will need a Facebook Acct or signup at scribd.com with an email address.

    Good Luck
  12. Sep 18, 2011 #11
    Thank you very much for your help ! I am not looking to merely pass the exams but to truly understand.

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