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Courses University Mathematics Abstraction

  1. Apr 25, 2016 #1
    I'm currently a first year MathPhys student, and next year I have to decide my stream. I can pick a combination (pure) Mathematics, Applied & Computationtal. Mathematics, Statistics, MathSci, Physics, Theoretical Physics or Physics with Astronomy & Space. Naturally there are restrictions, and I have narrowed it down to

    - ACM, pure maths and stats. This will allow me to pursue any of these degrees, a joint honours between two of the subjects or MathSci.
    - ACM, TP and Physics. This will allow me to pursue one of the degrees.

    I found the physics modules very bland and unsubstantial this year, so am leaning towards picking the first choice. I am however struggling currently with abstraction. It was introduced at the end of Linear Algebra in the context of vector spaces etc. and currently I am taking Real Analysis which I find very challenging. I am worried if I proceed into a mathematics course the level of abstraction and my ability to deal with it will become overwhelming and I simply will not be able to cope. Despite it being challenging, I find aspects of analysis interesting, such as Cardinality for example.

    I think because I have never had to think in such a manner, there were no introduction abstraction or set courses and me not working hard enough this year has led me to this fear. Even if I had worked harder I still do not know if this would have allowed me to cross the conceptual gap over to the world of abstraction. I plan to spend some of the summer reviewing various aspects of analysis and abstract algebra with the aim of qeulling my fears, however I have to decide my subjects by July, so I am limited with time.

    Has anyone on the forums ever had similar experiences with abstraction or moreso University Mathematics in general? Any advice, suggestion or opinion would be most welcome; I am apprehensive to find some sort of potential solution to this problem.
    Last edited: Apr 25, 2016
  2. jcsd
  3. Apr 28, 2016 #2

    Stephen Tashi

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    Science Advisor

    One way to evaluate your talent for abstract mathematics is to observe how you do technical writing and speaking about non-mathematical subjects - something as simple (or complicated!) as directions for changing the oil in car. Do you write precisely? Can you take a legalistic and hair splitting approach to things ? Formulating thoughts in higher mathematics is done in English (or in whatever your native "common language" is). Some people never master technical writing. They expect to express mathematics in a sequence of "steps" that solve a problem.

    At the undergraduate level, most people begin by having or developing a good intuition about a mathematical topic (e.g. vectors). Then they superimpose a precise technical view of the subject over that intuition. So there is also the question of whether you can develop a good intuition for mathematical topics. I think that must be considered on a topic-by-topic basis.
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