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Recently I have started Tutoring First Year University Mathematics 2, as opposed to Mathematics 1, at a local Hall of Residence at my University. As I am being paid quite a bit, I would love to get some tips on what to do, what not to do, and some common tricks of the trade so that I can be a better maths tutor. The topics that the students are covering in their course are the following;

Calculus:

  • Sequences and Series (Geometric, P-series, taylor, etc)
  • A bit more tricky integration (still single variable though.)
  • Some differential equations

Algebra:

  • A bit more advanced,but still rather basic, vector algebra.
  • Solving Systems of linear equations using Matrices.
  • Finding the inverse of matrices bigger than 2x2.
  • Linear transformations
  • basic counting principles.

This mathematics course is also not very formal yet as it is more of an advanced introduction to more complicated mathematics.

My "class", if you will, is quite small, only three students. My students are also quite bright, they ask deeper questions such as "Why can we express all differentiable functions as a taylor series", or "what are the implications of matrix multiplication being non-commutative".

I am sorry if this question is a duplicate, but I can't seem to find a similar question dealing with Uni level maths tutoring.

My exact job as a tutor for this Hall of Residence is just to be there to answer any questions that the student's might have. Close to tests or the exam period at the end of semester I will also be there to give them tips on how to answer the exam and maybe fill in some of the necessary gaps in there knowledge to help them do well in the course.

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    $\begingroup$ Can you add a description of your job, what you are supposed to do? Are you there to provide extra content for interested students? Do you have weekly topics or exercises you are supposed to discuss and teach? How strongly are you bound to the curriculum of the class, e.g. are you supposed to only repeat what they did in the lecture or can you do whatever you want? Depending on these points, what to do might differ quite a bit. $\endgroup$ – Dirk Aug 2 '17 at 10:15
  • $\begingroup$ Suggestion: use a book that covers the material and has also hints for advanced explorations. $\endgroup$ – Miguel Aug 2 '17 at 14:36
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    $\begingroup$ A quick comment -- not all infinitely-differentiable functions can be expressed as Taylor series -- or rather, the Taylor series are not guaranteed to converge at all. en.wikipedia.org/wiki/Non-analytic_smooth_function $\endgroup$ – Opal E Aug 2 '17 at 21:46
  • $\begingroup$ Yeah I get that Opal, I was just quoting the question directly. But thanks for the comment anyways. $\endgroup$ – Jandré Snyman Aug 2 '17 at 22:12
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Here's a simple tip: ask questions!

Ask questions that lead them to the answer. The student will more likely learn something than had you just given them the answer (unless it's exam time and you're tutoring hordes of students). I used this approach when I tutored back in university and still use it now, years later, as a professor.

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