When did math test you the most?

How to learn math

A. Neuendorf - Student - (04/30/2002) This text is primarily aimed at those who are specifically preparing for an examination in linear algebra, such as the pre-diploma or the intermediate examination. Some of the advice also applies to doing math during the semester. The most important thing is to "stay on the ball", in particular by solving the exercises yourself and clearing up any ambiguities regarding the subject matter as soon as possible. Of course I can't go beyond that the Give a magic recipe for learning. Rather, I would like to give food for thought on how to deal with mathematics, based on my experiences.

Anyone who thinks about the learning phase with horror should be comforted. Learning can also be fun if you get involved and create suitable boundary conditions. In detail, I can make out the following points:
  1. Start learning early!
    Eight weeks and up is realistic for the linear algebra exam.
  2. Don't overdo it with your daily workload!
    I myself notice after two to three hours of uninterrupted, concentrated work at the writing desk, how my concentration is clearly decreasing. I find it pointless at this point to continue the learning process violently and with poor results. It's better to take a long break until your brain has recovered. In total, I get five to six hours of real learning a day. Anyone who sits at their desk for ten hours, but only really learns five of them, is wasting time unnecessarily and is only annoying themselves.
  3. If you start the learning phase in good time, you can take a day off in between to enjoy the other beautiful sides of life. The same applies to the daily rhythm and getting up. If you don't like to get up really early, you're definitely not doing yourself a favor by sitting at your desk at seven in the morning.
  4. It is important to use your working hours in a concentrated manner without being distracted. So turn off your computer, television, music, etc.
Prepared in this way by the external circumstances, one should still think about one's attitude towards learning.
First, you study voluntarily. You always have to remind yourself of this when, for example, you are watching envious walkers and cyclists on their way into the countryside, but you are sitting at your desk yourself. But it could also hit you worse: Who would instead like to camp outside with the Bundeswehr on a cold winter night or (even worse) do weapons drill?
Second, there seems to be a lot of hair-splitting, especially at the beginning of your studies. The more you know your stuff, the more sense things suddenly start to make. For example, if a vector was defined as a tuple of real numbers for school purposes, this definition is generally incorrect. If, for example, one considers the vector space of all functions from the real numbers to the real numbers, one certainly cannot write its elements as tuples of numbers.
  1. Work through the transcript of the lecture and look for (alleged) errors, i.e. those parts that you cannot explain to yourself directly!
  2. Why does it say something strange?
    Either you made a mistake or the lecturer himself, or in the case of a reshaping, e.g. several steps were carried out at the same time. The statement of a sentence not mentioned may also be included.
  3. Try to answer the questions yourself!
    Otherwise, write them down precisely and discuss them with fellow students or Prof. Dr. Schoenwaelder himself in the discussion hour or in his office hour. He proved to be very helpful and patient with me.
  4. If that is not enough for you or you have additional questions, consult the relevant literature. (Herr Schoenwaelder publishes a list of literature.)
    This promotes in particular the use of different spellings, which otherwise happens again and again with other lecturers during the course. In addition, another author often sees the same topic from a different point of view, which often leads to an "wow factor" and better understanding.
  5. Do the exercises, and not just in a way that is likely to score points. Copying may be kind of fun, but you don't learn anything, and you also get the practice points you need by doing the exercises yourself. Anyone who gets to the point where he is copying the solutions because he cannot work on the tasks to the satisfaction of the corrector himself has a serious problem: the exam is level with the exercises. So if you can't do the exercises, you have bad chances for the exam.
  6. Get involved with the task as such. For more advanced tasks, the solution is often that you can no longer use the usual procedures, but have to find another way yourself.
    Look for any further problems that may arise from the task! Often the places of particular interest are those that require additional requirements, for example if the denominator of a fraction could take on the value zero. At the latest if one does not encounter such situations in the context of a task to be submitted, one must be able to confidently recognize the problems. That is also what you have to learn here.
  7. Work cleanly!
    A clear formulation of the assertions, for example, speaks for the fact that one often suggests false statements with the help of careless expressions. This results in apparently proven sentences that are fundamentally false and from which any number of false claims can be inferred in further proofs.

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to the Faculty of Mathematics, Computer Science and Natural Sciences, to the RWTH.

-> On this page from U. Schoenwaelder, a student reports on his recommendations based on his own experience.