Tips for Success in Undergraduate Math Courses (2002)
I&#x27;m a math major.<p>This list reads like my strategy to do well in a math class without learning the material (literally; this method got me through numerical methods and advanced calculus, both classes that I had no interest in and took only to satisfy the degree requirements).<p>My thoughts on the particular points:<p>&gt;Keep a list of THINGS TO MEMORIZE.<p>If this list is anything but empty you should feel bad. &quot;Memorizing&quot; something in math is a way to act (and test) like you understand it without understanding it. The one exception is in computationally heavy classes, where you memorize the completed solution of common forms. However, if your goal is to understand the material, you should be able to derive everything you are memorizing without thinking. The memorization is only to save you time on the exam by skipping the computation. Having said that, as I mentioned above, if you do not understand something but still want a good grade; memorize it. The professor will never see the difference.<p>&gt;Watch for example problems.<p>Because these will be the problems on the test.<p>&gt;Know how to do every homework problem assigned!<p>Yes. Also, know how the book&#x2F;teacher wants you to do the problem. It is often times hard to write a problem that can only be solved one way, so it is sometimes possible to avoid using a method you don&#x27;t like or understand.<p>&gt; Start the homework at least a few days before it is due.<p>Yes. Also, if possible, consider homework due at the last office hours before it is actually due. Otherwise, you can&#x27;t go to office hours for help.<p>&gt;Keep a running list of HARD PROBLEMS.<p>Good advise if you are going the memorization route; otherwise, this is just memorizing the solution to a particular form of questions. Also, in my experience, if you are going for the understanding route, this list just does not stay relevant long enough to justify keeping it.<p>&gt;When you get your homework back: Look over the things you got wrong.<p>Always good advice. Having said that, if you got a problem wrong (for reasons other than computational&#x2F;algebraic mistakes), the bigger issue is that you thought you got it right. This means that you not only did not know how to solve the problem, but that you have misunderstood some concept that you need to learn.<p>&gt;Find a quiet place, set a timer for the amount of time you&#x27;ll have in the exam, and take the practice test. Don&#x27;t look at the practice test before you do this.<p>Good test prep advice in general.<p>&gt;If a problem is hard, skip it and come back later.<p>I triage problems much more aggressively. If a problem looks time consuming I skip it. If a problem looks like it involves thinking, I do enough work to verify that it actually involves thinking then skip it.<p>&gt;Do a quick check of each problem to be sure your solution is reasonable. E.g. if the problem asks for a distance, is your solution positive?<p>Do this check after you finished the test. If you got something wrong, but didn&#x27;t finish the test, then knowing you got it wrong doesn&#x27;t help; you still didn&#x27;t have a chance to correct it. Also, you are more likely to notice an incorrect answer after spending time away from the problem.<p>Having said that, sometimes you answer &quot;feels&quot; wrong as you are solving it. If this happens and you see where you went wrong, correct it. Otherwise, complete the incorrect solution (if feasible), and mark it. This gives you the chance for partial credit; and sometimes your feeling is just wrong, and the answer is weird.<p>&gt;Write SOMETHING on every problem. The grader really wants to be able to give you some partial credit.<p>If you have time. If you really have no idea how to approach a problem, then your time would be better spent doing better on the rest of the exam instead of producing a plausible looking solution. Mark these problems, and, if you have time at the end, come back and look at them again.<p>Having said that, this is still good advice. If you think you know how to solve part of the problem; do it. If the part you know how to do requires you having computed something that you do not know how to compute, then clearly write &quot;let a = thing I can&#x27;t compute&quot;. Graders don&#x27;t have time to look closely at your answer; make it easy for them to give you partial credit.<p>If you are answering a proof based question, and cannot figure out how to prove a particular fact that you need for your proof, consider writing &quot;it is clear that&quot;. You will be amazed how often this works.<p>&gt;When you&#x27;ve tried everything, go back to the problems worth the most points first.<p>Triage. Go back to the problems that you think you got wrong and can improve first.<p>&gt;Given time, double check your algebra carefully!<p>If possible, verify your answers using a different method. For example, if you are asked to find the integral, verify your answer by taking its derivative. You are less likely to make the same mistake, and for many problems it is easier to verify an answer is correct then to find the answer<p>&gt;After the Exam<p>Write down what you can remember about the problems you could not solve (including ones where you put down something that might be correct, but were not sure about). Solve these problems (using book&#x2F;notes&#x2F;TAs&#x2F;etc if needed).<p>When you get the exam back, compare it to the list of problems you knew you didn&#x27;t get. You don&#x27;t care about these problems at this point; you already knew you missed them and worked through them. You learn nothing new by the grader telling you that you missed these.<p>The problems that you did not know you got wrong are where you should focus your attention. If you just forgot about them, then work through them like you did the ones you already knew about. If it was a computational&#x2F;algebraic error, don&#x27;t worry about it (but do do more practice if these errors cost you a significant amount of points). Pay special attention to problems that you thought you got right but didn&#x27;t. These highlight the areas where you have a misunderstanding of the material.<p>Final remarks:<p>HARD PROBLEMS list:<p>As you might have noticed, I don&#x27;t like this. What I do like is a concepts list. When you go to study, read through the list and make sure you understand all the concepts. It should be small enough that there is no point in creating a separate list for hard concepts; and what you consider to be an easy&#x2F;hard concept will change as you get more practice with some things, and never see other things between the first month of class and the final.<p>Studying for the test:<p>As you probably noticed, my opinion is that many of these points are techniques to study for the test. This is a valid thing to do in school (after all, you are graded on the test, not understanding), but be aware when this is what you are doing. If you plan on taking another class that builds on this one, then this method will come back to bite you then.<p>In class notes:<p>Do not make them. The only reason you should be writing during a math lecture is to use the paper as a scratchpad to think about what is being said. Anything else is a distraction from the lesson. All the material should be in the book. If it isn&#x27;t, you can ask the professor for a copy of his notes. If you want your own notes (which can be a good idea), write them after class. If you do take notes, keep them in a separate notebook. Interspersing them with problems and scratchpads just makes it more difficult to use them.<p>LaTex:<p>If you are taking math as a gen-ed requirement, ignore this. If you are going into a math heavy field, learn LaTex as early as possible. Write you notes in LaTex. Do your proof based homework in LaTex. This will pay off down the road, when you A) know LaTex and B) have a digital record of you previous math classes. Plus, turning in proofs written in LaTex make them feel far more correct, so you might get graded easier.<p>Study groups:<p>Form a study group of people with similar skills as you. If you try studying with people far better than you, then you will end up just having them give you the answer; in which case you are better off talking to a TA (who is probably better at explaining things). In a study group, you want  to be part of finding the answer. Along the same note, if part of your group just gets the answer (and you are in the part that does not), start by talking with the other people who do not know the answer. That way you can figure it out together, instead of just being told what the answer is.