Study habits for math

Study habits for math

What are some study tips from a Statistics scholarship winner? Part 3 on prerequisite courses.

(g) Material from prerequisite courses. With regard to material from previous courses, I don't really take any time before the start of a course to review the prerequisite material, but do actively refer to notes/textbooks on those topics throughout the term, especially in the beginning, to help with the current course. Based on my experience there are usually only a few things from a previous course that are heavily used, and by going back to the notes on those topics in the beginning of the term, I usually find it to be quite manageable. Sometimes the same concepts are taught in a different perspective, and I think it's important to build that connection between the different interpretations.

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What are some study tips from a Statistics scholarship winner? Part 2 on exam preparation.

(d) Review notes: before each midterm and final exam, I always read the slides and textbook, and make a set of review notes. This includes key concepts, important derivations, and simple examples. I find myself understanding the material much better after writing the important things down neatly. I put more emphasis on things that I am confused about and refer to this set of notes through my exam prep period.
(e) Questions: while I make my review notes, I write down any questions that I come up with beside the corresponding section of the notes. After the notes are completed, I come back to these questions and see if I can answer them having gone through all of the materials covered.
(f) Exam and homework problems: I always keep all of my returned midterms and homework sets. I think it’s important to look back at the problems I have done after a while. For the questions I got wrong, I analyze what caused the mistakes and make sure I understand the concept so that I can avoid making the same mistakes again. For the questions I got right, they can serve as a good refresher to the concepts that might not have been touched on for a while.

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What are some study tips from a Statistics scholarship winner? Part 1 on lectures.

(a) Pre-reading: I try to go through the pre-readings for the next class a day in advance. I don’t necessarily aim to understand everything, but rather get familiar with the material. I find the lectures to be much easier to follow this way.
(b) Formulas: I always derive the formulas and equations introduced in the class at least once, in a way that I am most comfortable with, which might take a different form than the ones introduced in class. This for the most part saves me from memorizing them and ensures understanding of the material.
(c) Note taking in class: I don’t think it’s enough to just listen in a lecture, no matter how focused I am. A lot of the times, it is not the things on the slides, but rather the professor’s explanations to what’s on the slides that help me understand the material. I write these things down in class, as quite often, these things are not documented in any of the materials provided for the class.

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What are tips that might help in preparing for exams in statistics and mathematics?

(a) Achieve in practice. Remember that, in the end, it is necessary to answer questions by yourself without any help. Prepare for that by learning the material and developing your skills. Keep trying. If you're working through practice questions and get one wrong, keep coming back to it and similar questions until you can do them yourself. Reading someone else's solution, or getting help from another person, can give insights and helpful pointers to things that need work, but that's only part of what's needed. Like swimming or cycling, mathematics is something that you do. It is tough to learn how by reading about it or watching someone else. When you have learned the concepts, and accumulated a lot of experience using them through regular practice, you'll have confidence in your abilities. Keep your goals in focus.

(b) Start early. Begin thinking about assignments the day you get them. It takes time to think about the questions and how the different methods you know might apply. Start studying for tests at least four or five days beforehand. This will give you lots of time to fill in any blanks in your understanding.

(c) Always start with things you can do. Look over all of the questions on every assignment or test and pick the low-hanging fruit first. Build on success.

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What are some good study habits for mathematics and statistics?

Advice from a document at the Department of Mathematics and Statistics, University of Victoria. Compiled by Gary MacGillivray.

(a) Be responsible for your own learning. Know your own learning style and use it in studying. Don't give up on concepts you don't understand. It is never too late. Mathematics is logical and cumulative. The more material from previous courses and from earlier in current courses that you understand, the better equipped you are to understand what comes next, connect it to other material, and apply it in different contexts.

(b) Get out a pencil and paper, and try to work through every step of each example or proof rather than trying to read your text or notes like a novel. If you get stuck, don't give up.

(c) Understanding beats memorizing. If you understand, then you'll remember. Unfortunately, it doesn't work the other way around. The first step in grasping a definition or theorem is being able to write it down, precisely, without any help. Trying to apply concepts when you're struggling to remember what the words mean is a tough battle. Be kind to yourself. Learn the vocabulary and the methods.

(d) Learn from your mistakes. If you make a mistake, try to understand what went sideways, and then take steps to improve your understanding of that. Keep going until you're atisfied that you really understand. Go over returned class work and try to take advantage of the feedback you've been given. It will help you identify concepts or techniques that need more attention. Do the same with practice questions.

(e) Get help right away. When you're having trouble with something, go for help on the same day if possible, and don't wait longer than the next day that help is available.

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What variety of courses are useful to prepare for a statistical career?

Advice from AmStat News, in an interview with Greg Campbell, biostatistician in the US Federal Government.
Most biostatistical jobs require at least a Master's degree on statistics or biostatistics, so one is well-advised to take lots of courses. I personally adhere to the philosophy that good applied statisticians need a solid mathematical underpinning. This will enable one to be undaunted in picking up a journal article with formulas in it or to innovate if the problem does not quite fit the textbook example. So, my other advice is to take a variety of coursework in order to expand your toolbox. And, of course, education need not end at the university; it can be a lifelong passion.

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