How to Study Mathematics - Comments

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    Mathematics Study
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Discussion Overview

The discussion revolves around strategies for studying mathematics, with participants sharing insights, personal experiences, and suggestions for resources. The scope includes theoretical approaches, practical tips, and specific topics of interest such as probability and statistics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Several participants express appreciation for the insights shared, noting their usefulness in self-study.
  • One participant mentions the challenge of retaining information from video lectures, emphasizing the need for repetition.
  • A participant shares their background in Electrical Engineering and expresses a growing interest in probability and statistics, seeking recommendations for study resources.
  • Another participant suggests an online statistics site as a valuable resource, while also recommending a specific textbook for statistics.
  • There is a discussion on the relationship between understanding proofs and solving exercises, with differing opinions on the order of study.
  • One participant reflects on the usefulness of the tips for their past experience as an instructor.

Areas of Agreement / Disagreement

Participants generally agree on the value of the tips shared, but there are differing views on whether one should be familiar with proofs before attempting exercises, indicating a lack of consensus on this aspect.

Contextual Notes

Some participants express uncertainty about their mathematical backgrounds and the applicability of certain resources, highlighting the varying levels of familiarity with concepts like Z-scores and statistics.

Who May Find This Useful

This discussion may be useful for individuals interested in improving their mathematics study techniques, particularly those engaged in self-study or seeking resources in probability and statistics.

micromass
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micromass submitted a new PF Insights post

How to Study Mathematics

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Continue reading the Original PF Insights Post.
 
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Superb write-up and gave me some excellent tips. Thanks.
 
RJLiberator said:
Superb write-up and gave me some excellent tips. Thanks.

Thanks a lot! :oops: If you're interested in me writing about other specific topics, let me know!
 
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Thanks very much. Lovely Insight and terribly useful too! Now to go apply this stuff!
 
very helpful indeed :)
 
Wow, what an unexpected topic, yet very useful. I imagine that most of us who self study do so without any advice at all. Thank you.

I am a fan of Leonard Susskind's video lectures on physics. But I note, that after viewing all 160 lectures, I have trouble remembering what was said in the earliest ones; so I repeat them all over and over again. Very enjoyable. But in one of the very first lectures, Susskind identifies his target students; very senior technical people who are in a big hurry to understand concepts in the little time remaining to them. That describes me very well. :-) I don't need the maturity in learning.
 
Thank you so much :)
 
micromass said:
RJLiberator said:
Superb write-up and gave me some excellent tips. Thanks.

Thanks a lot! :oops: If you're interested in me writing about other specific topics, let me know!
Perhaps probability and statistics? I am becoming very interested!
 
ElijahRockers said:
Perhaps probability and statistics? I am becoming very interested!

OK, I will write on that. But perhaps I can already give a quick recommendation to you already? What is your math background?
 
  • #10
micromass said:
OK, I will write on that. But perhaps I can already give a quick recommendation to you already? What is your math background?

B.S. Electrical Engineering, focused on DSP. I have taken a couple courses in probability, but nothing in statistics. I am familiar with Markov chains, and Kalman filtering for example, but not in Z-score. (I have only heard the term). Probability is more interesting to me than statistics, but statistics is becoming more and more required for my work.

(by the way you participated in a thread I created about p-values very recently, thank you for your input)
 
  • #11
ElijahRockers said:
B.S. Electrical Engineering, focused on DSP. I have taken a couple courses in probability, but nothing in statistics. I am familiar with Markov chains, and Kalman filtering for example, but not in Z-score. (I have only heard the term). Probability is more interesting to me than statistics, but statistics is becoming more and more required for my work.

(by the way you participated in a thread I created about p-values very recently, thank you for your input)

OK, then you might want to have a look at this online statistics site: http://www.math.uah.edu/stat/ It is basically an online textbook on probability and statistics and one of the best resources I have ever encountered. There are many helpful data sets and simulations. A possible downside: it is quite mathematical in nature, in the sense that everything is derived rigorously from its beginning. This makes the text long and perhaps difficult.

As an (easier) alternative, consider Wasserman's "All of statistics". It contains a surprising amount of information on statistics and it is all explained very well.
 
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  • #12
Nice post. But shouldn't one be familiar with the proofs before solving the exercises?
 
  • #13
Sure, but in my opinion, struggling with the exercises before reading the proofs motivates the proofs a lot. You won't be able to solve most exercises without reading the chapter in detail, but that is not the point. The point is to try and become familiar with the problems. Then the proofs and theorems will look way more useful and motivated.
 
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  • #14
I sure wished I had these hints and kinks when I was an instructor. Very good indeed!Regards,
ES
 
  • #16
Thank you very much.
 

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