Problems with Self-Studying - Comments

  • #36
Gold Member
(asking too much on here makes me feel a little stupid)
A teacher one day said (when half the class missed an assignment because they didn't understand):
Only stupid people are afraid to ask questions. What idiots!
He was pretty upset, or perhaps disappointed in the class. Of course I'm calling you neither, but just something to think about :smile:
  • #37
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
but I do wish I could get questions answered without going through 20 articles or going on here

Why don't you find somebody to help/tutor you?
  • #38
micromass submitted a new PF Insights post

Problems with Self-Studying


Continue reading the Original PF Insights Post.

Great article with many good insights; I wish more people here were as patient and generous helping others as you.
  • #40
Thank's for sharing your experiences, it has massive value for us who are struggling with self studies in math!
  • #41
Gold Member
I'm a bit late to the party. My question is "Do you have any success story Micromass?". I mean by that student(s) who really learned a lot and had a good academic start or so.
  • #42
Gold Member
That was a good article that I thought was mostly relevant to me. I do read textbooks on my own and some of the points are relevant to me; points one and five weren't as relevant to me.

I understand the feeling of it being easier to read a fiction book than a math book. I don't read 1 thousand pages of a fiction book before I read five pages of a math book, however.
  • #43
Science Advisor
Gold Member
Great insight. 4 and 5 have been the most prevalent for me, especially when I try to work through an entire book. I have only been successful working through the majority or more of a book a handful of times - the things they tend to have in common are
1. Book is at the right level
2. Book is concise - it covers most of what I want and not a lot of extra material I don't care about (Axler's Linear Algebra Done Right is good example of a concise book).
3. I was fundamentally interested in the subject - I wasn't learning a topic to simply prepare me for something I was more interested in
4. book was adequately engaging.
Finding the right book has been key for me. One killer has been setting artificial goals, such as doing half or more of the problems in each chapter; when I do this I find that I don't spend my time very wisely.

Most of my self-studying is more focused. Sometimes it is just a chapter or two in a book to get a better understanding of a topic of current interest; or more often the standard research problem of seeing a result quoted in a paper that I don't understand or want to understand more fully, so I look up the references and/or books (or just try to work out on my own) until I am satisfied.

  • #44
I'm a bit late to the party. My question is "Do you have any success story Micromass?". I mean by that student(s) who really learned a lot and had a good academic start or so.
I'll offer my son as an example. He self-studied starting in 8th grade when I pulled him out of public school in California. After five years of studying only math (much self-study, plus auditing (mostly graduate) classes at local universities) he went to Cambridge. He is now about to start his third and final year. His knowledge and understanding of mathematics was and is well beyond his fellow undergraduates.

Of course this early in his life it is hard to say whether he is going to be a real success story of any sort. We shall see whether he stays interested in mathematics and where his interests lead him. But his foundation of self-study is great for being independent and self-motivated, and I am very pleased that he seems to care about the math way more than the grades he gets. I am guessing at this point that he will choose to go to grad school.

By the way, I think his two (or four) favorite books for self-study were Tom Apostol's Calculus (Volumes I & II), and Nathan Jacobson's Basic Algebra (I & II). His approach has always been to read everything and do every problem (although he would skip many exercises). He likes his math dry and rigorous.
  • #45
I'm a bit late to the party. My question is "Do you have any success story Micromass?". I mean by that student(s) who really learned a lot and had a good academic start or so.

I have a success story, but it's not the one you're expecting. :)

Success in this context means a lot of different things to different people. Folks of a variety of ages are here self studying and for a lot of different reasons. I've read posts from retirees, all the way down to twenty somethings and teens.

Myself, I'm in my 40s, my kids are all in high school/university and my career trajectory is basically ballistic now. I started self-study late last year and have been slowly plugging away ever since. What got me going was how helping my kids with their math and physics homework reminded me just how much I enjoyed all this stuff as an engineering student, many years ago.

Lacking background in physics to even know what questions to ask, initially my goals were quite vague. I started out wanting to understand special and general relativity and to make sense of what the Higgs boson really was. I remember the insane pace of my degree program, having ~= no life and how I used to joke, only half seriously, that true understanding and intuition of any given course came only mid-way through the follow-on course!! So this time I wanted to take my time and understand what I'm learning, deep in my bones, every step of the way.

micromass (what a great guy!!!) in combination from a lot of reading on these forums, was kind enough to help me get started. I thought I did quite a lot of math during my degree but one of the first questions micromass asked was if the math I had done was computational only. I had to stop for a minute to even understand his question! You mean there's more than one kind?? :) So, it's been almost a year now, on his recommendation, I've been working through a text on math proofs and started reading about real analysis (advanced, axiomatic calculus). Also, from a less rigorous perspective, I've brushed up on enough calculus 1 and 2 (which came back fairly quickly, kind of like riding a bicycle actually) to get about 1/4 of the way through the problems in Morin's classical mechanics book. Also, I'm about 1/3 through introductory linear algebra. (I highly recommend to other self studiers having several subjects on the go at the same time. A beauty of self study is that when I start getting bored of one subject, I can just switch to something else. I don't have to worry about an exam in 2 days. :D)

But wow - it's slow going and it's easy to feel like my goals are infinitely far away. As is common for people who don't know much about a subject, I grossly underestimated how vast these subjects were and how long they would take to learn. It reminds me of being back in high school, excited for aerospace engineering and imagining myself single handedly designing the next moon lander, not realizing the less glamorous and highly specialized reality!

The time I'm able to spend on this has been wildly inconsistent. Some weeks I manage only an hour or two. A lot of days I come home pretty brain dead from my day job and the best I can do is surf physicsforums for an hour. So I can completely relate to the things micromass' has posted about being things you have to stay strong in the face of.

I suspect those who are interested mainly in the pay off and less in the intellectual journey are the ones who struggle most. I imagine it's like learning music. Once you can play, there are rich rewards such as learning new songs, composing or performing. But it can be a tough slog getting to that point and if you aren't able to appreciate the little rewards along the way, knowing that the big rewards may be a long time coming then you might not make it through all the practicing of scales and increasingly complex versions of Mary Had a Little Lamb.

That said, like music, this hobby is one that doesn't have an "end" - there'll always be something new to learn. And I do love the little eureka moments, and those moments where I make a connection between two topics I've been learning about.

Anyways, I'm still happily chugging along. For my personal self study effort, this is what success looks like.

p.s. I loved the goals that andrewkirk set for himself earlier in this thread. Paraphrasing:
  • understand the derivation of Newton's gravitational law as an approximation of Einstein's general relativity equations.
  • understand the derivation of the equations that describe a hydrogen atom and its electron orbitals.
  • understand the proof of the Jordan Curve Theorem.
  • understand the proof of Godel's Incompleteness Theorem.
Seeing these has made me realize that it's time to take my initial vaguely formulated goals and be more specific!
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Likes Saph and IGU
  • #46
Hi. Inexperienced self-studying student here. I know it's very commonly repeated that you can't force yourself to absorb some topic all at once, but I was wondering if you could feasibly get through a book on a topic like analysis with 2 months of time "on average." And by that, I mean something like working through four different subjects concurrently over the course of 8 months or so. Is this any different from working through each subject one at a time, spending two months on each? I'm thinking extending the study allows you to digest it better even if you spend the same amount of time at the desk, but I don't see much information about it. Can anyone compare the two different setups?
  • #49
Science Advisor
Homework Helper
@mathemasochist: how long to spend on a book depends on how densely it is written and that reflects often how expert is the author. I am a professional algebraic geometer and have owned a copy of David Mumford's (fields medalist) red book Introduction to algebraic geometry for 50 years, perusing it from time to time over that period. Now I have been reading it carefully, in retirement, for about a year, and am less than half way through, in trying to actually understand everything I read. So even though I already "know" much of it I am spending about 2 years on this one book, and gladly so. of course i also do the yardwork. oh now i see you are long gone.

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