# Problems with Self-Studying - Comments

• Insights
MathematicalPhysicist
Gold Member

As for reading the books for the parts relevant for me it seems reasonable but then I assume I would be redirected to previous chapters, so I prefer to be the ant here from Zeidler's volume 1 quote:"
We may distinguish between the ants, who read page n before reading page
(n + 1), and the grashoppers who skim and skip until something of interest
appears and only then attempt to trace its logical ancestry. For the sake of the
grashoppers, herewith is a listing of certain basics.
"
Never understood the Grasshoppers, what a headache is to trace the logical ancestry of something and you're never sure if you haven't missed something important,
not that I say you couldn't try reading a book from where you want if you know the other results that are covered in the previous pages.

I don't think it would be a waste to read and try solving all the problems, it would be time consuming but I want to gain a good grasp of the theory.

That said I have returned to Munkres' Topology book, and it would seem I'll need to use the Grasshopper method, I believe it takes more time than the ants plain method.

Anyway, haven't we all returned to something we learned a few years ago just to notice that we forgot how to prove it, for this case it's good to reread the proofs and do the exercises.

Anyway this is a habbit I have since my first two logic books i learned from in high school years ago, to read them cover to cover and solving every exercise.

Isaac0427
Gold Member
I must say, as a self-studier, I have ran into all problems listed (except number 5, I could truly never seem to get bored). Great article, however I wonder if there could be a set of ways to avoid all these problems.

A. Neumaier
2019 Award
I don't think it would be a waste to read and try solving all the problems, it would be time consuming but I want to gain a good grasp of the theory.
You can do this only with one of the extremely rare books without any errors in it, or you'll stall indefinitely trying to prove wrong things.

The right method is to be a hybrid of ant and grasshopper, and to know when and where to switch from one mode to the other.

Last edited:
blue_leaf77
Homework Helper
Completely agree with point 2), in self-studying abstract math, one occasionally needs to stop and muse what he/she just learned all mean. Abstract math as the name implies can sometimes be so abstract that no everyday events can be taken as an analogy. Definitions needs to be memorized (as it is all that can be done with definitions) in order to aid learner in doing proofs.

Homework Helper
Gold Member
One goal in learning is to make the learning an adventure. It can help to have an instructor or a mentor. Learning isn't always an adventure-sometimes it is a lot of toil and work, but if the self-study is an adventure at least some of the time, then it would seem the person is having at least some degree of success.

I enjoyed this insight article - and found a lot of encouragement in it. I just started "Category Theory for The Sciences" by Spivak. The first chapter almost stopped me in my tracks because it was so freakin dry dry dry... I just can't memorize abstract rules of maximal precision without connection to something... but now that he is introducing types, aspects and ologs it is easier going and I feel more hopeful it is going to be an exciting book.

Gold Member
Last edited by a moderator:
ProfuselyQuarky
Gold Member
I have ran into all problems listed (except number 5, I could truly never seem to get bored).
For me, it's predominantly the second one: I go too quickly thinking that I understand only to realize that I don't really understand a couple of pages later when new material is added. Aaah, so frustrating sometimes.... you then have to go back and unwind all the progress that you *think* you made. But that's learning for you.

Isaac0427
IGU
You can do this only with one of the extremely rare books without any errors in it, or you'll stall indefinitely trying to prove wrong things.
I think that one of the hallmarks of the effective self-studier is the self-confidence to decide that the book is wrong. It's actually pretty common that there are mistakes, so this is an essential skill. Then you figure out what the problem was supposed to be and what the real solution is. Or not. But yes, getting stuck is to be avoided.

Isaac0427
Gold Member
For me, it's predominantly the second one: I go too quickly thinking that I understand only to realize that I don't really understand a couple of pages later when new material is added. Aaah, so frustrating sometimes.... you then have to go back and unwind all the progress that you *think* you made. But that's learning for you.
2 is a big one for me too. 3 and 4 also get me a lot, especially when seeing how long lectures are. 1 is a little less but I do wish I could get questions answered without going through 20 articles or going on here (asking too much on here makes me feel a little stupid).

ProfuselyQuarky
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

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?

Isaac0427
Gold Member
Why don't you find somebody to help/tutor you?
I'd love to, but I have no contacts.

Thank's for sharing your experiences, it has massive value for us who are struggling with self studies in math!

fluidistic
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.

RooksAndBooks
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.

jasonRF
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
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.

jason

IGU
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.

mathwonk
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!

Last edited:
Saph and IGU
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?

mathwonk