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I am a second year PhD student in probability from the UK. I enjoy what I do, but here is a problem:

as I dig deep into my study, I realize I have to read a lot of stuff I do not fully understand and they often arise in fields of study which are not probability, but related areas: e.g. PDE theory, functional analysis.

I have a basic understandings about some of these things, sometimes I might even feel I have enough to get by, but I am unsatisfied. This is perhaps due to the fact I never studied some of these topics as an undergraduate, but to be fair, no one told me an understanding of PDE theory is very useful to probability (I even think this only depends on what you do)

I do want to know more and previously I tried to attend multiple courses in a term to make up for some of this - this was not effective. Going to 1 or 2 courses a term is fine, but doing any more is a big drain of time if I want to fully understand the material lecture.

So have others experienced this? What is the best way of getting around this?

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I will share with you what happened to me a couple of years ago. I am from the field of software engineering (starting the 2nd year of my PhD). I was discussing the topic of "affects, emotions, and moods" with my supervisor. I told him "These stuff is obviously pretty serious in psychology research. There will be-I don't know-30k papers on these topics only. What should I do?" His response: "Well, you better g**damn start reading them". –  dgraziotin Jan 15 at 13:02
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What I try to do is read the papers "backwards". Let me explain. I don't go for the foundations and then read everything in the area, on the contrary I find a paper that (I'm sure) is interesting to me (probably very recent as well) and I backtrack through the citations and searching on the web for information until I can understand it. Therefore reading a paper takes very long and I don't get a wide knowledge, but it's deep and guaranteed to be necessary (to understand the first paper). This isn't perfect, but it's possible to survive like this. –  Trylks Jan 15 at 16:30
    
@Trylks I guess that it is a case of the snowballing technique. I once met a guy claiming that there is evidence that snowballing is as effective as database querying, once a topic has been identified. However, I have never seen any study on this. –  dgraziotin Jan 15 at 20:15
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@dgraziotin as I said, this isn't perfect. You point one limitation, which is the topic identification or identifying what is relevant for the state of the art (SOA). There is another limitation, you don't know what you don't know, and often understanding the SOA isn't enough to propose something that goes beyond it, it is often the case that you need a good understanding of a broader picture, but then you are in front of a vast ocean and your only hope (AFAIK) is having someone (e.g. a supervisor) that can tell you the direction to explore, so that you are not completely lost. IMHO. –  Trylks Jan 16 at 8:20
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@PiotrMigdal absolutely not. I read something like 100 papers. But this is mostly because it is part of my PhD central topic, and it was not part of my background (I need to read more because I tend to understand less). Another reason is that psychologists do not like to agree on definitions and theories :-) –  dgraziotin Jan 16 at 18:04
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up vote 17 down vote accepted

so have others experienced this?

Basically every smart person feels like that when starting their studies. The majority of the people for which this is not true are usually not the second coming of Terence Tao or Dr. Sheldon Cooper, but simply affected by the Dunning-Kruger Effect. You are not supposed to know everything, and in fact you never will. You already have a head start on your colleagues, who have simply not yet discovered (or wilfully ignore) that they do not fully comprehend many of the seminal papers in your or related fields. You, at least, can work on this in order to produce better research.

what is the best way of getting around this?

There is no getting around this. To paraphrase the title of your question, many things are to be learned. That's part of doing a PhD. The trick is to learn what you will really need for your research, and to not get lost in the things that are interesting but ultimately not relevant to you. This requires some experience. Hopefully, your advisor or a postdoc will put you on track of what to focus on for now.

As funny as the advice mentioned by @dgraziotin above sounds - in practice, what you really need to develop is a good mental filter to select the 15 or so papers from a 30k papers field that are really relevant to to you.

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the first part made me feel so much better... but there is still a lot to do. –  Lost1 Jan 15 at 14:55
    
Thank you, i think i can offer you something better than an accept - a populist badge, as a sign of gratitude. This is gaming the system, but i dont feel too bad about it –  Lost1 Jan 16 at 14:13
    
You have lost me here ... –  xLeitix Jan 16 at 14:36
    
i misread the description for populist badge, never mind :P –  Lost1 Jan 16 at 15:26
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Man... I have this problem on an hourly base. Here I will throw a bunch of "strategies" I have been accumulating for you to consider.

Sleep on it

Seriously. If I have to actually learn everything I think I should learn, I'd need to be live beyond 480 years old. And since the more you learn, the more you don't know... this route is not viable.

A lot of the times, I suppressed the impulse and slept on it. In the process I usually think about this questions:

  1. Do I need to learn this or do I want to learn this? Would the new knowledge make my work complete or make it better?
  2. Can the piece stand alone fine without it? Can it still contribute to the research questions I need to answer?
  3. Can I explain what I wouldn't learn as a potential extension/development in the Discussion section? Perhaps other people can work on it?

Usually after a couple rounds of iteration, I could ditch most of what I wanted to learn, and focus on learning the skills that would make my projects a complete project.

Keep a wish list

Be it a go or not, I always write that down whenever I thought I need to know something. I use EverNote to document all these strayed thoughts. And if I come across any relevant materials (review articles, short courses, software, etc,) I'll document them with the same tags.

Draw a skill tree

It also pays off to sit down and analysis what are your knowledge and skill sets. A skill tree is simply just a conceptual framework or mind map that links up your skills and domain knowledge. Some people may grow a big deep-rooted tree while some may favor a garden of little bit of everything. We need both types of people but generally I would consider in academia it is better to have a good big tree with some side bushes.

Now, you can focus on a few major branches, what are the domain knowledge? What are the skills associated with them? And what are the applications that are associated with each skill? I found it easier to start with my courses I have taken and the syllabi of those courses. You can also consider using some competencies published by professional organization as a blueprint.

For myself, my big tree is statistical analysis applied in biomedical studies. If someone asks me to work on a project about, say, psychometrics, which is part statistics part psychology... I may return to look at my trees and think if this new skill will make a logical branch, or it's too far off. And if it's too far off, is it worth to plant a new one for this? And what kind of root (aka basic courses or books) do I need to plant? Then decide if it's a go or not.

I found this exercise pretty useful because i) it's therapeutic, you may be amazed by your domain knowledge. And you're likely going to feel better about yourself. And ii) having a bird view network helps a lot on deciding the relevance of the desired skills.

Think return of investment

Before diving into the skill, think how much the skill can help you back. There are many sides to consider:

  1. Will it lead to higher competitiveness or salary?
  2. Will it complement/strengthen your skill tree? Would there be any synergy?
  3. Can you re-purpose or re-use this skill? How versatile it is?
  4. Will I be using this skill enough to rip the benefit of the time and resource I spent in the learn process? etc.

Return of investment exercise is best done when you have competing desired skills to learn. Put them side by side, design a rubric if you must, and evaluate which one is better to go for.

Gathering good resources is 80% of the game

Okay... after much thought, we decided to learn a skill. When learning a new skill the major problem is not knowing where to start. I usually perform this beginning rituals:

  1. Read up on Wikipedia or other encyclopedia to acquire general lingo.
  2. Read a couple relevant review articles.
  3. Schedule a meeting with a someones proficient in that skill/knowledge and ask for a few recommendations on i) text book, ii) journals, iii) controversies, and iv) prominent schools of thought and researchers in the field.
  4. Search for some syllabi that teach these knowledge and document their text books, software, course structure, etc. Those usually give you a good sense on what to cover.
  5. Gather all materials, and start working on it.

Immerse at least 20 hours into it with undivided attention

This is a slight modification of Kaufman's The First 20 Hours: How to Learn Anything... Fast!. The book itself is not super groundbreaking but Kaufman also pulled a stunt journalism and explained how he learned some new skills and brought them up to functional level in 20 hours. It's an entertaining read, but what I got away from it is the importance of preparation and immersion.

I usually spread my learning into many 90-minute chunk, and then make sure to enter these blocks first at the start of every week. I laid out what I need to learn, read, do exercises, watch videos, perform self-evaluation, talk to others (e.g. your committee members or other scholars)... It's actually pretty amazing looking at how I become a half-baked specialist in a matter of week.

In the learning process, I focus on learning the basics really well, and I write down a lot of questions (for me or my specialist friends to answer later.) I also try to figure out the flow the ideas and their connections. When working on a problem I don't insist of getting it right, but I do insist on getting why it's wrong.

Compose a self-learning syllabus every 6 months

Every semester I also compose a self-learning syllabus. Basically I design courses for myself. I started doing this last year because I was getting tired always having to catch up with tasks that require me to learn new skills. I wanted to turn the table: I am going to learn some skills that I chose, and I'll look for opportunities in the tasks that I can apply what I learn and enrich the contents. I feel that being even just very so slightly more proactive has injected a good sense of control into my life.

Closing remarks

I can't say I am a successful learner, but I am moving along bit by bit. Action, even just very little each time, is the most important ingredient. Hikers may know this feeling... all the hills look so darn tall, but once you stepped onto the trail, the scenery was great, the air was fresh, and suddenly you forgot to wonder how tall the hill was.

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If your question is:

How do I learn (quickly) all the material that I need in order to be proficient in my area

then Penguin_Knight's answer has some excellent suggestions.

If the question is also

How do I avoid feelings of despair and hopelessness when I think of how much I have to learn

then the trick is to change the premise. You're not acquiring knowledge in a Ph.D as if you're drinking from a (very large) cup that needs to be finished before you can move on.

Rather, you've been plonked down without preparation in the middle of a raging river, when all you've ever dealt with before are little rivulets that drip into a cup.

Accordingly, the goal here is not to try and "drink the river", but merely to observe little eddies and streams in the torrent and learn something about them. As you become more and more proficient, you'll see more and more of the river and you'll be able to manipulate it better, but you are never "in control" of the entire torrent.

I might be stretching this analogy further than it can go, but hopefully my point is coming through: that you shouldn't fall into the fallacy of having to learn "everything" in order to be a competent researcher. Rather, as Penguin_Knight says early on, you should think strategically about what you really need to learn and how you can pick up relevant skills based on what you're working on.

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One way to keep it in perspective is to realize that these feelings are only going to become more extreme as your career progresses, but they aren't actually a problem in themselves. Instead, once you get used to them, they can actually be a source of joy.

You're never going to catch up, because the amount you learn will grow at best linearly with time, while the amount of research you recognize to be relevant and important will grow rapidly (seemingly exponentially) as you learn more. You'll never be able to say "Well, now I've got a solid foundation in everything I need to know," because each topic you learn will naturally suggest two more. And the more you understand how deep and interconnected everything is, the more you will realize how limited your understanding actually is. Anyone who thinks they have the world all figured out is not a researcher.

As I see it, this is cause for celebration. The scope of your favorite subject is unbounded! In a few years, you will happily be using ideas you barely understand right now, or perhaps haven't even heard of yet. From a broad enough perspective, you have interests in common with researchers who superficially seem to be doing something utterly different. Why would you give up infinite possibilities in favor of a limited world?

I can sympathize with feeling overwhelmed. I remember sitting in a class thinking to myself "This is beautiful stuff, but I'm glad I won't need to use it myself, because that would be a lot to master in addition to my own research area," and then, a few years later, realizing to my horror that I did need to master it. It's not easy, but you shouldn't let that put you off. Research isn't easy for anyone. Famous mathematicians are also missing knowledge that would help them in their research, just like you are, so nobody can judge you or look down on you for your ignorance. Ultimately, we are all ignorant and struggling to become less so. Fortunately, what we learn is enough to justify the struggle.

As for concrete suggestions, the other answers have lots of useful information, especially the one by Penguin_Knight. One thing I'd emphasize is the importance of keeping at it over time, even if progress seems slow. It's easy to get depressed if you work intensely on something and have to give up when you can't sustain the time commitment. By contrast, slow but continual progress will really accumulate over time.

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You have 2 choices.

1) as a probability researcher, invent the infinite probabability drive and use this to increase the probability that you can instantly learn everything that will ever be known.

2) go back and read xLeitix's great answer.

http://hitchhikers.wikia.com/wiki/Infinite_Improbability_Drive

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