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I am trying to self-study a graduate-level physics book that was recommended to me, but it doesn't have any exercises. Also, it's a specific enough topic to where I can't really find any other textbooks that cover all of the same topics. What are some good ways to learn this book besides just reading it?

Update: this is the book. I do have some colleagues in condensed matter generally, but none in this specific field.

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    Are you studying alone (self-learning) or are there others you can work with? FWIW, I find this an immensely difficult question to answer. I remember trying to learn Fortran from a textbook and making all sorts of intuition errors about the meanings of things. (Long ago and far away). It had exercises, but I had no way to execute the code.
    – Buffy
    Nov 10, 2021 at 21:34
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    Mod's Note: Please understand that the asker is about to earn a PhD in physics, and the book is a highly technical, graduate-level book. Answers proposing basic study strategies are not responsive and may be removed. Please avoid writing answers in the comments.
    – cag51
    Nov 13, 2021 at 7:41
  • When I was in grad school, we would be so happy when the professor assigned a Dover book as the class text. Dover sells prints of older textbooks that have fallen out of copyright and so cost about $20 a pop. It's never bad to have different authors' take on the subject, especially when it comes to graduate level topics. I don't think it would be too hard to find a Dover book that has useful problems to work.
    – David Elm
    Nov 13, 2021 at 18:05

10 Answers 10

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(I'm in mathematics...) My advice is to not think in terms of "exercises", in the traditional sense of posing some sort of "challenge" which can allegedly be "responded to" using the ideas of the preceding chapter. :)

Rather, I strongly think that it's better to think in terms of "examples" ... of the phenomena discussed, not only in the "chapter" or other body of material at hand, but also phenomena that may not fit exactly into a limited range that is perfectly addressed by just one particular method/idea.

In my own little world, I've often found it extremely illuminating to try to conceive of the simplest-possible version of a general issue, on the principle that if a "trivial" (in math-style talk) version is not solvable or comprehensible, the fancier versions are ridiculously out-of-reach. Further, in the kind of math I do, there are often no alternative understandings for relatively fancy things, so it's hard to do sanity checks... while for "trivial" (math-talk, again) examples, there can be alternative viewpoints that do provide sanity checks.

And, from a teaching viewpoint, beyond a certain point it's really hard to compose exercises that are do-able without considerable run-up beyond "theory". That is, again, examples.

And, seriously, the intellectual model that exercises "are a thing" is a bit odd. :)

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    What is your last sentence supposed to mean? Exercises are a bad idea? It is very hard to understand.
    – toby544
    Nov 12, 2021 at 14:36
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    @toby544, I mean that thinking of a subject and one's knowledge of it in terms of exercises is a strange approach. Breaking something into tiny pieces and randomly fooling around with those pieces, as a supposed way to understand the whole? Nov 12, 2021 at 15:48
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    "Breaking something into tiny pieces and randomly fooling around with those pieces, as a supposed way to understand the whole?" --- well, yes, exactly, how else would one learn a new piece of mathematics? Nov 13, 2021 at 18:21
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    @JohnPardon, well, it is often very difficult to guess the purpose or intended function of a small idea if one does not see how it interacts, or is intended to interact, with other things. What are the goals? Often many small details are most easily explained with hindsight, in my experience. That kind of thing. Nov 13, 2021 at 18:25
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I've found that writing up detailed notes on a topic I've been reading about is invaluable for exposing what I do and do not understand about a topic. It also sometimes has the side benefit of letting me come back to something more quickly after I've been away from it.

For this to work, these must be topic notes, using your own organization of the topic informed by what you read, not notes on a particular item you're reading. If you find that the organization of your notes directly parallels that of a book or paper, you're not doing it right and will likely come out little better than if you'd just taken a highlighter to the document you were reading.

(Another warning sign may be being able to write the notes very quickly for a topic, unless you already feel qualified to teach that topic. For complex topics that are new to me I typically spend at least twice as long writing and reworking the notes as I do reading the source material. This time may include devising and performing small experiments or simulations to help me confirm that certain things I've written down are correct.)

It's of course hard to give concrete advice on how to build an organizational structure for your notes; doing this is similar to sketching an outline for a textbook. (That this is difficult is exactly why the technique works.) If you're having difficulty getting away from the organization imposed by the particular document you're reading, it may help to find a couple of other documents that have at least some coverage of the same area, sketch out the organization of all three (or more), and then combine and change those until you come up with a new organization for your own notes that subsumes all the information from all three documents. What you should eventually find is that, despite coming from different sections of the source documents, these separate but related pieces of information end up together, illuminating each other, in your notes.

I certainly don't have any examples from chemistry, and it's hard to say how well examples from other fields will work for you given that they have to be fairly technical and moderately deep in order to actually to demonstrate the process. But in case it helps, you can have a look at my notes on analogue video as an example. The information here comes from at least twenty different sources and most or all of the sources from which deep details came were specific to a particular video format (NTSC, PAL, RGB, etc.). I had to identify the "high-level" commonalities between all of these and then come up with new sections for each of these, integrating the information from various parts of the source documents.

For example, all the video formats have logically separate display and synchronization information, and the synchronization signals are always logically separate horizontal and vertical signals. However, some formats transfer horizontal and vertical sync over separate wires, others combine the two, and the sources for the latter often discuss the combined version as just the "sync" signal, without really going much (if at all) into the logical separation between the two. In my organization I have separate sections for horizontal and vertical sync containing all information I have about each (whether the information came from a separate sync or combined sync source), and yet another section describing how the two are combined (and any implications of that).

I don't know how much that helps, but perhaps you can at least take away the idea that taking apart source information and putting it back together in a different way is the key to this technique.

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Invent your own exercises sparked by what you've read, then try to solve them. When you read something, try to ask yourself what it's good for. What can you do with this that you wouldn't be able to do before? Can you demonstrate it? I'm not a chemist so I can't answer in your domain but if it were in mine in computer science and I was perhaps reading about a new algorithm, I might try to code it and see if I could make it work.

Think of it as if you were going teach this material in a class where you can't just assign problems out of the book, you need to create projects and write your own exam questions. You would just dive in and do your best to create some interesting problems.

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    Maybe, but it is often harder to come up with decent exercises than with the text itself. A start, anyway.
    – Buffy
    Nov 10, 2021 at 21:15
  • Only slightly different is to try to write an exam based on the chapter /paper etc. Especially if you include a range of Bloom's Taxonomy type questions eg 1. Define x, 2. Contrast y and z conditions, 3. Evaluate the effect of changing a, B, c criteria. Specifically aim to capture any premises of the chapter /paper, the boundaries of the field (where this effect does /does not apply) Nov 11, 2021 at 9:03
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    @CiaranHaines, yes, but a sort of hyper-analytical approach to things can lead to the kind of over-analysis of acquired intuition, so that it becomes impossible to walk, because it's simply toooo complicated. :) Nov 12, 2021 at 23:16
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    +1 I feel like at the graduate level, one should definitely be able to write their own exercises, although the words “example” (used in another answer), or “thought experiment” might be closer to the mark than “exercise”. If the text presents formulae, invent or find real world numbers to plug in and see how things change. Build a computer simulation of concepts described in the text. And so on. Part of the joy of teaching oneself is learning how to teach and learn. Nov 13, 2021 at 3:35
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Setting your own exercise (as already mentioned) is a good method.

Also consider more generally the Feynman technique: https://en.wikipedia.org/wiki/Feynman_Technique

In order to truly master a topic, you need to be able to teach it. So try and produce your own teaching materials, such as a summary, a diagram, an exercise, etc.

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One question would be what level of a student are you, and why are you reading this particular book? Based on an earlier question you've asked, you appear to be an experienced undergraduate or a beginning graduate student. So, what are you expecting/expected to learn from it? Further, how are you accustomed to learning?

Since the book does not provide exercises, I can well believe that the book is not a textbook, but rather a monograph ("a detailed written study of a single specialized subject or an aspect of it"). Not surprisingly, one uses a monograph differently from a textbook, and undergraduates rarely encounter monographs as a learning tool. So, you are correct to wonder just how to deal with it.

I would argue that monographs are written for researchers and are approached very differently than an undergraduate would approach a textbook. For an undergraduate class, the textbook is, in essence, the stuff you need to learn, and then demonstrate on an exam, and is written (mostly) by experts in how to teach the material to undergraduates. The exercises are the practice to help you learn the material and learn how to do the questions that will be on the test.

By contrast, the monograph is a whole bunch of detailed information presented by an expert in the field to present it all in one place to somebody new to the field but interested in becoming expert. There is no expectation that, by reading the book through once, you are suddenly an expert. There is no exam at the end of the ‘class’. Instead, the monograph is useful in several different ways, some of which only emerge over time.

So, how do I generally approach a monograph? Remember, I’m not an expert (yet), but am interested in the subject matter, likely because I see a need to understand it for my own research path. Maybe I will end up diving really deep, maybe not. First step is to look over the organization of the book – what does it actually cover, what order does it go in, are there technical (journal) references readily available in the text or as end notes. This step is to evaluate the relevance, and sometimes I don’t proceed from there. Now, in your case, the book was recommended to you, and if by your advisor the ‘recommendation’ is more than a suggestion.

Next, I read the first chapter. Often this is an overview of what the monograph covers, and I may have already skimmed it in my first step. But this is the time to pay a bit more attention. Is there jargon I don’t know, is the point of the monograph detailed, is the subject of the monograph placed in context of the field?

Assuming the first chapter is an overview, it is time to start into the meat of the monograph. But, I’m not reading for all the gory detail, but I’m also not just skimming it. What does the chapter cover, do I get the general idea, am I totally stumped? If totally stumped, then it is time to put the book down and go find a textbook with more basic stuff in it to review. If I’m getting the general idea, great, but may still choose to skip over more detailed parts for now. If that chapter goes well, I continue onward as long as things seem OK and interesting.

At the end of reading, I am not an expert. I do now know the areas that the monograph covers, and where in the book they are covered. Maybe I’ve looked up a few of the papers in the references. Maybe a section or two has really caught my eye as being directly applicable, and those I’ve probably read more carefully already. Am I done now? Perhaps, but it is time to evaluate what the next steps are, based on why I’m reading the book in the first place. Do I need to read more background material? Do I want to go and talk with somebody to clarify something? Did something really catch my eye? Evaluate where you are and what to do next.

Sometimes the book goes on my shelf and is not touched again. Sometimes it migrates to my desk since I keep referring to a specific section in it. Sometimes it gets pulled down a read through again, more thoroughly. It all depends on what your specific need is for the information.

This is, in the end, not all that different from how I approach journal articles. Something catches my eye and I download it. I’ll skim the abstract and the intro, glance at the experimental section and the figures, skim the final section. Often that is all and the paper gets filed away in case I need more info. Sometimes it gets read more carefully, sometimes I look up some references, sometimes I discard the paper.

Ultimately, as you transition to graduate work and research, you start learning differently. You start evaluating for yourself what you need to know, and how deeply. Frankly, it starts being a lot more fun. Good luck.

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Many textbooks come with examples of implementations of the concepts covered, for example a dynamics textbook will likely show a step by step derivation of the dynamics of a double pendulum. My suggestion is to try and follow those steps and replicate the examples on whatever platform is suitable (for dynamics you could use matlab, mathematica or python, or even pen and paper!)

You can then check your output against what the textbook shows and see if it matches.

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Once, I took a graduate-level physics course, in which the book had no exercises, and literally what the professor did was to stand at the front of the room and read the book to us. To this day I'm unsure why I went to class (he wasn't interested enough to take attendance). There were just mid-term and final exams to determine our grade (I forget whether I got an A or B).

What I found really helpful was, after learning a chapter, to go back and start at the beginning. Usually, you understand the beginning of the chapter very differently after you have learned the whole thing.

Also, as others mentioned, it's very helpful to make notes that summarize the topics in a way different from how the book organizes them. Though, in a pinch, even summarizing the way the book organizes it has value. If you're interested in remembering it, writing your notes works better than typing them. (I later took graduate courses in Science Education that explained why.) By all means, feel free to type them after writing them; that's probably even better than just writing.

Here's an interesting idea: once you've studied (not just read) a chapter, look at the Wikipedia entry for that topic, and see if there's some way you can improve it. That's maybe a more modern version of the Feynman method. Even if you can't improve it, looking for a way to improve it is a good exercise.

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  • Wow, my sympathies for that terrible class you endured... Pathetic for a prof to be so disinterested, and also immoral/unethical to so-disserve students. Nov 12, 2021 at 2:08
  • @paulgarrett - Yeah, I would have expected better at an Ivy-league university, if not for hearing worse stories from my friend who went to Harvard. (He was there for 3 years before he even had a class taught by a professor.)
    – Jeffiekins
    Feb 3 at 0:08
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I'm confused. You read the book. You try to understand what is written. You look at the new material and find analogies to what you already know and make note of what is new.

I must say that I nearly never did any exercises that were not assigned (in either undergrad or graduate school, both in Chemical Engineering). Relying on examples and exercises is really not how I learn. I respect that we have different learning styles, but reading and understanding is key to formulating the view you you end up having of a subject. It's the same whether you are reading a book or reading a paper.

I once took an entire graduate class that included exactly two examples in class; and the second one started with the prof saying "Consider a system in N-Space". It was a class on State Space Control Systems (from the department of Electrical Engineering - hint to others: never take a graduate level Electrical Engineering class without ever having taken any other Electrical Engineering classes before). I was very proud of that B.

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Make your own exercises. Your physics textbook doesn't have them, but it probably has examples? Exercises is just more examples. Change some or all of the parameters, do the math.

A physics book may have one example of a ball rolling down an inclined plane. To make an exercise, change the angle and height of the plane. Consider a ball of different weight, consider doing this on the moon where the gravity is weaker. If the physics is advanced enough to include friction/drag, then change the friction coefficient too. Find out how long time various balls takes to roll down different planes.

Similar for all other problems. They provide one example, your exercise is to work out examples with different numbers. If the book doesn't give examples at all, make your own. Make up problems so you get to use each and every formula a few times.

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  • And after the OP has made said exercises, they can publish their own handbook of exercises on the subject matter that may be useful to others.
    – user32966
    Nov 13, 2021 at 18:23
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When I was in grad school, we would be so happy when the professor assigned a Dover book as the class text. Dover sells prints of older textbooks that have fallen out of copyright and so cost about $20 a pop.

It's never bad to have different authors' take on the subject, especially when it comes to graduate level topics.

Looking at their selection, it looks like the Goodstein book might be a good choice.

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