Studying Advanced Subjects Without Answers

[rxh140630]

How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?

 

[undefined314]

Eventually, there comes a time when one must become their own critic; perhaps by asking 'how do I know when I am right?' You will not always have a mentor to look over your shoulder and verify your work.

While it's nice and convenient for textbooks to offer selected answers, or even solution outlines, they are not necessary (though many provide sample exercises as they introduce the material).

 

[PeroK]

How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?

Once you progress to material that is at your limit of understanding it's very difficult with no support other than the textbooks and internet resources.

It's tough, I know.

 

[gleem]

You could work out the problems and submit them for review at PF. Show your work and approach to get feedback.

 

[haushofer]

Approach Ed Witten and make him like you enough to hand over his phone number.

 

[Vanadium 50]

To answer your question, one is supposed to take a class with a professor, other students, and maybe a few TAs. That's the supposition.

Now, it may be that for good and sound reasons one doesn't want to go down this path. That's fine, but one needs to realize that this isn't the intended path, and textbooks are intended to be used differently.

Also, and my experience with physics texts (but this is, after all Physics Forums) is that the solution-less problems are all of the form "show that". So the answer is there. The solution is not, but typically these are called "examples" and not "problems".

Finally, I think there needs to be some expectation management. Many people who want to self-study also want to whip their way through it (recall the "read it three times" thread). Usually it's the reverse - it takes longer to develop an understanding (if it happens at all) with self-study.

 

[Stephen Tashi]

Usually it's the reverse - it takes longer to develop an understanding (if it happens at all) with self-study.

I think a big reason for slowness is that a person who self-studies can become a prisoner of his personal concept of what understanding is. For example, a self-studier may wish to have an intuitive understanding or, more rarely, a completely rigorous understanding. In a course, material is explained by giving some mode understanding and that is usually sufficient to deal with the course. Students adapt their personal tastes about understanding to include methods they see other people using. They must broaden their concept of what understanding is.

By contrast a person studying alone may want to have everything explained in a certain way - for example, in a geometric or visual way. If he tries to read a textbook where the mode of explanation is different - for example, one that emphasizes symbolic manipulations - then he doesn't have the benefit of a teacher and classmates to show him the variety of ways in which things can be understood.

 

[rxh140630]

Once you progress to material that is at your limit of understanding it's very difficult with no support other than the textbooks and internet resources.

It's tough, I know.

I guess I will look at this positively instead of negatively.

 

[symbolipoint]

rxh140630,
Can you be specific about what topic subject, and what textbook? The responses you receive might be more clear.

 

[Leo Liu]

I think a big reason for slowness is that a person who self-studies can become a prisoner of his personal concept of what understanding is. For example, a self-studier may wish to have an intuitive understanding or, more rarely, a completely rigorous understanding. In a course, material is explained by giving some mode understanding and that is usually sufficient to deal with the course. Students adapt their personal tastes about understanding to include methods they see other people using. They must broaden their concept of what understanding is.

By contrast a person studying alone may want to have everything explained in a certain way - for example, in a geometric or visual way. If he tries to read a textbook where the mode of explanation is different - for example, one that emphasizes symbolic manipulations - then he doesn't have the benefit of a teacher and classmates to show him the variety of ways in which things can be understood.

I cannot agree more.
I didn't understand probability while taking a stat class in high school because the concepts seem quite counter-intuitive. I got 60ish on my first test and 70ish on my second test. I was worried about my grade so I asked a friend who did fairly well in my class to help me with it. He showed me his understanding of probability, and afterwards I got a low 90 on my midterm without spending too much time on the exam preparation.
As you can see, a helpful peer can even save one's grade.

 

[FactChecker]

How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?

How advanced? If you are talking about general undergraduate subjects, I am a big fan of Schaum's Outlines. They always have a lot of worked examples and exercises.

 

[rxh140630]

rxh140630,
Can you be specific about what topic subject, and what textbook? The responses you receive might be more clear.

I have no book in mind right now, I just remember when I was at my school's library I was flipping through some books, definitively advanced physics, stuff at a graduate level, and I remember there being no solutions. Was a bit discouraging.

 

[rxh140630]

I cannot agree more.
I didn't understand probability while taking a stat class in high school because the concepts seem quite counter-intuitive. I got 60ish on my first test and 70ish on my second test. I was worried about my grade so I asked a friend who did fairly well in my class to help me with it. He showed me his understanding of probability, and afterwards I got a low 90 on my midterm without spending too much time on the exam preparation.
As you can see, a helpful peer can even save one's grade.

Im interested in a truly deep understanding of all of the subjects that I'm studying, not meaning to apply that there isn't a correlation between the grade that you receive and understanding though.

How advanced? If you are talking about general undergraduate subjects, I am a big fan of Schaum's Outlines. They always have a lot of worked examples and exercises.

Graduate level math/physics.

 

[FactChecker]

Graduate level math/physics.

I think that you should look at the Schaum's Outline series. I used them to drill for the Ph.D. candidate acceptance tests. That being said, I just used the problems for drills, not the text for understanding, which I already had.

 

[Leo Liu]

not meaning to apply that there isn't a correlation between the grade that you receive and understanding though.

Can you explain what you meant by this?

 

[Infrared]

I want to second @undefined314's remarks. If you're studying an advanced subject that you're ready for, then you should be able to evaluate the correctness of your solutions on your own. Coming up with the solutions in the first place should be the hard part!

And if you're not able to solve the exercises, I don't think having access to solutions will help your understanding.

 

[hmmm27]

How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?

Over the decades I've seen/used/(and in one case, co-written) textbooks, designed for many different types of learning paradigms.

One of those paradigms there's a "Teacher's Edition", which - and this inspires no confidence in the educational system, whatsoever - contains the answers to all the exercises, that the student edition omits.

Another, some of the answers are in the back of the book, but not all. (can't recall, maybe just a random sampling, or omitting the "too easy" and "extra credit" ones)

 

[vanhees71]

Well, without "teacher solution books" the teachers are even more lost than the students. I had a high school teacher who claimed we had wrong answers in a test, but there were several of us having the same answer, which would be quite improbable if the answer were really wrong. Arguing with the teacher we calculated everything in great detail on the black board. After that she admitted that it sounds right, but she cannot tell with certainty. She had another answer to the question in her teacher's solution book! It ended up with asking another teacher at our school about his opinion, and it turned out we were right. So whenever you write a textbook at least provide correct answers to the teachers, because otherwise many may be lost!

 

[member 587159]

Well, without "teacher solution books" the teachers are even more lost than the students. I had a high school teacher who claimed we had wrong answers in a test, but there were several of us having the same answer, which would be quite improbable if the answer were really wrong. Arguing with the teacher we calculated everything in great detail on the black board. After that she admitted that it sounds right, but she cannot tell with certainty. She had another answer to the question in her teacher's solution book! It ended up with asking another teacher at our school about his opinion, and it turned out we were right. So whenever you write a textbook at least provide correct answers to the teachers, because otherwise many may be lost!

Sounds like a really bad high school teacher.

 

[Infrared]

@Math_QED I actually want to give the teacher some credit. When confronted with an issue she didn't understand, she admitted to the students that she wasn't sure, sought clarification from someone who knew, and then communicated her finding to her students. This seems to be exactly the right course of action (as opposed to pretending to know that she's right, etc.).

 

[member 587159]

@Math_QED I actually want to give the teacher some credit. When confronted with an issue she didn't understand, she admitted to the students that she wasn't sure, sought clarification from someone who knew, and then communicated her finding to her students. This seems to be exactly the right course of action (as opposed to pretending to know that she's right, etc.).

Yes, that's the right course of action but if you can't solve a problem without a book, why do you expect students can solve it without the book?

 

[Infrared]

She apparently thought that she understood the problem, and then realized she was mistaken. I'd forgive this as human error. I've had several professors assign problems with errors, and I certainly don't judge their teaching ability (or mathematical understanding) on it.

 

[FactChecker]

Many teachers are excellent teachers even if they can not answer all the questions. Some of the best teachers I ever saw were people that I never asked, or cared, whether they were excellent in the subject matter.

 

[Vanadium 50]

but there were several of us having the same answer, which would be quite improbable if the answer were really wrong.

You have never seen students do problems the same wrong way before? I suggest you give them a marble rolling down an inclined plane. A good number will solve it with conservation of energy, but will neglect rotational energy.

 

[Infrared]

@Vanadium 50 Even worse, I was TAing an analysis class a few years ago. The textbook is widely used and someone had posted solutions for its exercises online. One of the posted solutions had an error, and many students in my class reproduced the incorrect solution. I was pretty disheartened when I figured out what happened...

 

[member 587159]

She apparently thought that she understood the problem, and then realized she was mistaken. I'd forgive this as human error. I've had several professors assign problems with errors, and I certainly don't judge their teaching ability (or mathematical understanding) on it.

But if the students can solve it correctly, so should the teacher! I'm speaking high school here. At the university level I can imagine this happening.

 

[weirdoguy]

I'm speaking high school here.

Well, as a tutor I teach high-school students on a daily basis for 12 years now, and I got to say - it's not always that simple. I did my masters in "normal" physics not physics for teachers, so I was learning very advanced stuff all the time - and still do that. And I think that because of that I tend to overthink some of the exercises and sometimes my solutions are wrong. I'm known for complaining about how those exercises are often poorly worded and sometimes I have a really hard time to think like a high-school student. But most of the teachers in high-school don't do the advanced things so it should be easier for them.

 

[jtbell]

In the US, how many high-school physics teachers actually have a bachelor's degree in physics? How many of them were, say, chemistry and math majors who took a few physics courses and got certified to teach physics on that basis?

 

[vanhees71]

Sounds like a really bad high school teacher.

She was a night mare. She couldn't even demonstrate the solution of a linear system of equations with 2 variables...

 

[Vanadium 50]

In the US, how many high-school physics teachers actually have a bachelor's degree in physics?

43% of the teachers (and 47% of the classes, which is perhaps closer to what you want).
Time to split off this thread drift?