Should examples be looked at before solving problems?

[Manny46]

So, with introductory level Physics, say Mechanics (Halliday's book or Kleppner and Kolenkow), am I making a mistake by looking at examples after reading, and understanding theory before trying to solve exercise problems?
How does this change with advanced undergraduate level/beginning graduate level?
The reason I'm asking this question is, because everyone says solve more and more problems if you want to get better at Problem Solving, and Physics in general. Does graduate level books contain examples or one has to build it with his own intuition from scratch?

 

[jedishrfu]

Looking at solved problems/examples is a good way to learn best practices at solving a problem. My strategy was read he chapter/section then do the problems and refer back to the solved problems when I got stuck. I would also check my answers in the back of the book if available.

Sometimes profs only assign even problems with no answers in the back so then you need to do the odd problems too to test your skills and so you'll have an answer to compare against.

Also don't forget that often books get it wrong and that you should search for an ERRATA sheet for that version of the book so you know what mistakes got caught and fixed in the newest edition. I'd markup your chapter with the fixes too so you don't get tripped up in the future. Also do your markup in pencil not highlighter in case you mess up or for future reference (you'll learn to hate overly marked up text).

 

[Manny46]

Looking at solved problems/examples is a good way to learn best practices at solving a problem. My strategy was read he chapter/section then do the problems and refer back to the solved problems when I got stuck. I would also check my answers in the back of the book if available.

Sometimes profs only assign even problems with no answers in the back so then you need to do the odd problems too to test your skills and so you'll have an answer to compare against.

Also don't forget that often books get it wrong and that you should search for an ERRATA sheet for that version of the book so you know what mistakes got caught and fixed in the newest edition. I'd markup your chapter with the fixes too so you don't get tripped up in the future. Also do your markup in pencil not highlighter in case you mess up or for future reference (you'll learn to hate overly marked up text).

Gotcha. How you deal with this at upper undergraduate/beginning graduate where there's hardly any solved problem (examples) if at all there's one?

 

[mpresic3]

I cannot say for sure whether it is a good practice to examine the example problems in the chapter. I strongly lean towards studying the problems before doing the problems. Higher undergraduate and graduate courses and texts tend to have fewer example problems for each concept, but they never disappear completely. The book Jackson treats example problems, as does the book Goldstein, Classical Mechanics. I believe the same is true for Landau/Lif.

The preface of the textbook generally introduces the author's strategy in presenting the material. In general, many times the author is relying on example problems to flesh out ideas in the textbook. You probably do not want to miss out on these ideas. In addition, I have found textbooks where I was able to do all the problems at the end of the chapter, and then when I examined the example problem, I learned a different technique. For example, I could solve the circuit problems using node-voltage, but skipped the section on mesh-currents. I later reviewed what I missed. I still prefer the method I learned first, but I see the mesh-current method is also useful.

By the way, almost everyone will say problems get harder as you go up through grad level. I found just the opposite. From High school to junior year, the "delta" in problem solving between high school problems and freshman sophomore problems, is greater than junior to graduate, or graduate to research. I found the problems in the first two years required several methods (kind of like solving difficult integrals in second semester calculus). Junior /Senior and graduate seem to be more "methodical" problems, and less "turn of mind" problems. However, this may due to training my mind to do physics problems for several years as my schooling progressed, so the "turn of mind" looked "methodical". I found the first two years undergrad were the hardest when it came to problem solving.

 

[symbolipoint]

So, with introductory level Physics, say Mechanics (Halliday's book or Kleppner and Kolenkow), am I making a mistake by looking at examples after reading, and understanding theory before trying to solve exercise problems?
How does this change with advanced undergraduate level/beginning graduate level?
The reason I'm asking this question is, because everyone says solve more and more problems if you want to get better at Problem Solving, and Physics in general. Does graduate level books contain examples or one has to build it with his own intuition from scratch?

I can say something about your first part but not much on your second part.

In studying the "introductory" stuff, you should read and reread the pages or sections, and do any and all example problems either as they come, or after you have done enough reading on that few pages or that section. Meaning, work with the example problems within a textbook section as you come to them in the reading&studying process. Once most or all of the assigned section you have finished reading, then START the homework exercises which you were assigned and pick any other homework exercises you like regardless of being assigned. Reread textbook as necessary.

 

[Manny46]

I cannot say for sure whether it is a good practice to examine the example problems in the chapter. I strongly lean towards studying the problems before doing the problems.

The preface of the textbook generally introduces the author's strategy in presenting the material. In general, many times the author is relying on example problems to flesh out ideas in the textbook. You probably do not want to miss out on these ideas. In addition, I have found textbooks where I was able to do all the problems at the end of the chapter, and then when I examined the example problem, I learned a different technique.

What do you mean by studying problem? Does that mean looking at examples and then jumping onto problems?

 

[Manny46]

@mpresic3 and @symbolipoint thanks

 

[Manny46]

@symbolipoint @mpresic3 @jedishrfu So, I think from all your suggestions, I should read the section, read the chapter and in between if there comes an example problem (usually solved ones), I should see if can solve them after reading the concept/section and if within 30 minutes I'm not then I should see the example line by line not completely. After finishing example problems I should move to exercise problems and there should be no 30 minute cap. Just invest appropriate effort and time and strive to solve it ultimately. Would that be a correct approach?

 

[symbolipoint]

@symbolipoint @mpresic3 @jedishrfu So, I think from all your suggestions, I should read the section, read the chapter and in between if there comes an example problem (usually solved ones), I should see if can solve them after reading the concept/section and if within 30 minutes I'm not then I should see the example line by line not completely. After finishing example problems I should move to exercise problems and there should be no 30 minute cap. Just invest appropriate effort and time and strive to solve it ultimately. Would that be a correct approach?

What you express does not make clear that you know what was meant. The examples within the textbook section are included to help you; and these should be used along with your reading of the textbook sections, before you start the end-of-chapter exercises.

A very broad but not specific example description:
You are reading first couple of sections of a chapter. You reread some of it a time or two. You find an example problem, already presented and solved in the book, right there. Read it and try to solve it as far as you can. How did your solution compare with what is shown in the book? If you missed some, try looking at some or most of the example problem's solution as shown in the book in the section. When you are ready and feel comfortable, move on to continue reading after the example problem. Come you to another example problem in the textbook section? If you are ready, try to solve this one on your own.

 

[Manny46]

A very broad but not specific example description:
You are reading first couple of sections of a chapter. You reread some of it a time or two. You find an example problem, already presented and solved in the book, right there. Read it and try to solve it as far as you can. How did your solution compare with what is shown in the book? If you missed some, try looking at some or most of the example problem's solution as shown in the book in the section. When you are ready and feel comfortable, move on to continue reading after the example problem. Come you to another example problem in the textbook section? If you are ready, try to solve this one on your own.

But that's what I said earlier that I should read/reread the section, read the example question, try to solve it on my own and if I missed something then I should take a look at solution (step by step, taking clues from them). Read the next section, repeat the process, and then solve the exercise problems. Isn't that the same thing I said?
Thanks

 

[symbolipoint]

But that's what I said earlier that I should read/reread the section, read the example question, try to solve it on my own and if I missed something then I should take a look at solution (step by step, taking clues from them). Read the next section, repeat the process, and then solve the exercise problems. Isn't that the same thing I said?
Thanks

I do not know. You at least know what to do now.

 

[Manny46]

I do not know. You at least know what to do now.

Thanks for giving some perspective. I apologize if I was being too naive or unbearable.

 

[mpresic3]

I misread your earliest post and thought you meant you skipped the examples entirely and went right to the exercises in the back of the book.

I think your program to work on doing the example problems is good but very ambitious.

What I did, (and it looks like you propose to do more) is try to follow the logic and even follow the calculation in the example, as I read the text. I did not try to "predict" the steps in the example and I do not think I ever spent your 30 minutes on an example. Most examples, were more transparent, and easy to follow.
Many generations of students complain the worked examples are often easier than the problems at the end of the chapter. I tend to agree I often worked more than 30 minutes on a problem, but not an example in the text.

 

[Manny46]

I misread your earliest post and thought you meant you skipped the examples entirely and went right to the exercises in the back of the book.

I think your program to work on doing the example problems is good but very ambitious.

What I did, (and it looks like you propose to do more) is try to follow the logic and even follow the calculation in the example, as I read the text. I did not try to "predict" the steps in the example and I do not think I ever spent your 30 minutes on an example. Most examples, were more transparent, and easy to follow.
Many generations of students complain the worked examples are often easier than the problems at the end of the chapter. I tend to agree I often worked more than 30 minutes on a problem, but not an example in the text.

I shouldn't spend too much time on examples (as with my earlier comment of 30 minutes).
Though I would like to ask here, what is the maximum time limit you would spend on a problem (end of chapter ones)?
Would you take help of a solution manual or something if it's taking far too much time (not solved even after a day or two, of course one wouldn't spend all day in it, just going to and fro with problem)

 

[mpresic3]

That's hard for me to say. I came of age in the 1970s, and there were very few solution manuals out there, and no internet. After a tough time with a problem, we did (sometimes we didn't) go to a grad student or professor during office hours.

Some problems that I thought were interesting, I worked on years later. Of course, I worked on a lot of problems in between, I did not work on one problem that I got stuck on for years.

I taught recitation sections out of Halliday and Resnick, and as a freshman had Kleppner and Kolenkow as a textbook. I would say in these textbooks, I would look for help if you are not making progress in 45 minutes. That is not to say done, but you feel you are on the right track after 45 minutes to an hour.

In grad school, I remember problems the professor gave us (not from the textbook) that would take 3-5 hours, even if you knew what to do. There was just an awful lot of calculation. One undergraduate problem the professor in quantum mechanics II gave us (he required it as a special problem, not from a textbook) took perhaps 8 total hours over 2-3 days . In both these unusual cases the professor warned us and we had perhaps two total weeks to do the problem set in which these were one problem and there were others that were significantly easier.

 

[mpresic3]

I thought I replied but I lost it.

I taught out of Halliday/Resnick, and used Kleppner /Kolenkow as an undergrad. I think after 45 minutes you should go to the professor, a grad student. I did not have computers and internet, and solution manuals in the 1970's. The solution manuals I have looked at since, are not necessarily good solutions.

 

[Manny46]

I thought I replied but I lost it.

I taught out of Halliday/Resnick, and used Kleppner /Kolenkow as an undergrad. I think after 45 minutes you should go to the professor, a grad student. I did not have computers and internet, and solution manuals in the 1970's. The solution manuals I have looked at since, are not necessarily good solutions.

Fair enough. In addition to a Grad student/Prof, we now have this wonderful PF and other forums online with solution manual. How much the latter can substitute for former?

 

[symbolipoint]

I thought I replied but I lost it.

I taught out of Halliday/Resnick, and used Kleppner /Kolenkow as an undergrad. I think after 45 minutes you should go to the professor, a grad student. I did not have computers and internet, and solution manuals in the 1970's. The solution manuals I have looked at since, are not necessarily good solutions.

One who teaches a course could write his own custom solutions manual.

 

[mpresic3]

In the early 1980's I was a physics recitation instructor at Rensselaer, where Resnick taught, and Resnick also had recitation sections along side the TA's. In those days, I think I had one fewer section than most TA's but I had the assignment to do all the homework and place the homework solutions in a glass showcase desk arrangement in a room where students could see them and transcribe them. Remember this is long before the internet.

I had all the solutions written every week. Approximately 10 -15 problems a week were assigned and I used index cards to write on and I locked the glass showcase on top so the cards wouldn't move. I think I probably used about 40 cards a week. I wish I had them now, just for memorabilia.

Perhaps a reader of the physics forum was a student at RPI in 1979-1983 and can remember those days fondly, and can respond.

I have a copy of the RH solution manual. I could do a much better job. P.S. I also supplied questions on several exams given at RPI in the 1980's. One of my quiz questions made it into an example problem in one of the editions of Resnick and Halliday

 

[Manny46]

@mpresic3 which version of Physics book (by Halliday, Resnick) should I buy Fundamentals of Physics (https://www.amazon.com/dp/111823071X/?tag=pfamazon01-20) or Physics (Resnick, Halliday, Krane) https://www.amazon.com/dp/0471320579/?tag=pfamazon01-20

 

[mpresic3]

As to which book to buy, I lost track of the textbook in the 1980's. Even by then , there were at least 10 editions and they seemed to come out every few years.

Actually Resnick told me a funny story about the several editions. He said in one of the chapters there is a person in a falling or rising elevator,(I forgot which). In one edition there is a man in the falling elevator. A woman suggested that this book should recognize women too, study physics. In a later edition, he put a woman in the elevator instead of the man. Some people complained about that too. Finally Resnick put Einstein in the elevator.

So if in your later editions you see Einstein in the elevator you know the story behind it

I have not verified this out but I was told the first book Mechanics etc. had authors Resnick/Halliday (or is it the other way around), and the second book treating electromagnetics and optics had authors Halliday/Resnick (Halliday first instead of Resnick) or is it the other way around.

 

[jedishrfu]

I went to both Union College and later to RPI. I remember the constant fear of driving up that incredible hill to get to the campus and dreaded the times I’d have to go when snow/sleet were forecast. I was a part time student in Physics and took QM with an Indian Prof from Univ of Chicago. He was a great guy but tough on tests. It was especially tough for me having been out of school for a few years and my math was lacking. He expected us to rattle off Bessel, Legendre and Lauguerre functions of memory and didn’t want to do take home exams saying they’d have to be a lot tougher.

I had an American Prof with a big floppy hat that taught Theoretical Physics. He was a bit quirky and his writing was somewhat sloppy and it wasn’t until a few weeks into the class that I realized that what I thought was one Greek letter was actually another in the stress tensor. $\zeta$ vs $\xi$

There was one grad student I remembered who would place her feet up on the desk in front while the prof was teaching. She was a part of a team that discovered a 4th arm of the Milky Way so she was on her way.

My one problem at RPI was the pressure to take the qualifying exam within one year even if you were a part time - one course at a time student. I just couldn’t do it and the final straw was when they wouldn’t allow me to signup for any course until until I paid for the next semester by some date I couldn’t meet with tuition fee nurse net.

 

[Manny46]

As to which book to buy, I lost track of the textbook in the 1980's. Even by then , there were at least 10 editions and they seemed to come out every few years.

Actually Resnick told me a funny story about the several editions. He said in one of the chapters there is a person in a falling or rising elevator,(I forgot which). In one edition there is a man in the falling elevator. A woman suggested that this book should recognize women too, study physics. In a later edition, he put a woman in the elevator instead of the man. Some people complained about that too. Finally Resnick put Einstein in the elevator.

So if in your later editions you see Einstein in the elevator you know the story behind it

I have not verified this out but I was told the first book Mechanics etc. had authors Resnick/Halliday (or is it the other way around), and the second book treating electromagnetics and optics had authors Halliday/Resnick (Halliday first instead of Resnick) or is it the other way around.

Well, when puts Einstein in the frame, it automatically makes it non inertial.
I just checked, you're correct, Sir. Volume 1 ( which includes Krane ) has Resnick/Halliday/Krane and Volume 2 has (Halliday/Resnick/Krane).

 

[mpresic3]

You probably had Dr Nemai Mukopahdya (This looks like the wrong spelling, I would never have spelled it incorrectly years ago) for Quantum Mechanics. I met him last when he was a visiting professor at the University of Virginia in 1988. I am sorry to hear he passed on.

The other professor with the hat was (likely) Dr. William McKinley. Most of my work today is centered on mechanics and theoretical physics. I went to RPI to sharpen my quantum mechanics and I had Dr Sperber for QM and he was very good. However, I credit Dr. McKinley for inspiring me to see the beauty of classical mechanics, that has sustained me to this day.

 

[jedishrfu]

My apologies for going off-topic here but hearing RPI brought back memories that deserved to be remembered to quote the History Guy on Youtube.

Dr McKinley rings a bell. One time in class he said "Consider this action" as he spread his hands out and the eraser went flying. The class was confused what action, the spreading of his hands or the flying eraser that appeared to be accidentally tossed.

Dr Mukhopahdyay doesn't sound familiar as I thought my prof was a few years older but not 10 years older. However, I think you're right and I'll have to check my transcripts to be sure.

I found this Physics Today article on his life and career:

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1333306

One story he told in his class was about his time at the Univ of Chicago where he took the qualifying exam and scored a 10 out of a 100 and he was quite sad about it. However, when he talked to the TA they told him he did quite well as the expectation was that students should get 2 on average.

He used it to encourage students who just took the qualifying exams and did poorly. One student reported the talk to the administration. Apparently there was a hidden rule that profs were never to talk openly about grades and the qualifying exams to students and he got reprimanded and promptly apologized to us.

I also took an Astrophysics course but don't remember the prof. It was focused primarily on the how the Sun worked using various quantum and classical mechanics ideas together to get ballpark estimates of things. I remember taking the exam in late December, my calculator died and someone loaned me their backup which was a non-scientific calculator and I felt so lost and wished I had my slide rule again. Following the exam and braving the snow and traffic,

I rushed to Albany Airport for a flight to Taiwan meet up with my wife and to visit her extended family for the first time. We traveled around a bit and while we were in SunMoon lake area at the Bamboo Culture Park, I heard someone yell out "RPI!" which caught me by surprise. It was a chinese student who had gone there and it was the first English I had heard in a few weeks outside of my wife's family.