How many of a chapter's problems do I do before moving to the next chapter?

  • #1

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A freshman here, Hi. I am taking the following courses this year:
E&M, Mechanics, Calc., Statistics and Chemistry.
i use Halliday-Resnick volume 2 for E&m, vol.1 for mechanics while i use Serway-Jewett as reference. for stats its Anthony Hayter and Ebbing-GAmmon for Chem

my problem is this, when i start a new chapter, what proportion of the problems should i target to finish before moving on? i want to keep a certain amount for final revision at the year's end but until then how much would be a good target as in for understanding and to get a good span of problems?

Normally, what did you do back when you were at Freshman year? Also is there any other text you would recommend other than those i have mentioned more tailored for freshman year for these courses? IS serway-jewett a good choice? i feel like the problems are more relevant to what i can do at this time but i need some expert opinion...

regarding other titles; i know Purcell, zemansky and Irodov are great for these courses , but honestly i feel like these are beyond my level, as in i cant go more than 20% into these at this point in time. i wanted to be more familiar with the subject material in a way that best prepares me for these books later at Junior year. Thanks in Advance
 
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  • #2
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This is not an easy thing to answer. If you really want to discover what you know and don't know then do all the problems. However, that often won't help completely because of the answers key given in the book which may encompass only even or only odd problems and without the actual steps to complete the problem. Also, it can lead to frustration unless you are proactive about it and look to your prof help in how to solve one you're stuck on.

All these things happened to me. I had to prioritize because I worked part-time. I had limited access to the prof being a commuter student. Evveryting was done by hand, personal computers weren't invented yet and there was no internet but we did have the telephone and no one to call.

Doing all the problems takes time, time you may need for other courses. So you will need to prioritize and develop a strategy where you solve a problem up to the numerical steps and then stop ie you diagram it, write down the equations and initial conditions, work through to a solution but leave it in numeric form unless it's easy to solve.

You're using multiple books so I would solve only the problems in the primary textbook and use the others for reference looking for problems similar to the ones you solved. I would also focus on the ones the prof has assigned as these are likely the basis for any quiz or test. One thing to keep in mind though is that the prof will insert a few problems beyond what you've been given for assignments because that's what profs do to challenge the best of students.

You also have Khan Academy and other online resources that you can tap to help in solving specific problems.

Plan, prioritize and solve your problems in a way that you can teach others to solve it. Keep the mindset of a teacher, try to think like your teacher, teaching it will bring out the flaws in your reasoning very quickly and writing your solutions to teach others will help you remember how to solve it when you study for your final.

You must make the material so familiar that it's unforgettable and like your own personal discovery so you will have confidence in tests.

Lastly, listen carefully to your prof's lectures as they will sometimes drop hints about what will be on upcoming tests. It won't be a direct hint, it might instead be a hesitation to answer a student's question.

One prof I had for Computer Logic gave a lecture on Karnaugh maps using zeros as the primary thing to look for and then he said that you could also use ones, hesitated and immediately went to the next topics. I was intrigued and looked into the alternate solution and wonder of wonders he had a problem on the test a week later that required that scheme to solve it.

Another prof in Calculus class did a double integral problem on the board and then casually mentioned that sometimes integrating over x and then y won't work but reversing the order will. On his Friday quiz, he had such a problem and rather than falling into the rabbit hole, I did as he suggested and it just fell into place while other students struggled to do it x then y.
 
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  • #3
berkeman
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Good advice by @jedishrfu :smile:
Normally, what did you do back when you were at Freshman year?
It depended on how heavy my course load was, and whether I had it mostly under control or not (that varied a lot from quarter to quarter for me). My preference was to do enough of the problems at the end of the chapter so that I had covered the material (there are generally several different groups of problems to cover the different topics in the chapter). I also tried hard to solve the last few problems at the very end of problems for each chapter, since those always seemed to be sort of "bonus" / extra hard questions or questions that involved multiple concepts at once.

Another measure for me was that I tried to keep a running "crib sheet" for each subject, to help me remember formulas and concepts and to help me in studying for exams. As I did the problems at the end of the chapter, I'd often find things that I'd missed adding to my crib sheet during the initial studying of the chapter. I could tell when I was getting the problems down pretty well when my crib sheet was stable for the last few problems that I'd done.
 
  • #4
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That's a good point with respect to solving the tougher ones at the end of the chapter. These are more likely ones that will appear in some form on tests, mid-terms, and finals.

My Calculus prof, would assign problems to do but told us he selectively graded only certain problems not all. I never knew if that was really rue and I figured it probably was and that he graded the last couple in the list. I never checked with him about it though.

Fairness is in the mind of the prof so a grading strategy where you looked for problems NOT solved as the easiest ones to mark wrong is quite conceivable. However, my math prof was a pretty fair guy. He was lauded by his students and loathed by his peers because he taught extremely well instead of doing the necessary paper publishing. His revenge was to become dept chair at another college when he didn't get tenure at our school.
 
  • #5
mathwonk
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freshman year i did at most what was required. then i flunked out. some years later as a temporary instructor i did them all (in calc). i went on to grad school, a ph.d. in math, and a long research career.
 
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  • #6
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I taught Physics Recitation at RPI along with Resnick about 40 years ago. In general, I remember we had students do about 12 - 15 problems from each chapter, approximately 1/3 - 1/2 of the problems. The problems had various levels of difficulty so the student did not get assigned all plug-in-chug problems. I was also in charge of putting my solutions (I was really good at solving these) in a showcase for students to copy. In those days there was no internet so this is where we posted solved problems after the student had to hand them in for credit.

I think if you can do half of the problems out of Resnick and Halliday, you are doing pretty good.
 

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