Other Is it worth doing EVERY problem in a textbook?

AI Thread Summary
A freshman Physics major is exploring Apostol's Calculus Volume 1 to enhance calculus knowledge and for enjoyment. The student expresses disinterest in certain proof-based problems, specifically regarding lattice points, questioning the value of engaging with them given their future aspirations in biophysics. Responses emphasize that the decision to tackle problems should align with personal interests and available time. Engaging with challenging problems is acknowledged as beneficial for learning, but it's also noted that not every problem needs to be completed, especially if they feel like busywork. The discussion suggests that the student could skip less interesting problems and focus on those that align more closely with their interests, with the option to revisit skipped problems later if desired.
XcgsdV
Messages
4
Reaction score
4
I am a freshman Physics major currently working through Apostol's Calculus Volume 1 in my free time, somewhat to further develop my calculus knowledge, but mainly for fun. Apostol's text is proof-based, and as such has a number of problems that are just proofs. As a hopeful future Biophysicist, proving that the area of a polygon with vertices on lattice points (x and y are integers) can be found by A = I + B/2 - 1, where I is the number of lattice points inside the polygon and B is the number of lattice points on the boundary, simply is not interesting to me. I know I am not beholden to doing every single proof laid before me, but for problems like these—that both do not interest me and where I don't see how the result is directly useful to the study of calculus—what am I losing by skipping over them?
 
Physics news on Phys.org
XcgsdV said:
in my free time, somewhat to further develop my calculus knowledge, but mainly for fun.
You've answered your own question. You have not indicated that you plan to double major in math and physics; and you are doing this for the reasons above. So, how much free time do you have, and what else can you do in your free time? If the answer is you have nothing else to do, then do every problem. If the answer is you have other things to do, then do a few of the problems to expand your knowledge, to learn how mathematicians think, and to have fun. But you don't need to master the material, according to your present goals.
 
Doing the problems you find easy is certainly not the road to learning. So it depends upon how you define "fun".....
 
  • Like
Likes topsquark, malawi_glenn and Vanadium 50
Whether one attempts all the problems or not in a textbook, depends on how the textbook's author has organized the suggested questions and problems. For instance, in the old good Berkeley Series 5-volume set, there are not too many problems, but the provided ones are lengthy in description and demand a lot of work by the reader. On the other hand, in today's standard college physics books like Halliday and Resnik or Serway, the student is offered a considerable number of problems, although well organized by topic and difficulty. Then it's up to the instructor to assign a profitable set of problems to his/her students.

However, in advanced physics books like Jackson or Peskin & Schroeder, the authors expect the reader to attempt every single problem in detail.

We can also recall stories from great physicists' college years as good examples. For instance, Dirac always worked all the problems, often driving his tutors to despair.
 
  • Like
  • Informative
Likes topsquark, symbolipoint and PeroK
hutchphd said:
Doing the problems you find easy is certainly not the road to learning. So it depends upon how you define "fun".....

I have no issue with solving *difficult* problems. I've labored over problems in this book for hours because I am well aware that you don't learn without struggling through stuff, especially with math. The difference is I enjoyed that struggle because it was with more interesting problems, problems that I actually wanted to solve. This feels like busywork to me, and while I could spend time thinking about lattice points on boundaries and not, I could also work further in the book and learn about math that actually interests me.
 
XcgsdV said:
I have no issue with solving *difficult* problems. I've labored over problems in this book for hours because I am well aware that you don't learn without struggling through stuff, especially with math. The difference is I enjoyed that struggle because it was with more interesting problems, problems that I actually wanted to solve. This feels like busywork to me, and while I could spend time thinking about lattice points on boundaries and not, I could also work further in the book and learn about math that actually interests me.
Again, you've just answered your own question.
 
Last edited:
XcgsdV said:
I have no issue with solving *difficult* problems. I've labored over problems in this book for hours because I am well aware that you don't learn without struggling through stuff, especially with math. The difference is I enjoyed that struggle because it was with more interesting problems, problems that I actually wanted to solve. This feels like busywork to me, and while I could spend time thinking about lattice points on boundaries and not, I could also work further in the book and learn about math that actually interests me.
Then read Rudin.
 
XcgsdV said:
This feels like busywork to me, and while I could spend time thinking about lattice points on boundaries and not, I could also work further in the book and learn about math that actually interests me.
It seems you feel compelled to work through the book in order. There's nothing stopping you from jumping ahead or skipping problems. You can always come back to them later if you think you might have missed something important.
 

Similar threads

Replies
7
Views
3K
Replies
2
Views
4K
Replies
7
Views
5K
Replies
5
Views
2K
Replies
1
Views
2K
Replies
4
Views
1K
Back
Top