Is it worth doing EVERY problem in a textbook?

[XcgsdV]

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?

 

[CrysPhys]

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.

 

[hutchphd]

Doing the problems you find easy is certainly not the road to learning. So it depends upon how you define "fun".....

 

[apostolosdt]

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.

 

[XcgsdV]

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.

 

[CrysPhys]

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.

 

[MidgetDwarf]

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.

 

[vela]

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.