Improve Your Study Habits for Maths: Tips and Strategies

[set]

I was able to solve most of exercise questions in textbook when I was in high school, but as I expected, university level mathematics is really difficult. I have been studying baby Rudin but I cannot solve most of exercise questions unless I see the solution first. But I am really worried because I am compelled to think that I should produce all the solutions on my own and looking at the solutions first won't get me far. Then, since trying to solve problems on my own is extremely diffcult, sometimes I just want to quit.

So how do you study maths?

 

[johnqwertyful]

Yes, your study habit is wrong. Unfortunately we have to take you out back and beat you. I'm sorry, it's the rules.

Uhh you just started university and you're using Baby Rudin? I think I found your problem. Focus on your course materials for now. I don't know of a single freshman math class that would use Rudin.

 

[set]

ooooppsss. sorry I meant Spivak lol. still, Spivak is hard :(

 

[johnqwertyful]

ooooppsss. sorry I meant Spivak lol. still, Spivak is hard :(

Again, why are you using Spivak when you're a freshman in college?

Focus on your course materials.

 

[set]

Oh? That is the textbook we use in our class. I assumed, when I said Spivak, I meant Calculus 4ed. (it's the grey one) I know that Spivak wrote many books, when I said Spivak, did you think of one of his books on higher level calculus? Sorry for not being clear enough :S

 

[Jorriss]

Spivak is very, very difficult. Do not be at all surprised if you can not do it as a freshman.

 

[WannabeNewton]

To be fair many freshman honors calculus courses use spivak so that isn't much of an excuse. Don't look at the solutions though as that isn't the way to learn. If you are having doubts then post it here for example. Don't expect to be able to do all the problems in spivak; some of them as you said are indeed extremely hard (attempt them of course). It's ok if you can't do some of them. Also try Apostol's calculus text if you want another book to work through; the aforementioned text is another popular freshman calc book.

 

[PhizKid]

He says his class textbook is Spivak so he doesn't really have a choice anyway

 

[MarneMath]

You need to burn/not loook at the answers or search for them online. You are taking a class that uses Spivak, so you need to be proactive. This means study groups with other students, going to a TA or professor for help. Spivak, in regards to other books you will encounter, is actually really straight forward. This is time you need to learn how to think like a mathematician. How to use previous problems to build solutions to current problems. Is it easy? Of course not, but the feeling of solving a problem after five days of nothing but mistakes is a great feeling. It's one you should love, if you are going to study math.

Nevertheless, trying to solve every problem in Spivak isn't and shouldn't be your goal right now. Solve your homework assignments, and problems that seem interesting to you. There exist a good deal of problems in Spivak that are neat, but skipping them wouldn't hurt.

*I solved every problem in Spivak one year (took a year), so if you need guidance or help from someone who will not give you the answer, feel free to ask! This forum has a HW section for a reason. Make a thread and point me to it and i'll do my best to give you some perspective on the problem.

 

[set]

Thanks for the suggestions and encouragement everyone!

 

[FalconOne]

I don't think what you're doing is necessarily wrong. When I came into physics, I had never taken intro physics, and so the initial homework sets for me were nearly impossible for my upper level courses. I would look at the solution to a similar (not identical) problem to learn the general processes. Because, hey, force diagrams are something that a professor would just blaze right through in an upper level course! Anyway, once I learned how to do a similar problem, I would be able to feel confident on the homework set. Then, once I was farther into the semester, I didn't need it at all. I think that if you are actually learning and can do your homework well and do okay on exams, what you are doing is just fine. If it's a crutch, not so much.

 

[micromass]

I fear that your university is making calculus into some kind of weeder class. Either you work extremely hard to succesfully complete Spivak or you drop out. That seems to be the situation for the majority of the students taking Spivak.

As a consolation, this class will probably be the hardest math class you ever take. Other math classes will be difficult of course, but by then you have already learned how to think like a mathematician and you are used to the abstractions. Indeed, if you get through Spivak, then you will have gained a lot of mathematical maturity.

Of course, getting through Spivak is not an easy task and requires much hard work. Do try to use various resource. For example, go to office hours, make a study group with your classmates, post questions on this forum, etc.

Good luck and I hope you do well!

 

[clope023]

You need to burn/not loook at the answers or search for them online. .

Ridiculous

 

[MarneMath]

Ok? Care to explain why looking at answers each time you get stuck is better than talking through the problem with a professor or on here?

 

[clope023]

You're making the fallacy of the excluded middle, you can look at the answers (within reason) and still learn and then apply what you learned from the answer to other problems. You should talk with professors, putting up questions in the homework section is useful but it is a slow process, that's why I amass solutions manuals and worked example books like the schaums. I can generalize the procedures and use that knowledge to do other problems without aid. There is no reason to burn solution manuals if you own one as if looking at them will stop your learning.

 

[SolsticeFire]

I'm with Marne on this one. Solution manuals just tend to make one lazy. Sure you can use the solution manual and follow how the proof was derived or the problem was solved. Then you proceed to generalize the methods and use them in the future to tackle other problems. But mathematics is a very sado-masochistic process - you need to come to insights and solve problems by torturing yourself and being with the problem 24/7 and taking a million wrong turns before you find the right one. Using solutions manuals you'll never know how to be wrong, and being wrong is more fruitful than being right.

You can argue that you can do more problems in a shorter time if you get help from solutions and that's a fair argument. But 'amassing' textbooks solely because they have full detailed solutions manuals is stretching it. Once you get into research, how will you find your solutions manual to 'generalize' the procedures then? You have to make up your own procedures. But all you have done so far is cruised through the problems and not struggled hard enough because you always had some help along the way. I think the saying "Smooth seas never make a skilled mariner." applies here.

SolsticeFire

 

[clope023]

I'm with Marne on this one. Solution manuals just tend to make one lazy. Sure you can use the solution manual and follow how the proof was derived or the problem was solved. Then you proceed to generalize the methods and use them in the future to tackle other problems. But mathematics is a very sado-masochistic process - you need to come to insights and solve problems by torturing yourself and being with the problem 24/7 and taking a million wrong turns before you find the right one. Using solutions manuals you'll never know how to be wrong, and being wrong is more fruitful than being right.

You can argue that you can do more problems in a shorter time if you get help from solutions and that's a fair argument. But 'amassing' textbooks solely because they have full detailed solutions manuals is stretching it. Once you get into research, how will you find your solutions manual to 'generalize' the procedures then? You have to make up your own procedures. But all you have done so far is cruised through the problems and not struggled hard enough because you always had some help along the way. I think the saying "Smooth seas never make a skilled mariner." applies here.

SolsticeFire

You'll never learn how to be wrong without a picture of what right is to compare your answer against. Often times the worked examples in textbooks are not good indications of what the exercises will be (like in Griffiths' Quantum book). Research is research, homework is not a good indication about what it's like and you've made a false (yet sadly all too common) generalization that if you use solutions you will be left clueless in research.

 

[micromass]

You're making the fallacy of the excluded middle, you can look at the answers (within reason) and still learn and then apply what you learned from the answer to other problems. You should talk with professors, putting up questions in the homework section is useful but it is a slow process, that's why I amass solutions manuals and worked example books like the schaums. I can generalize the procedures and use that knowledge to do other problems without aid. There is no reason to burn solution manuals if you own one as if looking at them will stop your learning.

Are you an undergrad or a grad right now? In which year?

Things like this might work for a while, but in the end they usually fail. Furthermore, solution manuals don't exist for advanced books.

 

[clope023]

Are you an undergrad or a grad right now? In which year?

Things like this might work for a while, but in the end they usually fail. Furthermore, solution manuals don't exist for advanced books.

Undergrad (EE + physics double major) doing senior classes in physics; I've done whole classes without a solution manual when I did plasma physics (Bittencourt's Plasma Physics book has no solution that I know of, I know I looked so I could be prepared for class). I spent a whole month on one cross coupled differential equation before my in class friends and I came up with the correct derivation, I know what it's like to struggle through problems and come up with the solution by myself.

Things like this work all the time, don't think grad students don't do it either.

Also solution manuals absolutely exist for advanced books (say Jackson E&M, though there are books more advanced than that one).

 

[MarneMath]

You're making the fallacy of the excluded middle, you can look at the answers (within reason) and still learn and then apply what you learned from the answer to other problems. You should talk with professors, putting up questions in the homework section is useful but it is a slow process, that's why I amass solutions manuals and worked example books like the schaums. I can generalize the procedures and use that knowledge to do other problems without aid. There is no reason to burn solution manuals if you own one as if looking at them will stop your learning.

I don't deny the idea that a solution manual can help someone in some instances; however, I'm not willing to say that in a course like Spivak (an honor's calculus) that a solution manual would benefit this student more than the process of solving the problem. It isn't the answer that matters, but the journey to the answer. Learning, often times, occurs during the struggles of putting together previous problems and theorems. Having someone put those ideas together for you only hampers the experience.

I also want to point out something on the larger scheme of things. Eventually, in the future, you will have to solve problems where a solution manual doesn't exist. Learning who to ask, and where to find the information, and putting it together is a valuable skill. Probably more so than being able to pick up a book and read an answer.

*Also a side note, I've also noticed in Spivak, the answers the solutions give are usually 'clever' solution where a short or clever rewrite makes the proof trivial. Some students may look at these answers and go "I would have never thought of that!" Well, that's probably true, but you probably could've thought of the more direct method of using definitions and theorems to come to the same conclusion.