How Can I Self-Study Advanced Math for a Physics Master's Degree?

[Jimmy84]

Im finishing my first year majoring in physics and I am interested in persuing a master in mathematical physics, however I don't live in a a place where educations is standar, the math level that I am been taught is very poor.

In calculus the teacher tries to avoid proving theorems in anyway, he attempt geometric interpretations instead. people over here never learn anything about proofs, set theory or where does mathematical concepts come from, which is frustrating.

In latter levels we are going to have very soft classes about linear algebra, differential equations and there are not even courses about analysis or multivariable calculus, but he would teach us those subjects really fast in the middle of other courses, the last subject we would see would be a soft introduction to matematical physics, some calculus of variation but "no functional analysis". relativity, quantum mechanics and particle physics are optional subjects.

Anyway I d like to self study math since education over here is not good enough at all in order to have a good preparation for a masters degree, but I have problems in making progress with rigurous books about mathematics.
I tried self studying spivak with the little time I have free, though it seems impossible. I am trying to get the solution manual of spivaks calculus to see if that can help me to speed up.

Eventually I am looking forward to read some apostol and Loomis Sternberg advanced calculus, but the later book dosent even has the answers on the end of the book, and therefore it is imposible to use it to teach oneself. How does mathematicians get through books like these which have no answer on the end, is there any solution manual for Loomis Sternbergs book?

The worst is that I cannot even hire a tutor because the math faculty has few students and my guess is that they won't be totally able to tutor me on books like Spivak or Loomis Sternberg. I heard they used Rudins in classes about analysis though.

How can I get my way through self studying Spivak and specially through Loomis Sternberg since it has no solutions at all? any suggestion?

Thanks

 

[BloodyFrozen]

The worst is that I cannot even hire a tutor because the math faculty has few students and my guess is that they won't be totally able to tutor me on books like Spivak or Loomis Sternberg. I heard they used Rudins in classes about analysis though.

How can I get my way through self studying Spivak and specially through Loomis Sternberg since it has no solutions at all? any suggestion?

Thanks

Well for starters, you could post any questions you are unsure about on the forums. Rudin is more difficult than Spivak.

Spivak, Apostol (Rigorous Calc I & II)
Rudin (Analysis)

 

[romsofia]

Well for starters, you could post any questions you are unsure about on the forums. Rudin is more difficult than Spivak.

Spivak, Apostol (Rigorous Calc I & II)
Rudin (Analysis)

He could also just ask the tutors, as I don't know why he would assume that graduate/upper level classmen wouldn't be able to comprehend Spivak OR Apostol...

 

[BloodyFrozen]

He could also just ask the tutors, as I don't know why he would assume that graduate/upper level classmen wouldn't be able to comprehend Spivak OR Apostol...

True. I don't see why students who take analysis would not understand Spivak.


And personally, I don't like solution manuals because you may be tempted to look at them (doesn't mean you shouldn't get one).

 

[Jimmy84]

I asked my math teacher if there was anyone that could tutor this math level of rigurous proofs but he said it would be very hard to find someone, he suggested me instead to go as a listener to clases in the math faculty, but it is almsot impossible since I have a lot of classes and lectures that I am already taking

Im not sure if students of analysis would feel like tutoring a book like spivak that depends of them, of coruse they can comprehend the subject but that is different from tutoring, some might be reserved and won't feel like tutoring unless they know that they ve mastered the subject and that they would be capable of solving all or most of problems.

I can understand also that solution manuals arent the best option, I guess most of advanced books in math don't even have the answers on the back of the book, that is difficult for me to understand sometimes but I think being able to self teach yourself books like spivak or apostol on your own as a laymen without spending too much time with them would be amazing even just to get the main ideas and knowing how to solve the problems is a preparation for more advanced and rigurous subjects that otherwise can't never be learned alone.
Im stuck in that situation that I feel learning these subjects without a tutor or a teacher is impossible unless I get the solution manual. My understanding is that these books open the doors for new and exciting subjects like analysis, differential geometry and others and I don't wish to spend a life time learning all those subjects on my own, but rather to use solution manuals to speed up things.

 

[Dr. Seafood]

So your school's math major courses are separate from your physics major math courses? That's like at my school, probably for many schools. If you're really interested in this, just take the math courses from the math faculty instead of the science-based math courses.

 

[Jimmy84]

So your school's math major courses are separate from your physics major math courses? That's like at my school, probably for many schools. If you're really interested in this, just take the math courses from the math faculty instead of the science-based math courses.

The policy for taking courses is not wise over here, If I try taking calculus III in the math faculty then I need to take all of the prequisite courses which are, basic math, calculus I and II, from the math faculty. The same goes for analysis and other subjects. there are so many prequisite courses in order to take an especific one. The same goes for physics courses.