Great books for the self taught?

[Bingo]

I’m an ME major and like studying certain math topics outside my curriculum in my spare time. I’m having a hard time deciding what books to get and I’m guessing that a good start would be finding a good book on writing proofs. I've bought one but there are no solutions for the exercises. This wouldn’t be a problem if I had a teacher to get feedback from but since this is self taught, I need some feedback. I have looked around on the forums and have not found opinions on books covering this while other topics there are so many recommendations that its difficult to decide since some cost so much $$$. I’m also interested in finding good books on PDE’s, analysis, complex analysis, and any other great book any of you would recommend :). I've had the typical college courses up to and including ODEs. Thanks for any replies.

 

[JasonRox]

I’m an ME major and like studying certain math topics outside my curriculum in my spare time. I’m having a hard time deciding what books to get and I’m guessing that a good start would be finding a good book on writing proofs. I've bought one but there are no solutions for the exercises. This wouldn’t be a problem if I had a teacher to get feedback from but since this is self taught, I need some feedback. I have looked around on the forums and have not found opinions on books covering this while other topics there are so many recommendations that its difficult to decide since some cost so much $$$. I’m also interested in finding good books on PDE’s, analysis, complex analysis, and any other great book any of you would recommend :). I've had the typical college courses up to and including ODEs. Thanks for any replies.

I learned how to write proofs while reading an "easier" kind of Topology textbook. A lot of people are intimidated and never take Topology, but there really is nothing to fear. You're dealing with sets basically. It will help with Analysis as well.

Anyways, they have many simple proof problems anyone can solve. It helped me build the logic and such required to write a proof. It's not all about deducing, but knowing what's concrete and such.

Also, Analysis has a lot of proofs too, but I'm not aware of any having solutions at the back of the book though. So, I don't know what to say there.

 

[morphism]

Springer have a series of accessible undergrad books (Springer Undergraduate Mathematics Series, or SUMS) with answers to all the exercises. My recommendation is to see if your school's library has copies on hand, or look for used ones. Although new copies aren't as expensive as most textbooks.

In fact, http://www.springer.com/west/home/math/algebra?SGWID=4-10043-580-173622659-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&RESULTS_PER_PAGE=10&resultStart=0 is the list of all books in that series.

 

[JasonRox]

Springer have a series of accessible undergrad books (Springer Undergraduate Mathematics Series, or SUMS) with answers to all the exercises. My recommendation is to see if your school's library has copies on hand, or look for used ones. Although new copies aren't as expensive as most textbooks.

In fact, http://www.springer.com/west/home/math/algebra?SGWID=4-10043-580-173622659-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&RESULTS_PER_PAGE=10&resultStart=0 is the list of all books in that series.

I have a textbook from them and have seen others and don't have solutions whatsoever.

Different version maybe?

 

[JasonRox]

I just checked again, and some do have solutions.

I recommend reading the Table of Contents to make sure there is a solutions section before buying it.