Math Degree: Bridging the Gap and Understanding Calculus

[bonfire09]

Well I've taken calculus 1-3 all up to differential equations and its been quite easy. Though I forgot most of the stuff already. I am going to be taking upper division math but I feel that my math background is still very weak because all I ever did was computations.I never understood why It works. I mean I tried to prove it but I never got it. I know that I have gaps. Anyone recommend any books or what should I do to close these gaps?

 

[member 392791]

maybe try and do the proofs and when you get stuck talk to your professor

 

[bonfire09]

yeah I tried. I am thinking of using a book called Bridge to Abstract Mathematics by Morash as a guide for self study but idk if I am on the right track.

 

[DeadOriginal]

I like An Introduction To Mathematical Reasoning by Peter Eccles.

 

[daveyinaz]

yeah I tried. I am thinking of using a book called Bridge to Abstract Mathematics by Morash as a guide for self study but idk if I am on the right track.

Looks like the right track to me. I think I might even seen this book before...from what I remember it had sections on how to write formal proofs by proving basic concepts a student having only encountered calculus might recognize.

 

[alan2]

I recommend "Reading, Writing, and Proving" by Daepp and Gorkin, and "A Transition to Advanced Mathematics" by Smith, Eggen, and St. Andre. Though not as general, "Set Theory and Metric Spaces" by Irving Kaplansky is a beautiful little book that was my first exposure to abstract mathematics.