xsqueetzzz
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I'm taking both in the fall, what should I review over the summer to prep up for this?
How Should I Prepare for Calculus III and Modern Algebra?
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YAHA
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Calculus II for Calculus III 
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Hi xsqueetzzz! 
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
hitmeoff
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micromass said:Hi xsqueetzzz!
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
Agreed. At my school, the Algebra sequence is probably the toughest sequence we have, and some of the professor that teach it will take no prisoners when it comes to level they expect you to perform.
So from my perspective, I personally think you are better off starting your "Junior Level" math course with something like Modern Geometry, Junior level Linear Algebra or even Elementary Number Theory. Usually, these three will serve as a nice bridge between computational math and abstract, proof based math.
Of course, in your school, Number Theory or LA or even Modern Geo maybe be deadly classes and Algebra may be taken more lightly! So it really depends. I would definitely look over your Elementary Linear Algebra book (you know the freshman/sophomore level LA), and practice some of the "Proof" problems. That should get you started on thinking more abstractly.
Chaostamer
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Honestly, it might benefit you to do some independent study in number theory, both because you'll get more practice with proofs and because number theory knowledge makes algebra easier--or so I've been told. "Elementary Number Theory" by Jones and Jones is an excellent book in that regard. It's really well written and has a comprehensive solutions key in the back, so it's ideal for self-study. Plus, it's pretty cheap. I'd highly recommend it if you want some accessible proof practice.
Sankaku
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It is a very good recommendation from micromass to make sure you are comfortable with proofs.
If that is covered, pick up a copy of Pinter:
https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
It is cheap, an easy read, and will introduce you to the basic concepts of algebra.
You can glance through Marsden's free Calc III book to get an idea of what that will be like.
http://www.e-booksdirectory.com/details.php?ebook=1564
If that is covered, pick up a copy of Pinter:
https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
It is cheap, an easy read, and will introduce you to the basic concepts of algebra.
You can glance through Marsden's free Calc III book to get an idea of what that will be like.
http://www.e-booksdirectory.com/details.php?ebook=1564
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