How Should I Prepare for Calculus III and Modern Algebra?

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To prepare for Calculus III after completing Calculus II, it's essential to familiarize oneself with mathematical proofs, as this foundational skill will ease the transition into more abstract algebra concepts. The Algebra sequence is often challenging, and starting with courses like Modern Geometry, Linear Algebra, or Elementary Number Theory can provide a smoother bridge to proof-based mathematics. Engaging with proof problems in Elementary Linear Algebra is recommended, along with independent study in number theory to enhance understanding and ease the learning of algebra. "Elementary Number Theory" by Jones and Jones is suggested for its clarity and comprehensive solutions, making it suitable for self-study. Additionally, Pinter's book is recommended for its accessibility and introduction to algebra concepts. Reviewing resources like Marsden's free Calculus III book can also help in understanding what to expect in the upcoming course.
xsqueetzzz
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I'm taking both in the fall, what should I review over the summer to prep up for this?
 
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Calculus II for Calculus III :biggrin:
 
Hi xsqueetzzz! :smile:

Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
 
micromass said:
Hi xsqueetzzz! :smile:

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.
 
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.
 
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