Need Advice - Six Months to Prepare for Analysis

[Sullen_and_Sordid]

I have six months before I go back to school (after being out of school for over 5 years - ex engineering student). I'll be pursuing a BA in Mathematics and Philosophy - I will have to take either Abstract Algebra or Real Analysis 1 for my first quarter. Which class would you guys recommend I take first and what can I do to prepare right now?

My basic maths aren't too rusty (all the pre-calc stuff), basic linear algebra and I just started working through Vellaman's "How to Prove It". My concern is that I don't remember anything from calculus - should I relearn it now or just take analysis w/o re-learning it? Do I have enough time to cultivate the mathematical maturity needed for these courses? if so, what should I focus on?

I welcome any advice or pointers! Thank you.

 

[jedishrfu]

I'd take Abstract Algebra. Of course you'll need to bone up on Set Theory and be familar with Groups and Rings... and know how to do proofs.

https://en.wikipedia.org/wiki/Abstract_algebra

vs https://en.wikipedia.org/wiki/Real_analysis

@fresh_42 can answer this better.

However if you're more in tune with Real Analysis considering your engineering background then do that. I think your decision will boil down to doing proofs or not.

You could ask the math profs or your advisor about it explaining your situation.

 

[jedishrfu]

I made the mistake when I went to college in attempting to learn Algebraic Topology. I squeaked by as a junior physics majors among a group of senior math majors. The prof was very kind. I then got into Group/Ring theory but in both cases got hammered because as a physics student I had little experience in doing real math proofs ( I naively thought that my high school geometry proof experience would be enough to get me by and how wrong I was).

One of my favorite math profs would say if you throw enough mud at the wall some of it will stick. Some did but not in an advantageous way.

 

[Sullen_and_Sordid]

Thank you, your comments are reassuring - from what I am gathering it seems like getting my proofs dialed in (not the sort we encounter in high-school) will be important. I guess I should ask this more directly - will I need to know any calculus before I take Real Analysis or Abstract Algebra? It doesn't seem necessary for AA, but I should work on set-theory. What about RA? For both, get my proof maturity down - got that, but how much calculating or applied maths will be sufficient? More clearly, should I put more time into my proof books or more time into re-learning calculus?

 

[fresh_42]

I have six months before I go back to school (after being out of school for over 5 years - ex engineering student). I'll be pursuing a BA in Mathematics and Philosophy - I will have to take either Abstract Algebra or Real Analysis 1 for my first quarter. Which class would you guys recommend I take first and what can I do to prepare right now?

My basic maths aren't too rusty (all the pre-calc stuff), basic linear algebra and I just started working through Vellaman's "How to Prove It". My concern is that I don't remember anything from calculus - should I relearn it now or just take analysis w/o re-learning it? Do I have enough time to cultivate the mathematical maturity needed for these courses? if so, what should I focus on?

I welcome any advice or pointers! Thank you.

Where to go to mainly depends on where to stand at, esp. what you mean by school, a term which depends on country, age, and goal. I've seen it used to mean High school, or college, or even university; terms (2 out of 3) which AFAIK themselves only apply to the US system.

I'd take Abstract Algebra.

That was my first thought, too, as I read "philosophy". The more as it is typically nothing to start with at university, so you won't repeat it in the first year. Algebra is about structures and their properties, a logical construction whose understanding might help you in philosophy.

However if you're more in tune with Real Analysis then do that.

This is true as well, especially if you want to do the usual math. But it can also mean a lot rather different things: calculus, measure theory, analysis. I think there is no way around calculus in its basics: real in one variable, complex, real in many variables. So it's better to stand at a point where others, who arrived there by a "normal" vita also stand.

I use to quote this post: https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947
where you might find a lot of valuable tips. It's up to you to decide, which one are more helpful than others as only you know the specific situation you're in.

 

[fresh_42]

... will I need to know any calculus before I take Real Analysis ...

Yes, at least as I understand the distinction. My book on real analysis contains a lot of measure theory, and calculus are the techniques one should learn at the start.

... or Abstract Algebra?

No. You should know what polynomials are and maybe a basic understanding of the usual characteristic zero fields $\mathbb{Q},\mathbb{R},\mathbb{C}$.

Considering proofs, I recommend to have a look at some books offered on OpenStax (link as quoted) and see, if you manage to follow them.

 

[jedishrfu]

You can checkout mathispower4u.com website where there's a lot ~5000 video clips on math from pre-algebra to first year college (Calculus 1,2,3 linear algebra and differential eqns)