Recent high school grad here. I'm planning on majoring in

Try a book on some easy topic like basic number theory or basic algebra, the only way to learn proofs is by doing them

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>>8957660
I found "The Book of Proof" by Richard Hammack pretty easy and informative, although I've also heard good things about "How to Prove It" by Daniel Velleman.

>>8957714
I got the latter, will check out the former, thank you.

>>8957751
I used that recently for my first majors only math class. It was like a prequel to real analysis. It's got a nice bit of logic and set theory if I remember correctly.

>>8957660
>Recent high school grad here.

Stopped reading there.

>>8957660
Like >>8957672 said, the best way to learn proof theory is to just do proofs. It's an intuition you have to develop.

If you want to go to the roots of provability, I'd suggest looking at discrete maths. The first section in Discrete Mathematics and its Applications by Kenneth Rosen does a real good job of introducing logic, and provability from there.

>>8957660
Just read Munkres. Memorize everything in the book and you'll be pretty solid.

>>8957660
MATHEMATICS: Its Content, Methods and Meaning by Kolmogorov is all you need.

Is this the new thing? Posting shitty /pol/ meme with a vague/dumb /sci/ question?

Do you retards really believe you're going to win people over as if its advertising?

I'm on a similar quest as the OP, though it's more about improving mathematical ability to the point where I'll consider minoring in it.

So far, I've tried to make a bunch of long booklists, but I realized that 1) they're often incomplete or lacking; and 2) they're pointless until I reach a sufficient level of competency to make thinking about them worthwhile anyway. I've shortened it quite a bit this time around.

This is my basic list:

>Chapter 1: Introduction to Entry-Level University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
The Art and Craft of Problem Solving - Paul Zeitz

>Chapter 2: Finishing Entry-Level University Mathematics
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Ordinary Differential Equations – Morris Tenenbaum
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe

>Chapter 3: Introduction to Proofs and Survey of Higher-Level Mathematics
How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
Mathematics: Its Content, Methods and Meaning - A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent'ev

>Chapter 4: Bringing It All Together
Calculus Vol. I & II - T. M. Apostol

<then whatever I want after that, now that I've developed basic proofing skills and mathematical ability>

What do you guys think?

>>8957660
>but have 0 background in proofs
that's the case for pretty much every high school grad unless you were in some advanced program or whatever, and your university knows this
take it easy lad, at my uni mathfags follow a general course called "intro to math" in the 1st semester that deals with things like proofs, and I can only imagine that's the case for pretty much any other place out there
as long as you keep up during the semester and don't fall behind, you won't have to do stupid things like study over the summer

>>8957660
Don't study over the summer, study hard when you get to school. You do yourself no good in college trying to get ahead of your peers. The only praise I remember a guy got in my graduating class was a top GPA because he got an A in every class... and nobody cared.

>>8957928
>the best way to learn proof theory is by doing proofs

Proof theory is not the same as knowing how to do basic algebra proofs. It is a field of mathematics that studies the formal models and their relation.

>>8958020
>That
>A /pol/ meme

You've been on here too long. The /pol/ boogeyman meme is really getting to you.

>>8958033
Not horrible, a little overly redundant and arguably ODES and PDES I'd wait until done with apostolic, but your choice

>>8958033
Nobody cares about your personal reading list. Fuck off.

>>8957660
Matters Mathematical by Herstein and Kaplansky

>>8959473

Thanks for the advice. There's a reoccurring theme that differential equations can't be explored to their fullest extent without some intro analysis. I still want to understand some basic techniques of solving differential equations such as the ones covered in a first year's difEQ course, so I'll search for an applied difEQ book with that kind of topic coverage and change my list accordingly.

>>8957660
>Could anyone recommend a good book as an introduction to proofs?

oh look it's this thread again

>>8957915
Ok
>>8958020
What were you hoping to achieve with this comment ?
>>8958080 >>8958045
I wanna take Math 55, but it requires prior experience with proofs