Preparing for math undergrad

Looking to come up with a plan to prepare for math undergrad so I can have a head start and a good understanding of what I'm going into before I just jump head first into it. Could you guys help? My current math knowledge:

>High school algebra, geometry, and precalc
>Currently taking (finish in a week) piss easy high school Calculus 1

I've done well in all my classes and have never had below an A, but again, it's a pretty shitty/ non-rigorous math program. I'd like to better prepare myself and expand my knowledge before I start undergrad. I have 8 months. This is what I was thinking

>Read through Book of Proof
>Read through How to Prove It
>Read through (not entirely) Spivak Calc
>Watch numberphile videos on the side for entertainment/ curiosity reasons (inb4 meme)

How does this sound? Any other advice or better methods to prep?

Other urls found in this thread:

math.osu.edu/sites/math.osu.edu/files/math-actuarial-science-double-major.pdf
math.osu.edu/sites/math.osu.edu/files/courses/1151_1.pdf
math.osu.edu/sites/math.osu.edu/files/courses/1161_2.pdf
math.osu.edu/sites/math.osu.edu/files/courses/1181H_1.pdf
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Don't bother. All this stuff you'll learn once you actually start.

You honestly won't be able to understand what you're going into. I'm a senior and have taken grad classes and even I barely understand what I've gotten myself into.

A better question to ask yourself is: do you get obsessed over math problems? Do you cum your pants when you see something new in math that reveals new things?

I'm being hyperbolic but the point holds.

So I shouldn't do anything before then math wise? (besides the shitty high school Statistics course I'll be doing next semester)

I feel like Spivak might not be necessary, but the stuff taught in Book of Proof/ How to Prove It seems like it's the kind of stuff that won't be taught as deeply in my college program.

You can if you want. I wouldn't waste the time. You'd just be redoing everything come first year college. Also, you'd be short changing yourself on what's arguably the more important skill: time management, handling several classes, and learning material you've never seen before, on the fly. You won't always be able to prepare for classes to come. This is what you learn at college.

And just to add, basic logic necessary for proofs is taught in college. Usually first year math course.

>A better question to ask yourself is: do you get obsessed over math problems? Do you cum your pants when you see something new in math that reveals new things?

I'd say yes, even though math sometimes does frustrate me a decent amount. A lot of math things get me excited (I annoy my family with talking about it sometimes). Some examples of things that have made me smile IRL after learning and thinking about:
>1+2+3+4..... = -1/12
>Proof of the irrationality of square root of 2
>"Ant on a rubber rope" problem and why it will actually reach the end
>Josephus problem
>Hilbert/Dragon curve

That stuff was really cool to me and got me excited, and to me seems like a good indicator that math might be for me.

depends on your uni's program, if I had to do it again i would be sure to understand how to write/do proofs before starting my degree

>depends on your uni's program

How so? I know what my program and what classes I'll be taking in general.

What uni are you going to and what program will you be going into

Uni is Ohio State University

Program, 90% this - math.osu.edu/sites/math.osu.edu/files/math-actuarial-science-double-major.pdf

Don't think I'm doing honors.

Oh very good choice. Their grad program is ranked about 28th in the country for math. It's huge too so there will be lots of research interest.

It's the perfect school for me in almost every way.

Just not entirely sure what track to go with entirely. I like math but ActSci looked like it'd be better job wise, since I don't want to go into academia. I have tons of options of what I can do and I'm not sure.
>ActSci
>ActSci + Math
>ActSci + Math minor
>ActSci + __ minor (computer science, economics, statistics)
>Math + Stats minor

I always see people recommending undergrads to learn proofs. What do they mean by "proofs"? Metamathematics (logic) ?

You'll have a head start for maybe 2 weeks.

Basically. Many people, when they get into college, don't know what to do when presented with a problem that starts with "prove that."

well, in some cases even the intro courses are proof based, for example in my uni calc 1 was taught using spivak wich can be really hard for someone with no prooving experience. On the other hand some time this courses are more computation based, so you don't relly need any prooving abilities

this In highschool all we did were problems about calculating something (roots, derivative, integral, etc.) Then in college you are presented with something like "Show that the 0 elent is unique", it's not hard but I was not used to those type of problems.

Moreso than any other type of course, I found that simply going with the flow is adequate. As long as you're not behind now, you'll be fine. It doesn't matter how much you prepare, you're gauranteed to get problems that make you scratch your head and struggle through. That's the best thing about math in my opinion. You can brush up on common types of proof and how to apply them If you want, but it isn't necessary and probably won't be terribly helpful.

Math will never stop being frustrating. Any good theorem or result, something that really helps you understand a topic, will be hard to understand at first. But if you really enjoy math, then go for it. That's what really matters above all.

Proofs basically ARE mathematics, you just haven't realized it yet.

It's so intrinsic to the mathematical mind that the two are basically the same thing.

Though, what people say about it is misleading. The whole "le endless rigor" thing is a meme. They teach beginning undergraduates to be super rigorous so they can train their minds properly. When you get into graduate school, proofs are more about convincing yourself why a statement is true, because absolute rigor is something mathematicians absolutely do not do, we handwave alot because we know the rigor could be there if one cared enough. Anyone who says otherwise is an undergrad. So to iterate: proofs exist to convince people the statement is necessarily true. They don't exist as some abstract, fluffy perfect logical ideal.

So when people say "learn proofs", what they mean is, you have to train your mind to not just trust things are true. When you open basically any calculus text, they throw constant theorems at you without explaining or justifying them. A mathematician always stops and attempts to justify statements as much as can be done. The intermediate value theorem is obvious, but explaining why it must be true is not at all obvious until you take some analysis and see the proofs layed out in front of you. Same with the first isomorphism theorem, fundamental theorem of algebra, whatever, truth is a different category from the methods we use to establish truth.

Then you notice other things, like how proof by contradiction sucks, not because there's any metalogical memery that makes it worse, but because it doesn't often help you understand why things are true. We can prove their are infinitely many primes by contradiction, yet we don't even have a nice function which outputs primes. So the proof doesn't actually tell us much.

Anyway. Hope this isn't too rambly.

Just turn back. There is nothing to be gained from a math degree except for unemployment and disillusionment. Want to go to grad school? I hope you're a golden boy who has no ambitions outside of academia. You have hobbies? Nope, fuck you. Get back to research, baby boy. There's always someone studying harder than you and they will take all your research and teaching opportunities. I hope you are okay with sucking professor dick. They are autistic retards who think mathematical ability is the be-all end-all? Better pretend to have that same attitude or else you're done-zo. Only golden boys succeed in academia.

You want to go to industry? Good luck busting your ass to learn another discipline while also doing your math courses. Other students take 10+ courses of that shit and don't have to worry about analysis or algebra. What makes you think you can compete? No one hiring gives a fuck about your "smart" degree. They want you to be able to do something. They want you to have skills---and pro tip: being 'trainable" isn't a skill, fucko. It's the bare minimum. A mythmatics degree will get you as many "thanks, but no thanks" responses as you can imagine.

You're getting a math degree? I hope that math is really your passion. I hope you are currently studying mathematics for 5+ hours a day and still can't get enough. I hope you've considered doing this for the next 40+ years and said "Yeah, studying this discipline most of my waking time on this earth will make this a life well spent!" I really hope you aren't doing it for "prestige" or because math majors are "smart." I really hope you aren't doing it because you think mythmatics is "beautiful" or "elegant." You won't find any of that by studying mythmatics.

OP here. Another question. I'll have credit for Calculus 1, but would like to retake a legit version of it before jumping into Calculus 2 (a notorious weed out class at OSU).

OSU offers regular Calc 1, Accelerrated Calc 1, and Honors Calc 1.. and I'm not sure which one to go into. Here are the three courses:
>math.osu.edu/sites/math.osu.edu/files/courses/1151_1.pdf
>math.osu.edu/sites/math.osu.edu/files/courses/1161_2.pdf
>math.osu.edu/sites/math.osu.edu/files/courses/1181H_1.pdf

Thoughts?