Hello, I've just finished high school and will take a year off. In this time, I'm going to work to save up some money and want to learn math as a hobby on the side.
I understand high school math well, but I'm not really excellent..I've learned from the beginnings of set theory up to integrals and undestand basic problems, however at some more tricky puzzles I can get lost and have no idea what step to take next. I have no idea where to go next, no guidance at all. How good does my high school math has to be to continue with advanced mathematics? Where should I go next?
I've watched this video ''The Map of Mathematics'' (youtube.com/watch?v=OmJ-4B-mS-Y) in particular, but have no idea what to start with.
Can anyone recommend some good books to start learning or youtube videos? Or even which topic to begin with? I'd highly appreciate all help.
So, should I study from the top of the list to the end? I've also read few things and it looks super fucking hard to understand, because:
1.) English isn't my main language 2.) I can't even put mathematical logic into my own language, even though I understand what I have to do
I think trying to push my head through these hard walls will be waste of time really.. It could be done of course, but I need something more simple and easy to at least know what the hell I'm reading..
No offense, thanks for help and will look even further into this, but from the first glance it's seems a little bit too much. Not that I'm not willing to work for it, but yeah, if anyone know something more easy ongoing and entertaining, I'd be pleased to know so.
Jack Phillips
definitely learn math in english if you can, most scientists and mathematicians use english.
I guess French or German would be fine too.
The reason is, for any learning, you internalize concepts in the framework of whatever language you learn them in; therefore, you would be better able to communicate with maths in the language you learned math in.
So, I could be a native english speaker, go to spain to study math, then come to the united states. I would probably speak english and do math in spanish for the rest of my life.
Sounds great! Basically what you will encounter in university (engineering, maths or physics) is:
Logic (definitely start with that): A and B is true if A is true and B is true. etc.
Linear Algebra: Vector space algebra is like a sophisticated geometry. You work with functions that map a vector to another vector, linearly.
Analysis: Basically what you did in High school, but in a more detailed way.
A good way to start, i would suggest, is to simply buy a textbook about Analysis or Linear Algebra. (or pdf) There are tons of textbooks about this.
A key advice: Mathematics cannot be learned by input-learning only. You cannot just read or watch it. You NEED to do exercises.
What interests you most? what do you want to study?
Ethan Anderson
OP, careful with this guy's advice.
Analysis and Linear Algebra are BIG topics, like REALLY BIG.
If I could describe analysis in a few words it would be: "Behind the scenes of calculus". It develops a framework that makes calculus rigorous, but it is still more than just that.
the archetypal book for starting analysis is Baby Rudin, but it would be completely impenetrable at your level. It requires great knowledge of proofs and basic calculus. Especially the fundamental concepts of calculus, not at all the applications of calculus.
As for linear algebra? there are some good intro books out there that are totally accessible to you, but you have to be careful. like I said, they are big topics.
To learn this subject, get a book that starts with the basic matrix algebra. I learned on Otto Bretscher's "Linear Algebra with Applications". This book is good for beginners, it starts with basic matrix algebra and then builds up structures from there. It also eschews a lot of proper mathematical jargon in favor of more familiar terms.
Cooper Martin
Thank you, both of you. I went to engineering gymnasium for high school, because I wanted to be an architect when I finished elementary school. However, I absolutely hate engineering after 4 years of studying, which I blame partly our teacher, but whatever.. I'm not sure what to go to college for really, but I'm going to computer science probablly.. Not because I like it really, but it does provide nice future and I have a lot of autistic friends that are 19 and go to college while working and making 1k€ easily as side job (which is a above avarage salary for where I'm from). So now that I don't want to become architect anymore and can learn whole programming on youtube and from my friends that work already, I'm going into that. However, I really want to work on my math skills also, it feels great understanding and solving problems, especially hard ones. I feel like I understand world/nature better the more I understand math.
Nathan Fisher
>2.) I can't even put mathematical logic into my own language, even though I understand what I have to do
Are you African?
Alexander Diaz
>Chapter 1: Introduction to Entry-Level Mathematics, P. I 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: Introduction to Entry-Level Mathematics, P. II Linear Algebra and Its Applications - David C. Lay Calculus of Several Variables - Serge Lang Applied Differential Equations by Vladimir A. Dobrushkin
>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: The First Test of Mathematical Maturity Calculus Vol. I & II - T. M. Apostol Analysis I & II - Terrance Tao
Owen Flores
lol brainlet
Angel Flores
>I've learned from the beginnings of set theory up to integrals
wat?
Cameron Bell
whatever you do OP, don't follow this
Noah Johnson
t. Rudin-worshipping autist
Noah Gray
Every fucking thread with this list has the same string of replies. Stop arguing with yourself and trying to force this whole thing as a meme, you absolute autist.
Jayden Roberts
I'm not arguing with myself. I do say the same shit to detractors, that it's somebody who would rather start a beginner with Baby or Papa Rudin, because that's the problem 70% of the time. The other 30% of the time is just a kneejerking faggot who doesn't have any real criticism and is afraid of seeing somebody learn some math.
I'd like to see somebody give some real criticism, like a better curriculum or something. Usually, it's always the same shit: 1) muh rigor not early enough; 2) muh book list too long and I cant pick and choose according to my needs; and 3) pointless kvetching for the sake of it. Everybody else who's looking to seriously learn math here ends up enjoying it.
Zachary Martinez
inb4 another raging faggot thinks this is all the same person even though it's most likely impossible given the post to poster ratio
