help

>>8515017
Turning immediately to the integration chapter and then complaining you don't understand the notation kind of go hand in hand. If you read it from the beginning (and the textbook isn't shit tier), all the notation the author uses will be defined, especially for an introductory text. As for the proofs, if you're not trying to understand them you're not going to understand them. I don't know what else to tell you.

>>8515027
I just kind of assumed that the topic could be read over in the textbook separate from the rest if you already have an understanding of it and the previous topics covered. I guess it would've been smarter to follow along through the book from the very beginning. Looking at it just intimidated me greatly since I'd like to be a math major (actuarial mathematics in particular)

Fortunately, I'm going to retake Calc 1 in college because of how shitty my HS calc class was, I'd like to get a better understanding of it.

>>8515017
Because you're a retarded high school baby who has only been exposed to basic algebra so far. Reading formal mathematics is a skill that you need to practice. So, yes, spend a bit of time trying to understand Spivak. Make sure you fully understand every single sentence and word and how each step follows logically from the previous. If you come across a term or a piece of notation you don't understand, flip back to the part of the book where he explains it. Every term has a precise definition.

It's a good thing you're starting to do this now, if you want to be a math major. The earlier you learn this skill, the better, because the math you encounter in university will almost all be formal.

>>8515039
Thanks

I know some people read preparatory books before university, like "How To Prove It", etc. Do you recommend some book like that to help prepare me in formal math? Or should I just start reading Spivak from the start?

>>8515055
Read Spivak + the free "Book of Proof" (google it).

>>8515060
Thanks for the recommendations bud

>>8515055
How to Prove It is also an excellent book. I'd read both (How to Prove It and Book of Proof), or at least read one and skim through the other one for alternative explanations. How to Prove It has better exercises, in my opinion.

>>8515055
Spivak or Apostol from the very beginning + How to Prove It or a similar text will put you well beyond most of your peers in your first year at uni (depending on where you go, obviously). You gotta do the exercises, though.

>>8515039
>>8515060
>>8515076
>>8515107
OP here, another question.

Going to Ohio State University and planning on majoring in actuarial mathematics. I'll have Calculus 1 credit, which means I'll be starting my first semester in Calc 2. This is notoriously a very hard weed out class, so I'm not sure if I should retake Calc 1 (my HS calc was shit, first math class would be one of my hardest, etc.). I feel like a legit university Calc 1 would be a lot better of a foundation for me.

What should I do? Retake Calc 1 or not? Perhaps I could take the accelerated version of it. Or would going through Spivak and Book of Proof be enough to prepare me for Calc 2?

>>8515140
Spivak certainly covers all of the material you would need for calc 2. But the bottom line is that in calc 2, they will expect you to be comfortable with everything from calc 1. They're not going to stop and wait for you to catch up. People say calc 2 is hard because throws a ton of new information at you very fast. So if you think reading a book will be enough for you, go for it. If you're not comfortable with most of the calc 1 concepts, then maybe you should retake it. Also note that the calc 1 course in college will probably go into a bit more detail than you did in high school.

>>8515017
Just giving you a warning OP: Spivak will kick your shit in. Judging from your post, you probably don't have much experience working with proofs. Spivak demands both a good grasp of Algebra and proofs; his style is also that many of the illuminating points are left for the student to discover in the problem sets, which can be difficult without guidance.

Basically, if you follow the advice in this thread, you will have to sink a lot of time building up the foundation of discrete math necessary to effectively work through Spivak's text, the chapters of which must also be methodically studied along with the problems.

All of the above is fine, as it's a rigorous entry into mathematics, but I get the feeling that you do not have much time on your hands. As such, I reccomend this free textbook: https://www.math.wisc.edu/~keisler/calc.html

I think it does a great job of holding the student's hand through gaining an intuitive and applied understanding of calculus without completely doing away with an axiomatic study of the subject. It is not nearly as rigorous as Spivak or Apostol (the intro itself states it is meant for average students) but you will be able to work through it easily, and it will surely fill in the gaps of your high school class.

After (or during) completing that book, you should read a book on proofs. How To Prove It and Book of Proof are both fine, and the latter is free: http://www.people.vcu.edu/~rhammack/BookOfProof/

After completing that, revisit Spivak.

Again, I only give this advice because I get the impression that time is a factor for you. An intuitive/applied learning of mathematics will only get you to a certain level before you will have to basically start from scratch in a rigorous fashion (definition-theorem-proof) if you want to be a mathematician.

However, in many disciplines besides math that have a mathematical foundation, you CAN fake it 'till you make it. See: statistics, engineering, and computer science.

>>8515351
My goal isn't to necessarily learn Calculus the easy way, I'm already doing that with my class. I want to start getting use to formal math.

Hijacking this thread because it's a pretty similar

What should I be doing if my HS calc class is iffy? She teaches from her own notes for the most part. Planning on majoring in comp sci (yes I know), and I will need to have a good understanding of calc.