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Math notes to take you from one year of college calculus to grad student level
61–70 of 70 posts
Re: Math notes to take you from one year of college calculus to grad student level
#62You know what I would like? Math material that is less concise. Some math concepts are too dense to grasp without first understanding the reasoning behind it, the axioms it's based on, real-world applications, metaphors, diagrams... heck, even the history behind the mathematician helps sometimes (e.g., knowing Newton was a theologist is relevant to understand some things about classic physics [1]). In fact, I love ho…
That's what university is for. ~There is no royal road to mathematics~
Let me guess, you have a major in math.
Re: Math notes to take you from one year of college calculus to grad student level
#63You know what I would like? Math material that is less concise. Some math concepts are too dense to grasp without first understanding the reasoning behind it, the axioms it's based on, real-world applications, metaphors, diagrams... heck, even the history behind the mathematician helps sometimes (e.g., knowing Newton was a theologist is relevant to understand some things about classic physics [1]). In fact, I love ho…
I think what you're looking for are textbooks.
You will have my eternal gratitude if you are kind enough to name one that doesn't suck.
Re: Math notes to take you from one year of college calculus to grad student level
#64I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…
probably not as good as a well written textbook with careful examples and exercises Name one. While I agree that this document (probably) won't compensate for a more complete education, including textbooks, the truth of the matter is that most textbooks (even many highly regarded ones) are horrible for learning on one's own. Rigorous and sound, yes, but many are bad for pedagogy, and even worse for self-teaching. A g…
Rudin's Analysis book is very good, so is Lang's Algebra. In college I found I learned much more from the textbook than from lectures
Re: Math notes to take you from one year of college calculus to grad student level
#65Earlier quoted context omitted.
I think what you're looking for are textbooks.
You will have my eternal gratitude if you are kind enough to name one that doesn't suck.
Elementary Analysis: The Theory of Calculus by Ross
IMHO very easy, introductory book on proofs and basic analysis. It's not a novel, you will need some effort to think through exercises.
Getting through this book is like unlocking GODMODE on the first 2 years of college math courses (Calculus mostly).
Re: Math notes to take you from one year of college calculus to grad student level
#66Looks like a very good summary of mathematical physics -- from ODEs all the way to Lie algebras / symmetries which are very important in quantum field theory and other advanced physics subjects.
Would it be possible to have a version in the computer moder font and without so much space between the lines. I would print this and try to read it.
I never liked/respected differential equations much, but this looks like a tutorial (300+ pages!!!) which could turn around my opinion.
Re: Math notes to take you from one year of college calculus to grad student level
#67Earlier quoted context omitted.
> For instance, a "burning" desire may be sufficient to motivate a 22 year old to study mathematics, however that same desire in a 44 year old might not overcome the pressures, realities and obligations of life, work & family. You'd be surprised at how many there are. I'm mid-30s and I've recently finished a maths degree via distance learning (Open University in the UK). During the time I've been studying I've moved…
So you're actually proving the point: you weren't born with this burning desire, you didn't learn it in college or high school or (as burning desire would indicate) when you were twelve - you waited until now, and were perfectly capable of learning it once your motivations changed. As they do, as time passes. Anybody out of their 20s will know that.
I had a desire to study it since I was young. I excelled at both Comp Sci and Maths during school[1]. Studied both all the way prior to University and then had to pick one (I didn't want to do a joint degree as I wanted to study one in depth rather than two partially).
A Comp Sci degree was going to be a bigger advantage for the kind of job I was looking for and so that won. The desire to study Maths has always been there, it's just taken a while since leaving University until I was in a position where I had the time/money to study it in my spare time.
[1] First computer was a ZX81 when I was just 5 years' old.
Re: Math notes to take you from one year of college calculus to grad student level
#68Re: Math notes to take you from one year of college calculus to grad student level
#69Earlier quoted context omitted.
You will have my eternal gratitude if you are kind enough to name one that doesn't suck.
Rudin, Apostol, Spivak, Lang, Munkres ..
I'd like to say that Apostol's "Introduction to Analytic Number Theory" is bloody awful and is in no way suitable to be an introduction to analytic number theory. A reference book of proofs of some common theorems, yes, but an introduction? No.
Re: Math notes to take you from one year of college calculus to grad student level
#70I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…
if you really wanted to learn this material you would have started already. People change.
I woke up one day 4 years ago and realised that I wanted to learn mathematics. I realised I had always wanted to learn Mathematics - only I had never before understood what it actually was. I now have a MSc in mathematics and I am getting to the point where I am able to bring that knowledge to bear on my satellite interests, mathematical physics and my own ideas for GAI.
It is documents like this which have helped me get to here and will take me to where I want to be.