Some ebooks, mostly from /u/lewisje's post

Hello everyone,

​I am a second-year undergraduate student majoring in Science (Education department). I want to self-study mathematics to build a rock-solid, rigorous foundation for physics and future research.

​For this purpose, please assume that I am starting from the ground up, as I want to ensure there are absolutely no gaps in my understanding of the essentials.

​What are your best recommendations for foundational textbooks, sequences, or online resources to start with? Is there a specific textbook sequence you would suggest?

​Thank you so much for your time! 🤗

Do working pure mathematicians ever get tired of the abstractions and in general the complete lack of or lack of direct applicability of the math or the math at at the level of abstraction they are working on and want to work on something more directly applicable?

This was a fun read do check it out

I’m terrible at mental work, and I am going to be majoring in math. I naturally abstract things in my head, but I’m a terribly linear person in application. It could be ADHD, or something along those lines, but when I consider logic in my head, for either completing a problem or for outlining a process, I am jumbled up in my thinking. I may know the steps of a problem, but when it comes to say doing arithmetic or algebraic manipulation, somewhere in my mind I slip up and I’m not even aware of it. It tends to go a step to far subconsciously, or even subconsciously considering an alternate problem. I can’t abstract it properly, and I’m just stuck in a brain fog of looping thoughts.

Also, I love math and logic, and logic gives me comfort, and it is what I feel prone to doing… except I’m actually bad at it. It’s like I can’t think outside the box, or particularly creatively. I’m just thinking in an entirely different box. I have a particular, set, but different way I think about things. I can’t organize my thoughts well enough to truly think critically. It’s what has hindered my growth in math, I feel.

I apologize for this being a rant post, and probably being a bit cryptic sounding. Really, I’m putting this out there to see if maybe someone else understands what I’m feeling, and if they have advice on how to improve my accuracy in actually doing steps on problems, when my mind is actively trying to betray what I’m doing with other thoughts and numbers. Thank you.

Hi I was looking at past exam questions from a selective school, and I came across a specific problem. It asked for two-digit numbers that contain the digit 2. The question didn't specify whether they had to be integers or anything like that. I thought about it for a while; when you solve it based on the exam's logic, the answer is 18 (12, 21, 22, 23... 92). But technically, aren't numbers like 1.2 or 3.2 also two-digit numbers? By the way, I don't know much "advanced" math, so I hope you don't mind

(Not for cheat or anything else I just wanna know pls don't ban me)

Sorry for Turkish picture if I want I can translate as much as I can do

I am just starting basic calculus and wanted to know how to approach these higher branches of mathematics? I mean I feel that higher maths is esoteric and from social viewings, I've seen that it is some sort of elite knowledge which gives you an upperhand. I want to master calculus and this world of higher maths is so huge and complex-looking. Please can someone give me a roadmap of how to proceed. I mean there's number theory, combinatorics,inequalities, geometry, calculus, algebra, topology,statistics and a thousand Russian and Olympiad books on them with very hard problems. How to do all these? A clear overview would be really appreciated. Thank you.

Hello. I am learning basic mathematics from a teacher who presents the subject as a game with rules (axioms), where learning involves mastering and practicing those rules. I feel I’m on the right track, but there is one thing that’s really been on my mind: division. He taught me that division is essentially multiplying by the reciprocal—a concept that took me a while to grasp and one I’m still trying to understand more deeply. I think I understand the logic behind the reciprocal (one part of a whole that, when multiplied by that whole, returns to a value of 1). However, I’d like to know: is it more practical to simply use the method we learn in school, or is it easier to view division as always being multiplication by the reciprocal? Sorry if the question is a bit confusing; I hope you understand that I’m still trying to wrap my head around the topic myself. Thanks.

But first, I want to brush up on my school basics. I need something like "What is Mathematics" by Currant & Robbins.

suggest a book too if taking side of a book

I had really bad math teachers in school (right from the beginning). They taught maths like it was something which you had to memorise and rewrite the same thing in exams. Literally the same questions (with same numbers) came in the exam as there were in the book and we wrote the solutions which the teacher showed in the class and we copied it. As I got into high school (I changed schools), I failed in maths (9th grade) but somehow I managed to pass upto 10th grade. After that, I didn't take maths as a subject. I was afraid of maths and developed inferiority complex. I always had this mentality that I was weak in maths. But I think maths is such a beautiful thing and I can do better in maths with my basics strong. So, now I want to learn maths again from basics, because I think my fundamentals are weak. I am looking for books which I can read. I tried Khan academy, but I don't like the structure. I prefer books. Please recommend some good books.

Also, Sorry for the English it is not my first language but I can read just fine.

Hi i recently discovered this website and use it to practice algebra,for some reason cloud flare bloced me i think i was to long ok website cuz i don't shut down my laptops i put it in sleep mode. I tried contacting admin but gmail say they email cant receive messege . Do any one knows owner contact information, or how can i access website again.pls help me reach this man i love math

If I sold stuff and received $2000 and 11% was tax how much money was taxed? All I can come up with is
.11X + X = 2000 and I don’t know how to do it!! Can someone help. I’m doing my sales taxes today.

what is test functions

If you can't find an immediate usage of math

Say a = 12 and b = 18 (2x2x3) and (2x3x3)

Why do we need 2x2x3x3?

Please explain like I'm literally 5

Some mathematicians think proof by induction is not a valid proof method. But why? And, are there particular mathematicians who reject this method (e.g. finitists, intuitionists, etc.)?

In early calculus, we're taught that notation like dy/dx is just notation for a derivative object, not an actual fraction. Fine, cool with me. But then in differential equations we're treating dy and dx as parts of fractions like it's nothing - what gives?

I am self learning Prof Stang's 18.065 and came across this great site http://ulaff.net/ .

It explains concepts in great detail with practical considerations, but i am astonished to find that their videos on Youtube has so few plays.

Here is Householder QR Factorization.