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I heard this podcast the other day where it was stated that mathematicians at the higher levels don't care about applications in the slightest. First I thought about myself and my peers, and figured that is accurate. But then I remembered I had this number theory professor who said he would actually avoid research topics that are "dangerously close to applicability". Hbu guys?

When people ask me what my master thesis is about, I have no idea what to tell them. By people I mean, people with no background in pure math, no matter their intellect or education, from a shop assistant up to an engineer. I just mumble the title of my thesis and the subject within math, which of course they don't know shit about, and I have no idea how to go on. Feels like explaining even the simplest concepts is just unrealistic.

I don't know if it's an impossible task to talk about mathematics, or is it just my lack of communication skills... I spent so much time thinking about it but didn't get any closer to a solution.

Any suggestions? Or maybe any explanation to why it is impossible.

Personally, when I hear mathematicians appear in podcasts, tv-shows, etc, they make things sound so dumb, in order to make it more understandable that just makes my stomach turn. And also I don't think it helps understanding, just makes it more relatable, perhaps?

I have been researching the fourth dimension recently and I have begun to wonder how a 2d object would interact with a 3d one. For this to be possible, would it be ok to assume that instead of having no volume, the 2d being instead has an infinitely small volume. This would also mean that it would be impossible(without infinite energy) for the 2d object to push the 3d object, and the 3d object would easily affect the 2d object.

Hello there, I’m a senior in high school. My unrealistic goal is to master differential geometry and everything leading up to it. A couple of months ago my only algebraic skills were basic solving for x problems, and I knew the distributive property, that’s it. I’m currently failing Precalculus despite my comprehension of the basic trig we are being taught, due to work ethic issues. I’m failing Ap Physics 1 due to both work ethic and comprehension issues, I am extremely unqualified for that class, and I feel that both my Precalculus and Physics teachers believe me to be their stupidest and most troubled student. I’m doing this for 4 reasons. 1. I want to prove certain people wrong. 2. I want to prove to myself that I can learn anything. 3. I want to go somewhere where nobody else has gone before. 4. Ever since I was a little boy I was fascinated by all the complex math I’d see in movies like interstellar, The theory of everything, a beautiful mind, etc. and I’ve always wanted to understand what the hell they’re actually writing and what it means. I cant promise you that I’ll achieve my goal, but if I do there’s only one way that I’ll have been able to achieve it. A reason I’ll explain when and if I get there. I will document the entire journey with a daily post. I’m scared.

So, is there something out there to take advantage of diff geometry, Galois theory or algebraic topology? I am looking for an idea that only a math professional could implement.

I’m a marine engineer student And I know that engineering is nothing more than 90% of calculus and physics So that’s why I’m here I’m willing to learn calculus from scratch and as I know that to be good in calculus I need to relearn / review Some fundamentals of algebra , trigonometry, and few of geometry

So my question here is Is there any free source or book do you recommend?

Hi everyone, thanks for reading my post. I’m looking for real analysis advice. I am an undergraduate math student. Currently I’m enrolled in an intro to proofs course. But I have read the first 11 chapters of the book for this course( Chartrands Mathematical Proofs) and am getting bored. Therefore, I decided to attempt to self study real analysis. My school uses Understanding Analysis by Stephen Abbot. The problem is, I read the sections and understand the material or so I think, but when it gets to the excersices, most of the time I have NO CLUE where to begin. It’s very demotivating and frustrating. I am not sure if there is a better approach or if I should just wait to take the real course instead of repeatedly failing being able to do any excersices.

What does everyone think?

I intend to write my graduation thesis on Predicate Logic, which is part of the requirements for obtaining a Bachelor’s degree in Mathematics, specifically in predicate logic because I am very interested in this field. However, the extent of my knowledge is currently insufficient to write a solid thesis, so I need intermediate and advanced books to study more deeply, especially concerning the meaning of predicates and the relationship between the predicate and the subject. I understand this concept intuitively, but no specific definition of this predicative relationship comes to mind except that it is a function that maps variables to a set of true and false. Nevertheless, I wonder how this function can be defined precisely. I am also particularly interested in studying the algebra of predicate logic. The courses I have taken in logic are:

1. Logic and Set Theory I in college.
2. Logic and Set Theory II in college.
3. I am well-versed in the ZFC model.
4. I have knowledge of Aristotelian logic and have read several books on this topic.

Hi. IM looking for a book that will teach me all the basic signology in mathematics, I just need it to skim through quickly so that I can Google the exact particulars that I want to get deeply into. It's with much consideration that I find It less prudent for it to be about presenting me with problems, and instead presenting with the solutions used throughout history to commit with the purveyance of mathematics.

I will be deeply grateful for any assistance and humbly thank you.

We have a group that wants to create an arithmetic number system or arithmetic base based on cognitive things like consciousness arithmetic and self-awareness. Does anybody have any suggestions on this? In short, we are trying to create an arithmetic equivalent of human consciousness with the help of number theory and algebraic number theory, systems like p-adic etc. are involved but still, does anyone want to help with something that could have potential for a perfect AI algorithm (just suggest arithmetic bases and growth functions would be enough) that could simulate an arithmetic human consciousness from 0 and create the concept of consciousness. Please let me know if anyone is willing to help roughly. People who have knowledge and help in algebraic number theory and Number theory please join our discord server, we want to create arithmetic diagrams and algebraic expressions together (our main goal is to have a new arithmetic constant and arithmetic system that can be perfect for everything, so we want to make something like an algebraic algorithm with an advanced arithmetic base) we are also working on new types of multiplicative algorithms etc. We are also working on new types of multiplicative algorithms etc. You can also independently propose your own mathematical ideas and open discussions on everything mathematical.

Our Discord Server : https://discord.gg/5TsGQVXJNB

I am an undergraduate student, I am going to start reading group on analysis as second course so if anyone interested DM.

Textbook:

1. Tao I and Tao II
2. Rudin for excercise
3. Carothers Real Analysis book

I hope you all are doing well! I am currently trying to deepen my understanding of some equations connected to the Pearson correlation coefficient, but I am having a bit of trouble grasping how they are equivalent. Specifically, I'm looking at the following equations:

r xy = r yŷ (that is, the bivariate correlation between x and y equals the bivariate correlation between y and ŷ )
r ^2 xy =S^2ŷ /S^2y ((which says that the squared correlation between X and Y equals the ratio of the variance of the predicted scores over the variance of the observed scores on Y.)
I understand the basic idea of the Pearson correlation coefficient r and how it measures the linear relationship between two variables. However, I'm struggling to see how these equations transform and show that they are equivalent.

Could someone kindly break down these equations and show through transformations that they indeed represent the same elements respectively? Any insights, step-by-step explanations, or examples would be invaluable to my understanding.

Thank you so much in advance!

Title pretty much. Doesn't matter if the book is proof-based or not, just looking for recommendations for a good textbook/resource for a first pass at ODEs