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599 advice questions.

I am having the option of take one of two courses: Measure Theory or Electromagnetism (physics course). The duration time is two months for both of them. I know that Measure Theory it is not as easy ...

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...

I was wondering what would be a list of Applied Math courses (sort of like a road-map for an Applied Math student interested in a Applied Math PhD) which preferably contains absolutely essential ...

I recently became interested in galois cohomology, but I don't know if I have enough math to learn about it or where to start learning it. What should I know before I start learning about Galois ...

I am a high school student with two years left until I graduate. I managed to move through my high school math curriculum quicker than expected and am on track to take AP Calculus AB this coming ...

I would like to find a book that introduces me gently to the subject of stochastic processes without sacrificing mathematical rigor. It would be great if the book has lots of examples and that the ...

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots ...

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...

I am a beginning graduate student in Mathematics. When I was in school, there were lots of math programs like summer programs to hone problem solving skills. But at the graduate level, I cannot really ...

It is now nearing summer time and as consequence, I will have a lot of time on my hands. As such I've been trying to figure out how to spend my time in a productive manner. However, I have had a hard ...

I recently started studying advanced mathematics on my own, after taking two classes in college (discrete math and advanced mathematical logic) that spurred my interest in the topic. However, I am ...

I am originally from India and there the mathematical curriculum was all about the formulas and not about the understanding.I used to excel at those exams,but since I have moved to Europe I have been ...

I am a layman interested in mathematics, and I would like to hear mathematicians' views on the following: Is it normal to be picky about mathematical stuff you find interesting? I ask because 80% of ...

I am looking for a comprehensive and introductory (lot of examples, exercises) book that deals with topics like group theory, Dirichlet characters etc. Thanks for the advice.

I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research sounds strange to me. What does math research entail exactly?...

I'm working on a project that requires the use of large data sets; vectors and matrices with millions of entries. Normally I've done my projects (small scale stuff) with Matlab and never had an issue. ...

For my Complex Analysis course, we are to look up applications of Complex Numbers in the real world. The semester has just started and I am still new to the complex field. I want to get a head start ...

I have taken course in measure theory based from Royden's "Real Analysis" last year and now am reviewing the subject using Folland. However, neither book seems to have many "computational" problems. ...

Can one take a probability elective course without taking any graph theory or advanced combinatorics class before? lets assume that one knows already the basic difference between variation, ...

How could I write $y=\ln(x)+x$ as $x^2=...$ Since there might be another solution to this problem I'll give some background. So I had a math test yesterday where they wanted you to calculate the ...

I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on ...

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic (...

I have completed my B.Sc. in math and will be starting M.Sc. math in a few months. During my undergraduate classes I found the real analysis and general topology courses the most interesting and the ...

I am planning to take Differential equations next semester, but due to a timetable issue I want to study most of it this summer in my spare time to make it easier. These are the Topics that will be ...

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...

I have built a reading list based on recommendations and suggestions found on several posts from this community. My intention is to use this reading list to acquire a good understanding about ...

I'm an Industrial Engineering graduate looking to make a switch into Pure Math at the Masters Level/PhD. I have undergrad experience in Calculus (upto Differential Equations) and Probability and ...

I'll major in math at a local University. I've finished High School Calculus and I've self-studied very basic Multivariable Calculus, Linear Algebra, and Real Analysis. I've watched video lectures of ...

First, I'm not trying to make this sound like a "poor-me" story. I understand fully that every decision I've made leading to this is my fault. I am genuinely looking for advice. So, I am a high ...

I am a senior in high school who has taught myself Calculus BC and I got a 5. However, I have taken all the math I can at my school. I also taught myself multi-variable calculus and much of ...

I did well at Mathematics at school (top 0.1% in the country, approximately), however I stopped studying it when I was 16. Since then I've studied a couple of highly specific mathematics modules in ...

I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a ...

I taught myself how to count before I even learned how to talk or read. Playing with numbers was all I did when I was young. I didn't have anyone to foster that type of passion that I believe I still ...

$$\left(\sqrt{\sum_{k=0}^{2i-1} 10^k} - 3\sum_{k=0}^{2i-1}\frac{ 10^k}{10^i}\right)10^{i+1}=b_i,\qquad i\in\Bbb{N^+}$$ I tried expressing $b_i$ as a function, which I would then derive (using Maple/...

So, my background in Number Theory is - Elementary Number Theory(that I did mainly from David Burton's text) and Serre's A course in Arithmetic(first half on algebraic methods that included p-adic ...

Find a function $f: X \rightarrow Y$ between metric spaces $X$ and $Y$ that is not continuous but has the property that for each closed ball $B$ of $Y, f^{-1}(B)$ is closed in $X$ Solution Attempt: ...

I am a 13 year old boy from Hong Kong, My dad is a math teacher which probably accounts for SOME of my interest in math. I am really interested in math. I self-taught myself (with little help form my ...

I'm currently taking a Discrete probability course at my University.It isn't going to well,the grad student taking the place of the professor is not able to teach the material effectively.Nor are ...

My university has released the modules that I am available to take next year in my final year of undergrad. A PDF was also provided grouping the modules into their respective mathematical topics. I'...

I’m trying to prepare for further study in Analysis and was wondering what advice you all would give. I have read (most of) Abbott’s Understanding Analysis and have started Rudin’s Principles of ...

It's the first time in a math class that I am allowed to utilize an index card for a test. I realize this is subjective, but I am not intending to sound naive or insincere. I am genuinely curious as ...

Related to this question. This problem is the root reason why I was never good at math - I am horrible at all forms of simplification in mathematics, hence I am bad at proofs. The problem is that ...

I am a high-school student. I have developed a recent affection towards mathematics (especially proofs), although I was always into logic (I've been a programmer since the age of eight). Now I am ...

Here's my problem. I'm studying math and when I really work hard, I think I understand things very good, but that comes at a big cost: in the last few years, I've had practically zero physical ...

I know that several similar questions to this one have already been posted, but I can't find an answer that really suits me and my needs and after some research and reading I'm starting to feel quite ...

I have studied mathematics upto High school level and also studied Calculus 1 and 2. I also have studied basic ODE. Recently i read a book "The Heart of Mathematics : Invitation to effective thinking"....

I am trying to learn about tensor products of modules in Dummit and Foote, but I am having trouble understanding their exposition. I am looking for suggestions for other texts that have good ...

I'm prepared for the competitive exam like this (a sample question). In order to solve the problems, first to familiarize with the prerequisite for the each concept. It's ok! My problem is: If I'm ...

I am reading Abstract Algebra by Dummit anfd Foote. I have already taken an introductory course in linear algebra, mostly at the level of Strang's MIT OCW Linear Algebra. My question is: Can I skip '...

I want to write that "this transformation changes either rank of effective matrix, or norm of effective matrix, or both" I want to avoid repeating "of effective matrix". How can I do this

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