Mathematics Definition and 995 Threads

Hi, I recently have rekindled my love for mathematics while in University for Political Science. I have reviewed all of my old pre cal books, but now I want to start learning Calculus eventually on to more difficult things like PDEs and things of that nature. I like having a series of textbooks...

I am an undergrad in physics and math (pure). I want to do msc in Applied mathematics . There are few things that worry me : 1. Topology, complex analysis, differential equations, calculus, Probability, 3 Analysis and 3 Algebra - these are roughly my courses. I didn’t take any “applied” kind of...

I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as ' a ' instead of ' a / b ' . ------ b

I have Thomas and Finney's book on Calculus for reference. Am I prepared for Feynman's Lectures? I've studied physics for two years in high school.

I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation. It is in aid...

I'm talking about "Mathematical Tools for Physics by James Nearing". https://www.amazon.com/dp/048648212X/?tag=pfamazon01-20 it seems it cover lots of math... but it feels like it's just a reference book.. will it be enough? or should i get more specialized books to learn each subject thoroughly?

Homework Statement A cyclist traveling east at 8 km/hr finds that the wind appears to blow directly from the north. On doubling his speed it appears to blow from the north-east.. Find the actual velocity of the wind.[/B]Homework Equations Wind(relative) = Wind(Actual) - Velocity(cyclist)...

Physics, Economists, Biologists, Astronomers and my brother all love the word "Random", as that allows allows them to get out of clockwork processes and allow for variations due to unknowns or whatever else. But, how does a Mathematician reconcile itself with the idea of random? There's no...

I found this interesting article https://blogs.ams.org/matheducation/2019/02/14/mathematics-gatekeeper-or-gateway written by Mark Saul So the question is: What is mathematics: A necessary evil or the universal language physics is written with? If you tune in on a random tv quiz show and wait...

Can an expanding balloon be considered a control volume?

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough The Representations Continue reading the Original Blog Post.

Good day to you all, dear dedicated scientists! My name is Daniel and I'm in my last semester of undergraduate mathematics studies, in Universidad de los Andes, Colombia. Although I'm always eager to discuss math and science, I'm also very interested in discussing the non-scientific aspects...

I found this interesting article about the balance between mathematical creativity and necessary content. https://blogs.ams.org/matheducation/2019/01/15/reflections-on-teaching-for-mathematical-creativity/ I don't want to make the discussion exclusively a pedagogic one, which is why I posted...

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough The Structures Continue reading the Original Blog Post.

This is perhaps the single most important mathematical physics papers I have ever read; I think everyone - especially (theoretical) physicists - interested in theoretical physics should read it. In fact, read it now before reading the rest of the thread: Klainerman 2010, PDE as a Unified Subject...

Greg Bernhardt submitted a new blog post Lie Algebras: A Walkthrough the Basics Continue reading the Original Blog Post.

Hello, I am a Belgian master in physics and astronomy with a couple of years of working experience under his belt, who recently decided to obtain a second master in statistics. Normally I should graduate in 2020. My goal is to become a data scientist, but preferably within a scientific context...

Having read many times about normalizing quantum mechanics to agree with classical equations, can you please give an explanation or an example of the mathematics involved? I have looked in Wikipedia, but was unable to find anything. Maybe I am using the wrong keywords. Is there an article or an...

Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)

When The denominator is checked, the poles seem to be at Sin(πz²)=0, Which means πz²=nπ ⇒z=√n for (n=0,±1,±2...) but in the solution of this problem, it says that, for n=0 it would be simple pole since in the Laurent expansion of (z∕Sin(πz²)) about z=0 contains the highest negative power to be...

I am Baibhab Bose, from India. I have just completed Masters in Physics from University of Delhi. I hope to delve into deeper insightful discussions on physics and mathematics and would like that there would be no 'Poles' of any order in the space of my understandings which is inside the...

Imagine two smooth scalar functions defined on the surface of a sphere. Is it possible to find a smooth coordinate translation that slides the values of the first function over the sphere, until it becomes equal to the second function everywhere? It seems reasonable that if the number of...

When you're studying abstract mathematics what are some effective techniques to use? When studying something like abstract algebra do you think something like this sounds reasonable? First learn the relevant section until you reach the exercises. While learning that write down the main...

One of the last classes I'm taking before finishing my degrees as an undergraduate is abstract algebra. My professor uses the textbook 'Contemporary Abstract Algebra' by Joseph Gallian. The book isn't written terribly nor is the teacher a poor one, but I just find this subject so...

I have little exposure to mathematics beyond high school algebra and physics, but I have become increasingly interested in physics, particularly its most towering achievements of modern times : Quantum Physics, as well as A. Einstein’s Special and General Relativity, the latter of a...

Hi, I'm currently a freshman and I need to choose my program next year! My goal is to pursue physics and go to graduate school for theoretical physics (experimental is still an option). I firstly planned to do a joint honours in mathematics and physics which is offered by the Math department in...

High school student here... Recently, I've found an interest in topology and am trying to figure out the correct path for self-studying. I am familiar with set theory and some concepts of abstract algebra but have not really studied any form of analysis, which from what I've read is a...

I just recently graduated with a mathematics degree. Lately, I've been very fascinated with quantum mechains and string theory, but when I try to do research I am a little overwhelmed by all the varying topics of advanced mathematics I have to know. Can anyone suggest mathematical topics to...

Hi, Before I post my question, let me admit that my foundation on mathematics is poor. I am trying to work on it, specifically on the application part. When I came through the following image, I was stuck to understand why I will need one like Taylor's series in a simple case like "F+ΔF = F...

High school student here... Over the past year or so, I've developed an intense interest in mathematics. I work problems every day and I am constantly working to grow my knowledge. As a junior, I am currently in AP calculus and will most likely be eligible for Calc 3 my senior year. I'm...

Hi all I am currently working on questions focusing on valuation mathematics. A question on equivalent rates is perplexing me. The first question is straightforward, but I get stuck on the second question. Q1. What is the value of the right to receive £100,000 annually in advance in...

I would really appreciate it if I could get book recommendations on the rigorous mathematical theory of x ray crystallography. Which areas of mathematics (pure and applied) would be most useful and applicable?

hi everyone, I'm electrical engineer student and i like a lot arnold's book of ordinary differential equations (3rd), but i have a gap about how defines action group for a group and from an element of the group.For example Artin's algebra book get another definition also Vinberg's algebra book...

Would you explain this sentence in detail?

Here's an interesting article by the AMS about mathematics in Sub-Saharan Africa. Also note the quotation on top: Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. (David Hilbert) http://www.ams.org/journals/notices/201807/rnoti-p798.pdf...

I'm a math major and therefore need to be able to define "mathematics" in a sentence. A few years ago, I would've said "the study of numbers", but with topics like "Set Theory" that have little to do with numbers, that definition seems inadequate.

Is there any way of obtaining the exact same theory of Special/General Relativity but using a completely different framework? That is, without manifolds, without vectors, etc...

I'd like a list of math papers that are useful not for the content but for teaching how to do math, that is, math research papers that teach how to come up with new mathematical ideas.

I'm going to Uni in October and want to get a head with maths for physics NOW so its not so daunting when I am there. What textbooks/resources are an excelent introduction to physical mathematics? Thanks Nathan

Hey folks! I have a degree in Electrical,Electronics and Communication Engineering and I work in Computer networking/Cybsersecurity field. Lately, I met one guy and we both decided to do some indepdendent research in electromagnetism as we both have fare amount of love for Physics( I'm in...

The society on Jupiter's moon Io has a very odd way of counting. They count in binary using special counters: small discs with 0 printed on one side and 1 on the other. To increase speed when counting they made a rule: Rule #1: To get the next number in the sequence, only one counter can be...

Hi guys! I'm starting my first year at u of t studying math and physics specialist. I was wondering if there is anybody who completed this program or is still doing it now. I wanted to know what is its level of difficulty and how is the educational environment. Please tell me your experiences I...

When I was in school for Biomedical Engineering, while playing with numbers I noticed a pattern while calculating an equation, so I tested it. This is for relatively simple equations but maybe there is a way to incorporate it at a higher level. I would imagine while crunching numbers there may...

So I am about to switch to mathematics, as I absolutely adore pure mathematics as well as applied mathematics and I cannot stand learning mathematics without going deep into rigor of it for now(I am aware however that at times one just has to quickly learn sth to proceed with a project). But in...

Hi. Usually, Computer Programmers use Flow Charts, Algorithms, or UML diagrams to build a great software or system. In the same manner, in Mathematics, what do Mathematicians use to build a great system that they want to build. Category Theory is at the highest level of abstraction; then...

Hello. I’m an 8th grader who wants to start a math club open to people who love problem solving. I wouldn’t want it to be a competition club, instead I want it to be a club in which at every meeting, everyone would select a problem (when I say problems I mean the type of problems you’d see on a...

What would be the best degree to have along side a degree in computer science? I am thinking it is either physics or mathematics. My interests involve, robotics, artificial general intelligence, 3D graphics, computer vision, neural nets, file compression and aerospace engineering(It’s an...

Hello,Lately, I have been interested in philosophy and in particular the branches of philosophy where there is a tie with mathematics and physics. From this point, I think the best branch to start studying would be the most robust one for scientists. i.e Logic. But I am having a problem finding...

Hi. I am trying to understand the images that I have posted below. Each layer of Mathematical Structure Hierarchy in the image in this post and Mathematical Space Hierarchy in the image in this post are: statements. 1. What do these statements of each layer of these hierarchies in the...

Homework Statement I've spent at least 1.5 hours on this problem trying to figure out what i did wrong and I can't find anything. With an exam in two days plus another chapter to go through. Regardless, here are the problem(6) and answer, as well as my work. Hope you can read it, and the...