Mathematics Definition and 994 Threads

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...

Hi, currently I am having a dilemma trying to decide whether I want to do a 4 year Msci in physics or mathematics. I am about to finish a degree in computer science I had started when I was 13 or 14 with the open university. Although, I still want to go to a real university for mathematics or...

A person told me that doing math research independently (alone) is very difficult, because the findings of someone who is not interacting with the experts in a given field of study will most likely not be "novel", that is, they would have already been published before. Is that true ? Can the...

<Moderator's note: LaTeX code edited.> 1. Homework Statement Hi, I have a question. I have a sequencing problem ##(N, \sigma_{0}##, ##\{p_{j}\}_{j\in J}, \{c_{i}\}_{i\in N})## with ##N = \{1,2,3\}## the set of players, and ##J = \{A,B,C,D,E,F\}## the set of jobs. The processing times of the...

I will be majoring in physics when I go to college in about 5-6 months. I have a lot of hours that I can put into study up before I go, like 400 hours on the low end. I would like to hammer away at the hardest and most time consuming areas of physics and math. I have learned most of precal but...

I am looking for a signal processing textbook that uses real, complex, and functional analysis with measure theory. In other words, mathematically rigorous signal processing. Specifically, I prefer the kind that takes time to review all the topics from mathematical analysis before jumping into...

Homework Statement A solid cuboid has a volume of 40cm3. The cuboid has a total surface area of 100cm^3. One edge of the cuboid has length 2cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 significant figures. This question recently came up on my maths exam today...

Is it usual people in your country migrating from physics to pure mathematics? I study in a federal university and two of my mathematics professors have a phd in physics and nowadays teach (and do research) mathematics at the uni. To work as a professor at this uni one needs to have a huge...

Hello, I'm just an undergraduate student in their final year at university. I've never been good at mathematics so I want to pursue it as a hobby and a challenge to myself, starting from the basics! I have a few questions of my own floating in my head so you'll definitely see me sticking...

Hello, I've been trying to improve my algebra since I've never been particularly good with math. I'm going through Serge Lang's Basic Mathematics textbook and while I have been learning a lot his proof-based exercises are a pain to get through and the back of the book only provides answers for...

I just found an interesting book at BN, titled Reverse Mathematics Proofs from the Inside by Prof John Stillwell. https://press.princeton.edu/titles/11143.html He mentions that it’s a growing field in mathematics where we seek to discover the right axioms to prove a theorem...

What do you enjoy/like about mathematics? Let me start: I enjoy the beauty of mathematics and how beautifully it describes the World. You? Feel free to post equations. Thanks.

Hi. π is a constant. The purpose of π is to use it to find circumference of a circle or area of a circle. Correct? Can you please elaborate? Can you point out any other two constants and its purpose? Thanks.

So in my future numerical analysis class the recommended book i liked the most was Numerical mathematics by Quarteroni : https://books.google.pt/books/about/Numerical_Mathematics.html?id=m-bHBAAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false Since i like this...

I'm a computer scientist with aspirations to apply myself to fundamental research, data analysis, or computation, in physics; And these are the books I've purchased so far but haven't read. Which order do you think I should read these? Or more generally, how should I schedule the reading of...

So you I've screwed up in Mechanical engineering courses due to a combination of personal reasons and some tough professors. I have discovered that it is possible to finish a BA in mathematics in the same time frame as the Mechanical engineering BS degree, only one semester + the summer. I've...

Hello everyone, I am currently attending a community college and at the end of spring, I will graduate with associates in mathematics and physics with roughly a 3.90(depending on the what GPA you're talking about). Physics and math are my life and I dedicate virtually all of my free time...

In multiverse theory, where it is supposed to describe ALL outcomes, a mathematical multiverse is the ultimate ensemble and there are not more levels than this, but it doesn't contain all the imaginable universes because, as Max Tegmark himseld quoted in a paper "the mathematical universe...

So I recently join an engineering course, in my pure math classes we are currently studying basic algebra, simultaneous equations or quadratics. I quickly found all this very abstract and presented as facts. Now, I don't know how to phrase this, rather than looking for a book that just states...

Hi, I've taken calculus during my engineering degree (that I'm still attending) two years ago. At that time I didn't realize the importance of calculus (and also linear algebra) so I studied it superficially. I think I'm quite good though because I had to use my calculus knowledge in all the...

What should the Mathematics requirements for Physics degree really be? The usual official requirement is three semesters of Calculus, and then one more combination course which combines some linear algebra and not-too-complicated differential equations. Often the Physics majors, at least for...

I think that the existence of subharmonics is also bifurcation.Is that true

Chaos is when the waveforms become aperiodic. I think bifurcation is the phenomenon inclusive of chaos and in addition, it is also termed for situations in which the waveforms become n-periodic.Does bifurcation include period-n phenomenon as well as chaos? From period-n it means that still the...