Mathematics Definition and 995 Threads

I have only taken mathematics up to trig and I was curious if I would be able to start reading books on more advanced topics like Abstract Alegebra and topology??

Hi there, Im looking for a theorem that relies on the axiom of choice, but is used in applied mathematics (economics, physics, biology, whatever). In other words a mathematical theory we use to say something about the real world. This is because I'm wondering if discarding the axiom of...

I'm studying engineering at the moment and within the degree there is only 3 compulsory courses of maths. I love maths and would like to get a bachelor of mathematics but I was wondering how useful it would be to a job in engineering. Thanks in advance for the advice.

Masters before Phd in Mathematics --bad idea? Hi all, I am a senior at a regional campus of a large state university in the US. I have always thought that since I love math (and I do really love learning and doing math), that love of the subject would be enough to propel me through a PhD...

A funny thing happened to me recently... I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing... and it kind of came out, unconsciously... I think I know why Poincare said that intuition creates while logic...

"Mathematics is the gate and key to the sciences", Robert Bacon said. That statement is as relevant today as it was 800 years ago. Human culture changes but mathematics is forever. Mathematical beauty will be as relevant to mathematicians and poets today as it was thousands of years ago. Surely...

I plan to study from Peskin and Schroeders book if it helps, I just need to know what topics I need to study and it would be greatly appreciated if someone could tell me what books are good on the subject, I have a limited budget however and if I could get a single or only 2 or 3 books covering...

Do you think that matter, energy, space, time, etc. are discrete, or continuous? If they are discrete, is continuous mathematics limited to a very, very good approximation for modeling physical phenomena?

Hello all, A brief history is that as a child (I'm only 26 now) I had performed poorly at Mathematics and it wrecked my confidence. I had no interest in long division, basic algebra etc and focused elsewhere because I never viewed it as a means to an end. Suffice to say I suffered a bit of Math...

Just like calculus (single as well as multi-variable) and linear algebra are not only useful but really similar to classical mechanics. What are the branches of mathematics that I need to know in order to have that same feeling of deja-vu when studying electricity/magnetism and waves/optics? I...

Hello everyone! As the title of this thread possibly suggests to you, I'm not very skilled with mathematics. I would like to say I don't blame my teachers, I'm not insinuating that by any means. What I'm hoping to find is a book that can teach me "from the ground up" (the basics to calculus...

Hello, I am currently in my final year at a California State University majoring in Mathematics (Applied track) and minoring in computer science. I've begun lurking forums such as the physics to figure out what sort of programs I am qualified to apply for, and what be good opportunities as well...

I'm interested in mathematical or theoretical physics (and, I am quite aware of how daunting it is to obtain a career in this field). I'm curious, if I do research with the mathematics department, does this look good? Currently I might have a project in dynamical systems, although I could...

What is a list of areas of focus for Masters/PhD pursuers for Mathematics? What has the best future prospect for careers?

My question is kind of simple, does the calculus of variations find its way into the design of the shape of an airfoil? I'm interested in what kind of mathematics gets used in basic airfoil design. I suspect the calculus of variations must be involved, but I know nothing about deriving the...

Hello, First of all i found too much helpful posts at physicsforums to understand many things and basic principles about the majors of Engineering, Physics and mathematics. I got recently B.Sc degree in Electronics and Communication Engineering and that was good now i decided to have a...

Hello, First of all i found too much helpful posts at physicsforums to understand many things and basic principles about the majors of Engineering, Physics and mathematics. I got recently B.Sc degree in Electronics and Communication Engineering and that was good now i decided to have a...

Hey guys, the title basically says it all! I'm looking for a book to work along side Serge Lang's basic Math's book. Something which goes into topics more in depth. I'm out of scratch with my Math's :( Hope someone can point me to a good text! Luke

(I know this has been discussed extensively, but please read my situation.) Hello, I will be a college freshman in this fall to begin my studies in the sciences. I have equal passion for both subjects so I am going to choose whichever I am better at. I have seen a number of threads in this...

How do you think of numbers when you're doing math? I particularly feel like sometimes we get to close to acting like computers. We just scan through a list of symbols and compute another list of symbols that makes sense in a certain context. We hardly ever think of things concretely and how...

Homework Statement Problem 1: If A is an m x n matrix and Ax = 0 for all x ε ℝ^n, prove that A = O. If A and B are m x n matrices and Ax = Bx for all x ε ℝ^n, prove that A = B. (O is the 0 matrix, x is the vector x, and 0 is the 0 vector.)2. The attempt at a solution First off, I understand...

I'm planning on taking a computer science course this fall on Theory of Computation. However, one of the prereqs is "experience in formal mathematics at the level of [course on Discrete Mathematics]." I've done a little bit of discrete math before (The Art of Problem Solving covers some discrete...

Homework Statement Hello. Here is the question: Determine whether or not R is some sort of order relation on the given set X. X = {∅, {∅}, {{∅}} } and R ε ⊆. I can't seem to figure out why the ordered pairs given are what they are. Homework Equations None. The Attempt at...

Homework Statement A persons desire to eat is inversely porportional to a persons desire to not eat. The problem is I don't know how to write this down mathematically. Let's give a value to someone's desire to not eat after 3 days [40], that persons desire to not eat is going to be [-40]...

Hi, I am planning to take my master next year, I have several misunderstanding that I wish anybody can explain. Okay, at first, last year, I've been checking Master programme on Universities. I found that some of them distinguished Master by research and master by coursework. And I keep...

I am currently seeking for any open internships. So, I decided to Google search what I could find in my area, and I found an engineering internship. Would this apply to me (I'll tell you more...)? Here is the description of the engineering internship (it's very vague): I have not took a...

I came to these forums with the question how do I understand math intuitively. I joined and started this topic https://www.physicsforums.com/showthread.php?t=614527. I wanted to be able apply the methods quickly, without any calculation, so I could gain some further understanding. I read a few...

Hi guys, I'm passionately curious about physics and applying it to pure mathematics, but for some reason I'm learning medical field and I'm senior high school student, What I want to know is : 1 - Which books should I cover to become good at mathematics ? 2 - How did Albert Einstein do that...

I have been thinking about doing my 'high school project' in mathematics and I would like to do some original research. So my question is: Which areas of mathematics would be most suited for me? Having in mind that I'm still in high school, although I have taken some (fundamental) math...

I'm a student from the UK who has just finished my A-levels. I am looking for further study materials/advice on how to get into more mathematics. I did not study Further Mathematics at A-level, I only completed a single Mathematics A-level. I am interesting in developing my pure mathematics...

Applied mathematics vs. "pure" mathematics in high school? I've just started working through "Basic Mathematics" by Serge Lang. It immediately struck me, when I skimmed through the pages, that there is a large emphasize on proving things and manipulating expressions, and very little exercises...

Hello, I was wondering if perhaps someone could provide some insight as to the PhD program that would prepare me the best for what I would like to do research in one day. I am currently a mathematics undergrad with 2 semesters left. I am torn between getting a PhD in photonics, physics, and...

Hello, I was wondering if perhaps someone could provide some insight as to the PhD program that would prepare me the best for what I would like to do research in one day. I am currently a mathematics undergrad with 2 semesters left. I am torn between getting a PhD in photonics, physics, and...

Getting far enough along into math where I'm starting to wish I had something beyond my ti83.. Any recommendations in reguards to which program I should start with? I've really no idea where to start, aside from googling "computational software" What is the foremost program...

Hi all, Can anyone recommend a good book on the history of mathematics in very recent times (i.e. since the 20th century, specifically including the mathematical beginnings of computer science, game theory, chaos theory, complex systems, recent developments in stochastics etc.etc.)? Most...

I know jack about math, and I struggled to get a passing grade in high school. But what are the greek letters used to represent in advanced physics and mathematics?

I'm currently studying calculus and I'm considering becoming a mathematician (possibly professionally, and definitely just for fun). What I would like to know is if more advanced mathematics could have any use for the business/business administration field. I'm thinking of anything from...

Hello, I'm thinking about going to school in the US (perhaps) and I'm curious on the things that top US high school students covers before heading to do a undergraduate degree in mathematics. Here is a list of topics i'll be covering, generally the harder stuff: -Hyperbolic functions (using...

Homework Statement c) Is 'g' a surjective function (onto) ? Justify your answer. Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the...

For example, finding the properties of an n dimensional figure. Is this called something in math, or do I just refer to it as 'geometry in multiple dimensions'? What subjects can I find this topic under?

I apologize for the repost, but I had no replies to my previous post. I figured that I didn't put down a good enough attempt of a solution. I will try to explain what I did in more detail. I have read the rules for the forum, but if I'm still doing something wrong, please tell me. I want to...

Getting into a Phd-good or bad?? Hi,this might sound familiar.I quit my masters in automotive engineering from a very reputed university in Germany.I had finished all my course-work in 2 years,had 1 year of thesis and internship left.But,I couldn't take the emperical dominated engineering...

This is a bit embarrassing I must admit, so let me preface my problem with how I have arrived at the problem. I had become jaded with mathematics in high school due to a horrible teacher and a terrible time in his class. (He continually berated us and insulted out intelligence, and considering...

Homework Statement Determine the dom(g) Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the entrance requirement : (x;y)...

Homework Statement Question 1 : a) Use Venn diagrams to determine whether or not, for all subnets A,B and C of a universal set U, (A-B) ∪ C = (A∪C) - (A∩B) b) If the statement appears to hold, give a proof, if not, give a counter example. Homework Equations (A-B) ∪...