Mathematics Definition and 995 Threads

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]...

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...

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) ∪...

Hello, all, As the title says, I want to teach myself mathematics, but I need help. I never took my education quite seriously--for a variety of reasons--until I reached the university level. At the university, I first studied solely for grades; next, out of interest; and lastly, out of both...

Hello, Does anyone know of any good books that covers the foundations of mathematics (i.e. mathematical logic, axiomatic set theory, proof theory, model theory, type theory, recursion theory...)? Keeping in mind that I'm still in high school. (Although I'm taking math courses at my local...

Hey guys, I know a topic similar to this has already been talked about, but my case is a little different. I am a maths graduate currently doing my honours year in maths. Just a quick rundown of what this means: Where I live a basic graduate degree entails 3 years of full-time study where a...

Question 2: -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations A+D is the set : (Choose only one ) 1. {1, 3}...

Question 1 : -------------------- Homework Statement Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 } Homework Equations Choose the correct option : D - B is the set ...

Homework Statement The Question data is as follows : Consider the following sets, where U represents a universal set : U = {1, 2, 3, 4, ∅, {1}} A = {1, 3} B = {{1}, 1} C = {2 , 4} D = { ∅ , 1, 2 ) Homework Equations Which one of the following statements is true ? 1. The...

Suppose that an amateur mathematician finds a solution to a major unsolved problem and they have written their full proof and would now like to publish it somewhere or at least have it critiqued by the professional community. What steps should they take? Additionally, let's say that the...

I currently have a B.S. in mathematics and just got accepted into a Ph. D. program for math. In this program there are 4 different specializations: applied math, statistics, pure math, and computational math. Out of these pure math interests me the most, however, I'm afraid I won't be able to...

could anyone recommend me a book which summarises a lot of the precalculus material which I can use as a reference. I don't have much to spend.

Hey guys, so here's the deal. I'm a Math and Computer Science major, about to enter my senior year. I'm pretty sure I want to go to grad school and I just started looking for schools I might want to apply to. The thing is, I'm not completely sure if I'd like to pursue a PhD in mathematics or...

Hi guys I'm wondering about something, currently in our mathematics our number system goes something like this, 1,2,3,4,5... etc all the way to 9, then the whole cycle is repeated when it reaches 10. I believe this method of counting seems to stem from the fact that we have 10 fingers and our...

Hey everyone, I'm starting college as a math major, partly because I'm not sure what I want to do yet and it seems like a very versatile degree. So here's my question: can mathematics majors pursue graduate studies (PhD.) in the natural sciences and engineering and go on to work in those fields...

in this day and age, when there are software like Maple and Mathematica and all the fancy graphical calculators, I often wonder how much time we waste even in higher learning when we use old paper and pen-methods to do our math. I mean that why do we learn and use step by step methods to take...