Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.
While pure mathematics has existed as an activity since at least Ancient Greece, the concept was elaborated upon around the year 1900, after the introduction of theories with counter-intuitive properties (such as non-Euclidean geometries and Cantor's theory of infinite sets), and the discovery of apparent paradoxes (such as continuous functions that are nowhere differentiable, and Russell's paradox). This introduced the need to renew the concept of mathematical rigor and rewrite all mathematics accordingly, with a systematic use of axiomatic methods. This led many mathematicians to focus on mathematics for its own sake, that is, pure mathematics.
Nevertheless, almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories. Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. A famous early example is Isaac Newton's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections, geometrical curves that had been studied in antiquity by Apollonius. Another example is the problem of factoring large integers, which is the basis of the RSA cryptosystem, widely used to secure internet communications.It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics. In particular, it is not uncommon that some members of a department of applied mathematics describe themselves as pure mathematicians.
From what I've heard, both do theory, but applied math has a lot more computational and applicable electives, vs. the theoretical based electives of pure math.
Hi all; firstly, I thank all of you who respond to my question in advance.
I'm a mathematics student with an advanced undergraduate background in most of what's associated with 'pure math', and my particular interest is in mathematical logic. I'd really like to teach myself physics - I have...
This is why I'm avoiding pure math --- axioms. There's no such equivalent thing in science as an axiom. It leaves pure math too open, almost like a programming language. Probably not a good idea for me to go into pure math if I don't understand any of the axioms, anyway; and, anyway, 1) the...
I was notified that these are all the proof-based pure math classes offered at my university for the undergrad pure math degree:
Linear Algebra
Advanced Calculus
Foundations of Geometry
Elementary Number Theory
Complex Analysis
Abstract Algebra
Since the essence of pure math is...
I'm currently a freshman and these are all the math courses I plan on taking in 4 years.
Undergrad:
- Calc II (taken), Calc III, Linear Algebra I, Linear Algebra II, Real Analysis I, Real Analysis II, Ordinary Differential Equations, Intro to Abstract Algebra, Complex Variables, Survey of...
So I finished my undergrad last year in applied math and physics. I'm currently applying to applied math phD programs (but they are separate depts from the pure math depts). I don't exactly what I want to focus on, but I was thinking something in mathematical physics, PDEs, functional analysis...
Hi everyone. I want to get into an okay PhD program for pure math (analysis or algebra). I don't care if it is a lowly university, just so it is accredited. What are my chances of getting into such a program with funding? To how many universities should I apply? My background is as follows...
I am at a crossroads.
I have a BS in pure math and I am in a masters in stats. Not sure what to do my thesis on yet.
The tear is between continuing with math and going into mathematical physics or crossing over to theoretical physics. I have a good idea what both are, but have never done...
Hi everyone.
I have recently completed a 4 year mathematics pure mathematics degree from Australia. I am now very interested in studying in an engineering field. I am most drawn to the idea of biomedical or aerospace engineering. However I am having a difficult time trying to figure out a...
I am unsure there is any thread similar to this. Today in morning I was making a thread but I can not find it. Anyway,
When I enrolled to CSE I was crazy about it but gradually I found myself in love of Math and I also found I am actually not good in CSE but in Math. I read in the best uni of my...
Hi All,
I'm currently teaching Intermediate Algebra and have taught the class how to solve algebraic problems where a denominator such as (x-2) exists. In other words, the term is not defined at x=2.
Now say that the alleged solution to the problem is x=2. In that case, the correct...
Hi. I'm entering university this year and planning to do a double degree. My chief aim would be theoretical physics.
I'm facing the dilemma that my university's math department offers Mathematics and Applied Mathematics. Since I hope that my second degree would compliment and strengthen my...
Hello,
What careers outside of academia can one hope to find with a bachelor's degree (Honours with GPA>3.5) or even a graduate degree in pure math? Let's assume I've taken Cal 1-2-3, Linear Algebra, Diff. Eqns, Metric spaces and topology, complex analysis, real analysis, discrete mathematics...
Hello,
I'm finishing up my personal statement for grad school, and wondering how much the things I'm worried about we also be cause for concern for the admission's committees? Briefly, my background is this: I switched to mathematics late, and did very few of the 1st/2nd year courses. My...
has luck been a factor in your exam? How does it compare in pure math exams to applied math exams?
I personally feel that in applied math I'm able to do w/e i have practiced, luck isn't that important. But in pure math i need a luck factor as well, along with a good practice. I feel like have...
How useful would a year-long course in advanced differential equations be for a pure math major who wants to go to grad school? I can't decide whether or not it would be worth my time to take this course.
Thanks in advance for your advice.
I heard a lot of great things about the quality of math education in Eastern Bloc countries. Also, a lot of those first place winners in the International Mathematics Competition for University Students is from Poland, Russia, Ukraine, Czech, etc. So I am thinking of going there next year to...
Guys ..i have a plan to learn calculus and I've heard g.h Hardy book:a course of pure math is good for beginner ,and I've heard a lot of good things too about this book ..so guys ? its true ? anyone who have had experience with this book so please tell me ..just make an agreement,or disagree...
Hi, so
I was just browsing this site and I've heard of most of the things being asked
in the Math forums, but I really only knew the answers to a few
I just finished my 2nd year of university (pure math major)
Ive taken an intro course in real analysis, abs algebra I and all the...
I'm highly interested in pure mathematics, so I wanted to know some of the best textbooks that would prepare me for advanced pure math classes in college. I already understand most math that would be taught in high school, however I would like to re-learn it in a more rigorous way. (Our school's...
This thread is intended to give high school students the necessary information to cope with university level mathematics. I find the “who wants to be a mathematician” thread too convoluted to be of use when looking for books, and that it serves college students more than k-12. Nonetheless, it...
Hi all,
The title is kind of straight forward, but let me add you a few background.
I am majoring in mathematics and minoring (or possibly double majoring) in undecided (i.e. I'm still looking for the second concentration... right now I'm thinking of either physics or computer science)...
Hi all
I was wondering just for curiosity what exactly are the practical applications of pure maths branches like number theory. As mentioned above, just curious to know what the racket about pure maths is all about.
I'm upset, I just had my first physics test and I got a B+/A-, depending on how the professor gives partial credit. This is horrible news, the material was really simple and I'm sure most of you would think the test was trivial even for physics I.
I don't get why I can do so good in pure...
Homework Statement
For any two integers m and n, let lcm(m; n) be the least common
multiple of m and n, i.e., the smallest non-negative integer d such that m|d
and n|d.
Prove that if p and q are distinct odd primes, and a is not divisible by
either p or q, we have
ordpq(a) =...
Most people on here are American and so usually most of the talk is about American grad schools, but since I'm Canadian I'm wondering what the best Canadian grad schools are for pure math? And how hard would it be to get into these programs compared to, let's say, the top 10 American Universities?
I'm a little dissapointed with the Real Analysis I recently learned. For one, I don't remember 90% of the results. Also, while it was a great mental exercise, I don't feel it enriched the way I view calculus in any way. It seemed like a technical exercise. Kind of like jazz music - just...
How competative is this scholarship? What is the level of knowledge needed for undergrad research for math. For example, if I wanted to do abstract algebra, would the dummit and foote book be enough to start looking at research or is a much deeper knowledge required? (masters level). Are there...
Hi, I have just finished first year in general math and am going to choose the pure math major at my university (uwaterloo). I have a few questions about undergraduate math education.
I wish to do research in math before I graduate, what should I be doing? I am currently learning analysis...
So I'm 29, and thinking of going back to school to study pure math. With the hopes of being a professor.
I know Terrence Tao works at UCLA, so he's an allstar of number theory. But that's also making UCLA super competitive in that field. Of course I'll still apply. And Caltech too.
But...
I'm just wondering
im going into 2nd year. ..I'm taking Analysis I, Differential Equations Calc III ,Probability all in the same semester and then Abstract Alg I , Linear Alg II , calc IV in 2nd semester
Just wondering what I can expect for the differnet years...how much more intense it is
Hey.
I am going to apply to university for next year very soon. At the moment my plan is to apply for a bachelor of engineering (chemical). I was just thinking though, i really like maths, so id like to do a double degree--the engineering, as well as a BSc majoring in pure math (maybe applied...
I have recently switched from Eng Phys to Math and Phys (double honours) with minor in Comp Sc. to start in the next semester, my 2nd year. I can imagine how anyone could mention that I threw most of my chances for a normal, based on employement life. What can I say? I just couldn't help it:-p...
Hello everyone,
I'm an EE undergraduate and I'm specializing in Signals and Systems. I'm also minoring in pure math.
So, in the fall I have to begin a 3-quarter sequence in one of the following math subjects:
Abstract Algebra
Real Analysis
Probability
Each of these subjects...
For those of you who don't know, "Formulas and Theorems" is basically a compilation of thousands of math theorems, 6000+ formulas, with a summary of their proofs, covering most of what was known in the late 18th century.
What I'm looking for is a comprehensive reference book with worked...
I know Berkeley has a slight edge in the "prestige" factor, but is this edge well-earned? Is there a significant difference in the quality of instruction and opportunities for research at these two institutions, particularly in the pure math department? Is there much difference in the...
I am interested to know everyones thought's about the role of computers in pure mathematics.
What is the distinction between computer science and mathematics?
"Computer science is no more about computers then astronomy is about telescopes."
pure math in astronomy-astrophysics.Suggestions needed
Hello,
I am an undergraduate student of mathematics, and I'm interested in
astrophysics-in a level of watching documentaries (no scientific knowledge).
I want to have graduate studies, I like the idea of astronomy-astrophysics
(even...
hey guys,
iam an engineering student taking a year off (after my first year) and i was trying to teach myself linear algebra and set theory from a mathematical point of view
( the way that linear is taught to engineers is frankly an insult to the subject) and i find that i keep...
physics + pure math or applied math?
Hi.
What is the most ideal combination of majors?
1) theoretical physics + pure math
OR
2) theo. physics + applied math??
thanks a lot.
My primary major is Physics, and my secondary major is Pure Mathematics (still a sophomore). However, I have started to develop an interest towards CS; in fact, my research involves programming. So, which of the two (Pure or CS Mathematics) compliments Physics better? How about job...