Pure Definition and 499 Threads

I have read quite a bit on here and elsewhere, but am still coming to terms with pure, mixed, entangled and product states. I know a state is either mixed or pure, but then is engtaglement a sub-class of being mixed? Or a sub-class of being pure? Or is entangled another name for pure? Or...

Books for self-study in "pure areas" of mathematics Hi, I am starting an applied mathematics course this year at university. Unfortunately I don't have the option to study "pure" areas of mathematics, but I would like to learn more about them to become a more complete mathematician at the end...

Pure maths is obviously abstract compared to the applied areas but which areas of pure maths are considered not as abstract or relatively less abstract?

Homework Statement a license plate has 3mos then 3letters then 3nos(numbers) if there are no constraints how many license plates are possible Homework Equations 9x9x9x9x9x9x9(..maybe) The Attempt at a Solution The same as the one above, I am very confused.

I am working on a Project that involves determination of Quality of Steam. In that I have few queries, so please help if possible: 1. Is there any mathematical relationship between Resistivity of water and temperature? because i am not able to find one, but since i am working on this...

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...

The only kind of electrolysis I've learned about is electrolysis of salts dissolved in water. In that case there's current flowing through between the two electrodes but what do you call the process where you submerge 2 electrodes of the same metal in pure water in order to produce a solution of...

"Pure" Mathematics vs. Applied Math vs. Discrete Math I'm approaching the point where I'm going to have to decide which four-year university I'm going to finish my Bachelor's degree at. I'm pretty much restricted to colleges in Georgia, and I am primarily looking at Georgia State and Georgia...

I am just wondering if pure carbon and graphite have the same resistivity? Resistivity for pure carbon = 3.5 x 10^-3Ωm:frown:

Hi all! I'm applying to several universities in the US. Among them is the University of Utah, I'm applying for a PhD in pure mathematics. Do you know what's the reputation of this university? I was told it is good, but I'd prefer to read comments from Americans or from anyone who studied...

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.

Homework Statement Prove that 10^n + 1 cannot be expressed in the form a*a*c, where n,a,c are positive integers. Homework Equations By considering the reminder of 10^n + 1 when it is devided by 3, I arrived at the conclusion that: a*a = 3z +1; c = 3v + 2 for some positive integers...

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...

Hi, I've posted this on other forums and have had little to no help. I thought this forum looked very good so hoping someone can help. Sorry for the non specific title of the thread, I don't know what the following problem should be called! I don't think it is too hard but I stopped...

Is this unheard or a lot of people do such a thing? I mean if someone like me would like to do research in both areas, but knowing that doing 2 phds is too much (although I have read of a few who have done two phds one in CS and one in maths), I think my compromise would be to do first in pure...

Dear PF members, I am about to begin my junior year as a math major, and I feel like I made one observation. That is, if I want to study math at advanced level, I need to choose either pure or applied mathematics. I have also noticed that if I get a title of "mathematician," that implicitly...

After reading some introudction of quantum states (pure and mixed), I know that states produced statistically are called mixed state. My question is: since there always exists stochastic process, so in practical system, how can we produce "pure" state?

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...

I've heard that breathing pure oxygen is bad for you, but I can't find any information about it online. Is it bad? Do scuba divers and astronauts breathe pure oxygen or is it diluted with other gases?

Pure water doesn't freeze at 32F ?? This has me curious. I am reading a Scientific American article, which the following is from(emphasis mine): In flight icing is where the airplane is flying through clouds made up of small liquid water droplets. These liquid water droplets can be sustained...

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...

What is the chemical formula of pure milk? What is the chemical reaction taking place when milk combines with salt? thanks in advance.:smile:

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...

What are complexity classes (P, NP, etc) in terms of pure sets? ZFC, I mean.

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...

Is there anyone who understands (or has ever heard of) the difference between a pure spin current and a spin-polarized charge current? It causes a great deal of confusion for me, because I cannot imagine a current flowing without an accompanying charge flow... Guesses and conjectures are...

Hello, Given (in spherical coordinates) the resulting 4-vector K of the composition of 2 Lorentz pure rotations R1 and R2, where only R1 is known, I would like to find the angle of the "overall" rotation resulting from this composition. In other words, I want to find the symbolic expression...

why do chefs prefer kosher salt as apposed to iodized salt they say the iodized reacts with the food to make a funny taste but is this really true or make that big of a difference.

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...

Do Theoretical physicist uses pure maths or applied maths? Thanks

Thanks

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) =...

Does the quote below (from a textbook) make sense to anyone? The context is that they are introducing mixed states, and the quote below is how they refer to the pure states discussed in previous chapters. Here is the quote: "In quantum mechanics, such maximum information is contained in a...

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...

Is there a need for pure mathematicians in the defense industry? I've tried looking online and one of the main requirements is that the person be knowledgeable about mathematics and physics, but this could be talking about mathematicians, physicists, or engineers. P.S. I don't mean to sound...

Square Root Of 2 (from Hardy "Course Of Pure Mathematics") I was surprised to find it in my local bookstore amidst math "cheat" books in the one-shelf math section (and the fact that it was the last copy left... ??). Is he asking to simply carry out the calculation? Or is he asking to...

sounds like the title of a SF book...and that is what this post will probabley be... "if matter and antimatter colide,they anihilate each other and turn into pure energy" here comes the questions: 1)what is pure energy?you can't go at the market to buy a jar of energy,you can't hold energy in...

i am in big dilema of what to take up in near future;either PURE SCIENCE or APPLIED SCIENCE let me tell you that i want to become a SCIENTIST in the field of atomic science. so please please help me to know which is better for me and in which my future is sceure...

Employment areas with PhD in Pure Maths?? I am currently filling out my graduate school applications for PhD in Algebraic topology and there are a lot of questions asking about my career goals. So I was wondering what are the employment opportunities for a person with PhD in Algebraic...

Hello All: A project of mine requires a bi-directional inverter that will take a 12VDC (most likely) battery to single phase 120VAC pure sine wave for utility tie (mains power). I will also require the inverter to be able to rectify to utility's power to charge the battery as well. Since...

Hello PF readers, I am currently doing Further Mathematics, and I was looking for a suitable revision guide for Further Pure 1 for ME, but I was unable to find one. Are there any attention worth revision guides that offer good explanation about the topic with given examples and questions to...

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...

Hi. I'm looking at Berkovits' pure spinor formulism of string theory. I am a PhD student studying mathematics and so am having trouble with some of the physics behind the mathematics. Say we have V a 10 dimensional vector space and we pick an irreducible representation of Spin(V) - which is...

Hello Everyone Can anyone tell me what is the speed of light in hydrogen or may be where can I find that for all the elements. Has these datas available already in or books. Thanks in advance !

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...

A piston-cylinder device contains 0.85 kg of refrigerant 134a at -10 degrees celsius. The piston that is free to move has a mass of 12 kg and diameter of 25 cm. The local atmospheric pressure 88 kPa. Now, heat is transferred to refrigerant 134a until the temperature is 15 degrees celsius...

Density = mass/volume (D=m/v), explain the difference in density of pure & salt water in words and using a mathematically based example