What is Mathematics: Definition and 997 Discussions
Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis). It has no generally accepted definition.Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.
Ahoy there.
I am twenty years old, and have (as a result of my interest in cosmology and astronomy, and the natural sciences) developed a keen appreciation for mathematics (in physics, primarily). I have always had an interest in the sciences, but lackluster teachers and personal disinterest...
I was doing this problem in calculus, and I came up with the answer dy/dx=n(n+1)(n+2)..(n+(n-1)) and so on. To me this looked like a factorial backwards, and I wanted to find notation that expresses such a series. I googled it and I found the "Rising Factorial" notation. However, as I continued...
A transverse wave on a cord is represented by D(x,t)=0.22 sin (5.6 x + 34 t)
Determine the velocity of the wave and the minimum and maximum speeds of the particles in the cord.So velocity can be found with v = f λ
f = ω / 2π and λ = 2π / k
so v = ω / k
= 34 / 5.6
= 6.1
I assume...
I am a first year computer engineering student. Having programmed several years, I realize my math skills are not adequate for my liking (planning on improving them before tackling some more advanced data structures and algorithm books).
My plan is to read how to prove it, spivak calculus, a...
Hello, I am currently an undergrad mathematics major who is still unsure in exactly what field of mathematics to study post grad (if I get such an opportunity). All the subjects I have taken so far seem equally interesting, and I could see myself engaging in post grad study in each of the areas...
I am currently in high school and have been driven to become a theoretical physicist in an unsure field for quite some time now. I have been unfairly placed in a very easy math class even though I already know it. I have been studying upon subjects such as algebra 2 and pre-cal and recently...
I will be doing a presentation in the science symposium at my community college. The common theme is always topics from biology or chemistry but never from physics or mathematics.. I am a Math major and love pure mathematics, I am interested in presenting the great theorems of mathematics...
Hello,
I'm Community Growth Manager at OpenSignal. Studied pure mathematics for my bachelor's degree, but never got around to going deeper with physics. Now that I'm in the mobile sensors, electronics, and wireless communications / telco space, I am extremely interested in everything connected...
I have already studied Single and Multi-Variable Calculus, Linear Algebra and Differential Equations. I am self studying real analysis now and I find it hard, do physics majors really need to study real analysis? I am studying this because I just can't seem to remember a lot of what I've...
I am self studying quantum mechanics from griffiths at the moment, and the formalism chapter (to me) seems to be an overview, and since most of the linear algebra i did was in real numbers, most of the stuff are new to me. So i want you to recommend a reference for math to go along with...
Dear Physics Forum mentors,
I am an undergraduate sophomore with double majors in mathematics and microbiology. I wrote this email to seek your recommendation on the discrete mathematics textbook that is in-depth, theoretical, proof-based, and also comprehensive. I am currently taking a...
Why in God's name is there such a pervasive prevalence of mathematics in just about every mechanical engineering curriculum in the world? It strikes me as profoundly useless for 99% of the engineering community in industry today.
It's easy to teach. Historically it was the only language with...
I want to read a book on mathematics behind QM and by that, I don't mean just functional analysis. Its been a long time that I hear about things like *-algebra, C*-algebra, Weyl algebra, Heisenberg group, Stone-von Neumann theorem and things like these and I want to understand them. Can anyone...
For example:
$$ y^{2} = 25- x^{2} $$
$$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$
This part: $$ , -5\leq x\leq 5 $$
What is the name of this?If it were a function, it would be the domain. And for equations, and resolutions of equations, what is the name?
Other example, the equation:
xy = 1...
Recently I started seeing integral calculus and right now we are covering the topic of the antiderivative. At first sign it was not very difficult, until we started seeing integral variable substitution. The problem starts right here:
Let's suppose that we have a function like this:
\int...
I note that I spend a long time taking/rewriting messy class notes, (~1-2 hours a day) time which I could rather be practicing/studying. Is it worth rewriting these notes and storing them in an archive, or would I better spend my time doing practice problems and just highlighting important...
Hi,
Well, my name is Etienne and this isn't my first time posting about my choice of major. I am in 12th grade, and I have an admission exam to UNAM next month, (National Autonomous University of Mexico), for APPLIED MATHEMATICS & COMPUTER SCIENCE or I have also seen it been called Applied and...
I have tried to search on the internet for a clear and concise definition for the mathematical term "pointwise," but I cannot find one that is comprehensible. The context of needing an answer to this question is this: "operations on real functions in a vector space are defined pointwise, such...
Does anyone know of any mathematics books that are not textbooks? Something that has problems but is more focused on building mathematical intuition rather than just laying out formulas and what not.
This is a pretty vague question/descriptor for a book, my apologies. If you need more...
I know a lot of courses like linear algebra have a ton of "building blocks" that one must memorize. Yes, you can derive these things yourself, but this often takes to long.
Does anyone here use any tools like SuperMemo to memorize math theorems or physics laws/equations/etc?
Also, I just...
How to get free mathematics and engineering textbooks? I need them in pdf file form. The textbooks I want are college and university textbooks.
Any website/link that gives free textbooks are welcome. I need them for self study and I'm compiling a library of textbooks.
I'm interested in getting involved with some research while I'm still an undergrad and don't quite know where to start. I don't meet qualifications for REU programs in my area and literature on where to start is scarce.
As for field of interest I'm interested in linear algebra/matrix theory...
I've been turning something over in my head for a bit and I wanted to check some math. It has to do with how long it would take a hypothetical alien civilization to colonize a big chunk of nearby space.
Over at the...
Hello everyone,
I have been trying to teach myself GR for sometime now, and while I started to learn through books like Schutz and Hartle, I reached a point where the motivation behind the mathematics they used didn't satisfy me nor did it appeal to me.
I think the worst I remember is when...
Per another thread I've decided not to pursue a PhD in mathematics, but rather do a Masters with a Thesis option. So it's time to start finding an area and zooming in.
I am interested in complexity theory, and have been watching the whole "Big Data" scene with interest (and ignorance). I...
Hi, I'm a long-time lurker, and finally decided to get in on the fun with you guys.
I have a list of courses I can take at my university, and I'm wondering which of these I could safely go without if pursuing the physics B.S. as my primary degree (as opposed to math - my current).
I'll put...
I have my highs and lows with mathematical understand. From those who are very good at mathematics what trait does you possesses that you think gives you the keys to understanding? I've been trying to become more visual with my learning of mathematics, such as visualizing/conceptualizing the the...
The derivation of the law have been put up in the forums but I have a question regarding its derivation.
I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step:
\frac{m}{k} = \frac{M}{k'} .
This is similar to
\frac{C}{M} =...
I am currently a freshman at Purdue University. Recently, I've just switched from First Year Engineering to the College of Science so that I may double major in Physics and Mathematics. I've taken the liberty to concoct a 4 year schedule that I will take. (As of right now, I plan on getting a...
What is the most predominant philosophical attitude toward mathematics among mathematicians?
I am talking about things like mathematical platonism, formalism, logicism etc.
In some circumstances I feel that I am a platonist (e.g when thinking about pi) in others logicist or formalist etc. Does...
I am taking AP Calculus BC and I want to self study math so that I can be good at it.
The field of mathematics I want to study is applied mathematics. What methods are good for studying math by myself and becoming good at it? Which topics should I study sequentially after learning AP Calculus...
Hey!
I have to do a work about one of the many applications of mathematics. I have to study the math behind a certain subject and use MATLAB to solve some kind of problem associated with the topic.
I am on the final year of graduation and I thought of doing about optics, fractals, relativity or...
Hello everyone!
So, I am a mechanical engineering student but I've recently discovered my passion for electronics and computer science. I would eventually like to pursue a graduate degree in either or both (if that's possible) of these fields. I am thinking to get a mathematics minor to help me...
Hey guys
First real thread besides my introductory thread.
I'm a Danish student in what is somewhat equivalent to my junior/senior year in the american school system. That was a small attempt at school system conversion.
I'm writing a project about the black hole Sgr. A* in the centre of our...
Hello all. I was wondering if anyone has any external sources for a list of math textbooks, particularly by the same author, going from arithmetic all the way to differential calculus (or some other harder form of mathematics). The reason I want it to be the same author, is so I can be sure that...
(Sorry if these are the wrong forums)
All right, so, I know the difference between pure and applied mathematics as well as mathematical vs theoretical physics. But, I don't quite get the difference between mathematical physics and applied mathematics. Aren't they both working on mathematical...
What, in your opinion, seems to be (one of) the most difficult equation(s) in mathematics?
Here is my choice:
Find the solution ##k## of the equation
$$2^{\aleph_0}=\aleph_k$$
Hi everyone, I'm new to the forum, so I'm not too sure whether I posted under the correct topic or not. I am currently a junior at a quite competitive high school. All around me, there are people thousands of times smarter than I am. I know very well myself that I am no genius, but I've always...
Homework Statement
Using \int_{-\infty}^{\infty}e^{-x^2/2} dx = \sqrt{2\pi}, Integrate x^(5/2) e^(-x) dx from 0 to infinty
2. The attempt at a solution
I tried substituting x = u^2/2 but i could not simplify further.
Please help me with the problem.
Thank you in advance.
Hey, I am a freshman in High School and I have a very superior IQ but I am in normal classes. This is due to ADHD and I used to be lazy in school. Anyways, algebra 1 is VERY boring. I want to teach myself geometry, algebra 2, Pre Cal, and Calculus because I love math. Also I feel like it will...
Hi, I posted a thread a while back about a problem I had in a class, it has resolved itself fortunately but now I have another question.
I am an undergraduate mathematics major and I initially planed to go to(and likely will go to) graduate school in applied mathematics.
I have always had a...
Is it true that a typical Electrical Engineering major involves much more math than other engineering majors? And that a typical Physics major involves much, much more math than all engineering majors (including Electrical Engineering)?
Hi. I completed my undergrad major in physics and want to go to grad school for astrophysics. I want to have a year revision of the mathematics needed for astrophysics. What type of math is needed to excel to be a successful astrophysicist. I have some lacking in integration . What others are...
Im about to graduate with a physics and math double major, so I'm currently searching for graduate programs that include applied physics, applied math, and engineering. Ultimately I am interested in applying science/math to practical applications in engineering or Earth science. My goal is to...
"Many credit card companies target entering college freshmen with attractive interest rates. What they do not emphasize, however, is that the low rate will be in effect for only a short time, changing automatically to a much higher rate, often in just a few months. Freshman Michael Bronson...
Hello,
I am 20 years old and I currently hold a bachelor's degree in law because of various reasons and causes ; however, what I wanted to study was mathematics. And I currently wish to study it but I lack all the prerequisites to apply for a major, as I have not taken any calculus classes...
Hey everybody how you doing? I am writing this because I just recently had a discussion with my older brother. He holds a Masters in Music and Administration. I am currently a senior undergraduate in Mathematics. He was saying that the Liberal Arts is a more difficult degree to obtain than a...
(Not a 100% this goes here but oh well)
I imagine there's not a lot of this, since visual presentation is pretty important in these subjects, but does anyone know any good lectures or audiobooks on highscool/Secondary mathematics or physics that one could listen too while taking a promenade...
Hey guys,
I was reading Kenneth's Discrete Mathematics and I came across this definition in the function chapter:
Let f be a function from A to B and let S be a subset of A.The image of S under the function f is the subset of B that consists of the images of the elements of S.We denote...
Although it gets better with experience, integrating an expression by hand is a really a trial and error procedure. A wrong substitution will get you nowhere in the available time. So I am wondering as to how they test your integration skills on GRE Mathematics Subject Test. Any help would be...