What is Mathematics: Definition and 996 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.
I have been reading a lot of books on deliberate practise like Grit - Angela Duckworth, Talent is Overrated - Colvin and Peak - Ericsson and Pool and I'd like to implement the principles in my training to become a good mathematician.
There isn't much advice on how to apply these principles to...
Humans created that tool, that language, that consists of axioms and their implications. Mathematics do a good job of communicating the behavior of physical phenomena. In some instances, pure mathematical areas have been found to describe some aspect of reality, only years after having been...
Hi there,
I'm currently a second year chemistry student in the UK. Since starting my degree I've found myself interested in theoretical/quantum chemistry. I would like to apply for a PhD programme in theoretical chemistry, which follows courses in quantum mechanics/statistical thermodynamics.
I...
Hi Everyone,
I have completed high school mathematics
which has:
1.) Algebra
2.) Trigonometry
3.) Co-ordinate geometry rectangular co-ordinates
4.) Basic Vectors and 3D geometry
5.)Calculus:-
Functions
Limits
Continuity
Differentiability
Functional Eqns...
Hello everyone! So, I'm currently double majoring in Math and Physics at my University. My end goal is to hopefully go onto graduate school to earn a PhD in Astronomy, the specific areas of Astronomy I'm interested in are Observational Astronomy, Instrumentation and Planetary Science.
Here are...
This was too funny to not share. Numerous agencies are picking up the story, but just in case:Professor's airplane math leads to flight delay
An Ivy League professor said his flight was delayed because a fellow passenger thought the math equations he was writing might be a sign he was a...
Are there "things" mathematics describes that can't exist in the real world; things mathematics says can exist but are actually impossible to ever exist in the world we live in?
Also, are there things that do exist in our world that mathematics says can't exist? The obvious answer to me is no...
I've seen a few threads discussing a topic similar to this, and I've been making some serious considerations and thinking about things.
I'm currently debating switching over from a Physics major to a Math major and minoring in Physics. There are a few various reasons to do this, one being it...
Homework Statement
Reading Feynman The Principle of Least Action out of The Feynman Lectures on Physics, Vol 2. Link to text http://www.feynmanlectures.caltech.edu/II_19.html
So I'm having a problem proving that, section 19-2 5th paragraf, that
"Now the mean square of something that deviates...
I'm currently building a PC and I want to buy components that will be able to support whatever programs/software I will be using while getting my degree. I'm going to be starting the physics program at my university this fall so I don't really know what my professors will be having me...
To what extent is the term infinity used in the physical world.
When talking in terms of mathematics we can have a set of all natural numbers called an infinity, then we can have a value that comes after this set of infinity (lets call it 'a'). After 'a' comes 'a+1' then after this set of...
How to self-study mathematics
https://www.physicsforums.com/insights/how-to-study-mathematics/
How to self-study basic high school mathematics
https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/
How to self-study calculus...
I'm currently a first year MathPhys student, and next year I have to decide my stream. I can pick a combination (pure) Mathematics, Applied & Computationtal. Mathematics, Statistics, MathSci, Physics, Theoretical Physics or Physics with Astronomy & Space. Naturally there are restrictions, and I...
What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.
Or basically anything that isn't a positive integer.
So I can prove quite easily by induction that for any integer n>0, De Moivre's Theorem (below) holds.
If ##\DeclareMathOperator\cis{cis} z = r\cis\theta, z^n= r^n\cis(n\theta)##
My proof below:
However I struggle to do this with...
I have a big choice to make which is not letting me sleep or study properly. For the last few years I have been attending community college. For financial reasons I left school during the 9th grade. Both of my parents were terminally ill. My father passed away, my mother still lives. I placed...
What is the most motivating way to introduce group theory to first year undergraduate students? I am looking for some real life motivation or something which has a real impact.
There is a table tennis tournament consisted of 8 participants that is guided by the following rules:
1. Each player plays with every other player for exactly one party
2. If in the i-round there was a party between A and B and a party between C and D, and A and C play In i+1, then in i+1...
Homework Statement
Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not?
Homework Equations
8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)
The Attempt at a Solution
Brought all e^(ax) values to one...
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Hello all.
Next year, I'm going to attend the university. I really want to study mathematics, since I enjoy doing this. My grades are quite high, but I spend a lot of time understanding what's really happening, although this is not always possible. I also spend time by learning things like...
What general advice would you give to a keen young (upper high school and undergrads) student of mathematics?
I would say most important is to develop your mathematical intuition by doing and reading as many examples and problems as possible. Anything else?
I'm having trouble with the mathematics of tensor products as applied to Bell states.
Say I have the state
\begin{align*}
\left|\psi\right> &= \frac{1}{\sqrt{2}} \left(\left|0\right>_A \otimes \left|0\right>_B + \left|1\right>_A \otimes \left|1\right>_B\right)
\end{align*}
How would the...
From "Road to Reality" chapter 3 part two. If three ratios are known: M:N, A:B, C:D. A:B is greater than C:D if: A added to itself M times exceeds B added to itself N times and D added to itself N times exceeds C added to itself M times. Show that the ratio A:B is greater than C:D.
I am making some modifications of snake and ladders so that this purely luck-based game can have a strategy and used to learn mathematics as well. So far I only have this idea:
Once a player roll the die he can choose to move his own piece forward equals the number shown on the die or move an...
Mathematics is a vast subject with a very long and rich history divided into many branches that usually begins by making precise and defining new intuitive rational concepts (often inspired by the perceived world or from existing mathematical or scientific theories) and develops by employing...
Everybody knows Mathematics it's an important field in every Science; and in Physics even more. So, if you have a PhD in Physics, for example Astrophysics; is it worthly to get a degree in Mathematics?
I know that maybe there's some courses that would be completely useless in Physics, but you...
Hi everyone,
I'm currently a third year Economics major hoping to switch to the Economics and Mathematics by the end of this year. Considering I should have been a Physics major in the first place, I have started taking Physics course starting from my third year in an attempt to eventually go...
Hi guys! I applied to a DPhil program on PDEs at the University of Oxford and recently got an offer without funding. I would love to attend this program, but as you may know, the tuition fees for international students are really high. My government could help me with 2/3 of the tuition + a (not...
My first 2 years in college I was a little lost in what I wanted to do so I completed almost all of my generation ed classes. I finally realized I love physics, I am interested in astrophysics although I know I have time and opportunities to change my mind . Happily I attend a school with a...
I am trying to work my way through Stephen Pope's "Turbulent Flows". I'm finding that my Achilles heel (as has been throughout my undergraduate degree) is maths. Since this book is essentially applied maths, I'm finding it difficult.
So I'd like to simultaneously work through a course in...
Homework Statement
At T1 the root mean square speed (rms) of compound P is 485.2 m s-1 and at T2 the rms speed is 504.1 m s-1. Using this data and the fact that T2 – T1 = 24.0 °C, determine the molar mass of P in g mol-1.
Homework Equations
From problem statement you have: (3·R·T1/M)1/2 =...
Hello I just want to know as an System Engineer student in my second year(I have 4 years in total) what kind of physics and mathematics will I use if going to work in a field let's say ( Electronic System or Electromechanical Systems or Computer).
Thank you,
Adrian
Hi, I wish to not only learn, but prove every theory I come across. This requires a ton of math research, and at this point, I am about to begin quantum mechanics, and general relativity after I finish up my differential geometry book. My question, I suppose, is after I finish differential...
Hi All,
Was there any use of the concept of amplitudes of probability before their use in quantum mechanics?
In connection to this question, who invented or was the first to use this resource?
Best wishes,
DaTario
http://www.pssc.ttu.edu/techhort/lasrvy/l_h.htm
My learning style seams to be more holistic than linear, but it appears to me that physics and especially mathematics texts are written in a way that is best suited for linear learners. They very often give little or no context or motivation as...
Hello,
I'm trying to self teach myself Fundamental Mathematics. I looked around, but I wasn't sure what to look for exactly. I read the part on Set Theory in "Book of Proof" by Richard Hammack. I enjoyed it, but I wasn't sure if it is rigorous enough to stand against a college level course...
Dear Physics Forum personnel,
I am an undergraduate pursuing a major in the mathematics. My current undergraduate project in the computational virology really got me interested in the worlds of microbiology. The project involves both the biology and computer science, which is specifically...
Hello all, hope all is well.
I come seeking ideas to present at my college's STEM Fair coming up in a few months. To give you idea of my mathematical background, I am currently taking Differential Equations(ODE) and Discrete Math. I have completed Calc I,II, Vector Calculus and Linear...
I am calculating the light intensity of Mercury.
I was given the average distance from the Sun in AU's which is 0.39.
Using the formula (1/(d^2)), I solved for the light intensity relative to Earth which I found to be 6.57.
I need to find the light intensity in (w/(m^2))
Hi everybody
I'm currently looking for an introductory quantum mechanics book which emphasizes the mathematical aspects of it. I especially need exercises in order to pass a written exam, but I'd like to have even lots of examples.
I've already gone through the whole "Picasso" (it's an italian...
I will be writing a paper by modelling a system and its differential equations. I have just started brainstorming ideas but I would also like to hear other peoples' ideas as well!
I have these ideas so far, can anybody suggest relevant articles or papers on these topics (avoid wikipedia if...
My Current Situation:
I am currently a second semester sophomore at university going for a double major (BS in Physics and BS in mathematics). I went to college to get a physics degree . The mathematics degree is added on because I love mathematics and due to my strange circumstances had quite a...