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.
Dear Physics Forum friends,
I recently got interested in the Russian textbooks in mathematics, which I am completely blown away by their exposition, insights, and excellent problem sets. I have been reading translated versions of Russian books written by authors like Kolmogorov, Arnold, and...
I've asked many... what does it mean to major in math (pure). I am a first year sophomore and still undecided about my major.I used to get full marks on math tests n high school, but how can I know if I'm able to be something in math. Anyone can learn how to do math, but few can actually make...
I am 15, didn't pay attention in school, because I thought it wasn't necessary, I am reviewing every mathematics concept I should know, but no clue which ones to start out with, anyone got a idea, and in which order I should relearn them in?
(Just btw, I learn faster then others, I just wasn't...
Are Newton's three laws all that was needed for the science that got us to the moon? Or did we need Einstein's theories to get there? I just started studying physics last week, so forgive me for my baseness.
I want a good linear algebra textbook in order to learn to use linear algebra in physics but also to use it in more theoretical mathematics courses.
I hope that with this poll i will also help others that want to study from a proper Linear Algebra textbook.
I just sent my UCAS application for these degrees. Most probably I will end up with Mphys (maybe Msci), but I will see which universities accept me.
Now my question is: what jobs/ careers can I pursue with this degree? What about this degree plus a PhD?
And that besides teaching careers (I...
Hi, I'm new here and I'm trying to learn GR. I wanted to know the math books that I need to tackle GR properly, so far the books that I came across are:
Tensor Analysis on Manifolds by Bishop and Goldberg
Tensors, Differential Forms, and Variational Principles by Lovelock and Rund
I have a good...
Hi. I've recently finished high school and am planning to study science/physics, hence I'll be doing a lot of calculus courses but I'm looking to do more than that. I was looking to find some good sources, whether they be online or in textbook format or whatever. As for where I'm at currently, I...
Hello Board!By eluding most math class' and homework as a youngster
I have deprived myself effectively of a tool on which I am dependent nowadays.
My love for mathematics if ever existent was ephemeral, unpredictable in its manifestation.
I would either almost fail the class or would have...
Many times I have seen the claim that some text on mathematics is written in a "good Russian style". What does that mean?
Somehow I've got an impression that it is a kind of opposite to the Bourbaki style. Namely, a Russian style would not consist of a dry series of abstract general theorems...
Note I'm not talking about Mathematical Physics. This is a Physical concept not a Mathematical concept.
Speed of light is less than 300000000m/s. Physically, 300000001 (+1) m/s does not exist, but mathematically, this isn't impossible. So Physics is limited by our universe, but Mathematics is...
Hello everyone, I am currently a sophomore in high school (year 10 by the US system), with two years before I graduate to university. Last year, I began to learn calculus and physics on my own because they interested me. There is more to this story, but basically I seem to be at a crossroads now...
Hi all,
I'm currently a freshman studying electrical engineering and I was wondering whether I should try to minor in Mathematics or Physics as a supplement to my studies. I feel like both of them have their individual pros and cons, but I'm not sure exactly what they would be/how they would...
Hello Forum Members
I have masters in physics and working in education field in India, but want to pursue higher studies in mathematics abroad. So I should start with MS in mathematics. I am looking for schools that offer MS in math but have low tuition for international students. So what would...
I want to pursue a matametical career but all of us know that a good research career or even professorship at good universities needs a good amount of research papers.
so what basically is research , is it contributing new things or giving depper understanding of a known fact for example a...
I am looking for a book concerning the foundations of mathematics. I am not talking about algebra or calculus but the foundation of the mathematical language( Axioms, sentential logic...). I hope you have understood the prior rubish. Thanks for any help.
Once the Spring Semester starts up, I'll be applying to become a mathematics tutor at my community college. I have good blessings for it from my Calculus Professor. I'll essentially be tutoring from basic developmental maths through precalculus and Calculus I. I've got the calculus down rather...
Hi,
I am struggling to understand the maths in the text shown below.
(1) How does: r(t) = Acos(wt)+Bsin(wt)
become; sqrt((A^2)+(B^2))cos(wt - arctan(B/A))?
(2) He states that we can represent the input as a phasor and in one of three ways but doesn't say which one.
(3) He then focus on the...
I started with Mary Boas' book "Mathematical Methods in the Physical Sciences". Now it is stressed in the introduction to make homework and do the problems. However, I would very much like to know if I got the answers right, and I even prefer if the problems are worked-out. So I guess my...
Dear Physics Forum personnel,
I am a collegiate junior at US with double majors in the mathematics and computer science, and an aspiring theoretical computer scientist. My current courses in the analysis and linear algebra, and undergraduate research in the theoretical computer science fired...
Hello,
If I have an MSc degree in mathematics specializing in machine learning, is it possible to enter a PhD program in computer science (also specializing in machine learning)? Will the fact that my degree is in mathematics and not computer science prevent me from doing that? I have heard of...
Forgive me if I sound ignorant, but is it possible that quantum affects (value of h, why physical dimensions appear to come in discreet chuncks, etc) all stem from our mathematics (which originated as counting numbers -quantum steps). I do understand that calculus was invented to help remedy...
I am planning on transferring to a 4 year university to major in physics. I am currently overseas and must take classes online. After an almost endless grueling search I was able to find a school that offered an associates program online that I feel is in the right direction for what I intend to...
Hello,
I am trying to understand the intuition of the definition of the period of a state in a Markov chain.
Say for example we can go from state i to state i in 3,5,7,9,11... and so on steps.
The gcd here is one. So is this aperiodic state or one with periodicity of 2.
Thanks
Hello everyone, as those of you who have helped with my other threads know I'm currently a high school student and an aspiring physicist. I'd like to start out my post by saying that I completely understand that I am very early to be thinking this far ahead, especially when I haven't experienced...
Homework Statement
Solve for the forces P and N acting on an object in equilibrium on an inclined plane.
Weight=10N, angle is 30 degrees
http://blob:https%3A//www.physicsforums.com/d431a152-5681-411b-ba57-809320539165
Homework Equations
Trigonometry, i.e. sin, cos, tan rules. The 'Z' rule...
hello everyone
I have always been curious about science and math but have been terrible at both as a result of my failure to study and pay attention, I failed math twice in high school from skipping, not studying and ignoring my teacher, I also failed physics twice for the same reason...
Dear Physics Forum advisers,
I am an undergraduate student in US and an inspiring applied mathematician in the fields of theoretical computer science. I recently have been reading a book called "Joy of Learning" by Hironaka Heisuke, a mathematician and Fields Medalist (1970); the book seems to...
Homework Statement
cos(x - 3p/2) = - 4/5
p <x< p/2
sin(x/2)*cos(5p/4)= ?
Homework Equations
The Attempt at a Solution
I made it as far as to determine that sinx= 4/5 and cosx = - 3/5 but can't seems to progress any further. I am looking for an easier way to find the solution without having to...
Homework Statement
For clarification a have posted the equation below as a picture file.[/B]
Homework Equations
log(a*b)= loga + logb
log(a/b) = loga-logb
log(a^n) = nloga[/B]
The Attempt at a Solution
I don't know how to start. I can't remember the rule for powering the logarithms if there...
Homework Statement
if x1 and x2 are solutions to 1) x² + x + 1 = 0, then 2) y1 = ax1 + x2 and 3) y2 = x1 + ax2 are solutions to which quadratic equation?
Homework Equations
ax² + bx + c = 0
x1∕2 = (−b ± √(b² - 4ac))/2a
The Attempt at a Solution
Well, firstly i solved for x1 and x2 getting...
Hello, before I start off, I apologize for asking a question which I am sure has been asked hundreds of times before: but I felt there is just way too much information out there which is a little confusing, so I am here with the hope of getting some personalized suggestions.
I am currently a...
I figure out a way to evaluate an integral with an antiderivative with elementary functions which had previously only been defined by an anitderivative that was not an elementary function. Everything checks outs. I used 3 regular substitutions and a trigonometric substitution and I just have to...
beneath all problems with gravitons to describe mathematically (simple said our idea of a graviton is a gluon with spin 2 which is only predicted through CFT in 5 dimensional AdS) we have another problem mathematically to describe.
We found 3 generations of neutrinos with mass through...
Hello,
At my exam I had to proof the title of this topic. I now know that it can easily be done by making a bijection between the two, but I still want to know why I didn't receive any points for my answer, or better stated, if there is still a way to proof the statement from my work.
My work...
I feel as if my understanding of physics require increasingly rigorous mathematical derivations the more advanced the notions get... since I started even high school physics, I lost track of the number of instances where the bulb lighted up in my understanding of physics due to a rigorous...
Hello, I'm currently in a physics/CS undergrad program and I would like to continue to graduate level in artificial intelligence. But recently I started to browse artificial intelligence papers and discovered that they are very mathematical. I ask myself if I should switch to maths/CS undergrad...
Hi all,
Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject?
Thanks!
Would it not be more efficient to write modular functions using the text formatting of logarithms? The modulus would be in subscript after "mod", and the expression to be used would be written after...
Ex. modnf(x)
I'm in the 11th grade and have little education of college level mathematics. I individually find myself studying one section of it but hardly have a grasp. I really want to read the Feynman Lectures to further my education of physics, but as I read over the pdf it looks like there is a lot of...
The question at hand:
Let A be a 10-adic number, not a zero divisor. Proof that a 10-adic number B is dividible by A if 2^q*5^p*B has ends with p+q zeroes.
My work so far:
Because A is not a zero divisor, it is not dividible by all powers of 2 nor 5, so it follows from a theorem that A =...
The distance covered by a car at time t=0 is 0 / at time t= 1 is 10 km/ at time t= 5 is 50 km,
With this example can you explain, what is function of what? f(d) or f(t),
I just need some direction. I just can't seem to solve anything in math or physics right now. I want to become good at both but I just am struggling mightily. First year in college in mechanics and calculus. Every one says to just work harder. This is very frustrating because I put in over 10...
Mirage: we consider the x-y plane describing vertical y and horizontal x directions, with an inhomogeneous index of refraction n(y). In this case, using calculus of variations, Fermat’s principle for the trajectory of a ray of light may be re-written as n(y)/√1+(dy/dx)^2 = A. Where A is a real...
Mathematics is the language of Nature. The more advanced topics we study , the more involving is the maths. To understand physics, I think i need to develop a strong mathematical intuition and learn to appreciate the beauty of maths. Can anyone suggest a good flowchart of topics so that my...
Good evening,
I really want to study mathematics, to learn to do (at least some level) of mathematic research. I am at a point in my life where I will not be able to pursue these studies in a university because of my commitment to the court calendar. I could devote 4-5 hours a day to study, but...
I'm applying for joint honor course in Mathematics and Physics and single honor course in Theoretical Physics at universities in the UK. I am struggling with putting into words what I enjoy about physics and mathematics in my personal statement. I have the other paragraphs in place (I think)...
I can either graduate in 2 years to teach just biology or stay 3 years and be certified to teach biology and mathematics. I just want to graduate but my parents think staying the extra year will make me more marketable. Thoughts?