What is Mathematic: Definition and 43 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.

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  1. Magnetons

    False. The statement does not logically follow from the given information.

    I think it is "True" because the hypothesis is true and the conclusion is False. :cry::cry:But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:## -1^2=-1## , not1."
  2. LCSphysicist

    What is the minimum mathematic requirement for learning Lagrangian and Hamiltonian mechanics?

    Homework Statement:: ... Relevant Equations:: . What is the minimum mathematic requirement to the Lagrangian and hamiltonian mechanics? Maybe calc 3 and linear algebra?
  3. Q

    I Mathematic Definitions and Ideas

    What is opposite in Mathematics? I argued with my engineering brother and his pal that "inverse" is indeed "opposite" if you use the general concept of "opposite." My brother claims that the idea of opposite in mathematics only means returning to null. Opposite: 1.) Having a position on the...
  4. babaliaris

    Uniform Circular Motion: some help with the math proof?

    I can not understand why ##v_x = -|v|sin(θ)## and ##v_y = |v|cos(θ)## I'm asking about the θ angle. If i move the vector v with my mind to the origin i get that the angle between x'x and the vector in anti clock wise, it's 90+θ not just θ. So why is he using just θ? Does the minus in v_x somehow...
  5. H

    How to find chords, intersections of chords on circle?

    Homework Statement Homework EquationsThe Attempt at a Solution this is the answer https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1038060.html but why the c1 = 0, c2 = 1, c3 = 3, c4 = 6 etc why not c2 = 2? c4 = 4?
  6. pairofstrings

    B What area of maths is common to all other areas of maths?

    Hi. I am very curious and fascinated to know what area of mathematics is common to all other areas of mathematics. Thank you.
  7. RabbitWho

    What to do with a mathematic equation

    Homework Statement A ball is thrown upwards at a speed of 29.4m/s Where is it 4 seconds after being released. Homework Equations d[/B]=v0t+1/2at2 So I understand what the letters all stand for because that information is explained, but I don't know what to do with it. The Attempt at a...
  8. srinaath

    Dynamic model of non-linear system

    i am finding it difficult to get insight about modelling of non linear system (electrical). my queries are, consider the system is DC DC converter... 1) I read that to study the dynamics of the system we linearise the non-linear system...why do we want to linearise it?... 2)can some one please...
  9. kolawoletech

    General Form of Canonical Transformations

    Homework Statement How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and...
  10. Q

    Mathematica Is there any way to improve my skills with Mathematica software

    Hi I am new at the mathematica software i would like to find way to improve my skils
  11. MidgetDwarf

    What Is Mathematic Physics? Not sure if I have a realistic understanding....

    Not sure what Mathematical Physics is. My assumption is that it combines rigorous mathematic formulation in solving or helping to create a mathematical sound framework for Physics. I think my view on this matter is wrong. I really like Mathematics and Physics, I do not really care for...
  12. MidgetDwarf

    Favorite Non Mathematic or Science books?

    Besides liking countless books on the subjects of math and science, what other books do physicsforum members enjoy? In my case, I enjoy Don Quixote, Les Miserables, Oliver Twist, and all Jack London's works.
  13. V

    Classical Interesting (common) problems solving by physic, mathematic

    Hello, I'm looking for some book of common (real) life or interesting problems, which are presented and scientifically sloved. I don't preffer any problem, but I mean some from real life, fridge, gyroscope, atc. Do you know any book of these problems and solution?
  14. Stephanus

    Music Unraveling the Mystery of Music Intervals

    Dear PF forum, Do anyone know, why music interval is always \sqrt[12]{2}?
  15. FuturePhysicist

    Mathematic subjects to self study.

    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...
  16. Barioth

    MHB What other fields can one pursue in applied mathematics?

    Hi everyone! I'm kind of lost lately... I finish my undergrad in Pure mathematic last semester. I got accepted for master in mathematic. But I don't know what field to choose.. I'm afraid I won't be getting any job after (and sadly with my student loan, I kind of need a job hehe). I was...
  17. L

    What are the mathematic prerequisites for learning relativity?

    Hello, I am interested in self-teaching special and general relativity at an undergraduate level, but was wondering what the main mathematical prerequisites are. I currently have almost no idea of GR and a very mathematically basic idea of SR, and have studied maths and further maths to...
  18. D

    HARD Mathematic examination question

    HARD! Mathematic examination question Homework Statement $$\int_0^2\int_π/3^π (x^2*\sec^3 x^3 -12\ /\sqrt{e^π+x^2 +2x})\,dx\,d(theta)$$ :cool: Homework Equations I could not find any relevant questions on the web, however this is simply a question from an exam written the 14th of October...
  19. homology

    Looking to discuss the philosophical foundations of mathematic

    Folks, A friend and I are interested in finding a forum to discuss the philosophy of the foundations of mathematics. He's a mathematician and I'm a mathematical physicist. Some of the topics we're interested in are understanding intuitionism and understanding Wittgenstein's lectures on the...
  20. Albert1

    MHB Prove the Following Mathematic Form

    $A=\overbrace{ 11-------1 }^{m}\underbrace{ 22-------2 }_{m}$ prove :$A=k\times (k+1),\,\, where\,\, k\in N$ (A can be expressed as the multiplication of two consecutive positive integers)
  21. P

    Magnetic field directionality, mathematic rigmarole?

    The force as a result of a moving charged particle through a magnetic field is perpendicular to the field apparently. Why should the magnetic field be perpendicular to the force created as a result. F.b=q(vXB) is the mathematical notation for this which accurately describes the world. But I...
  22. N

    Theorem mathematic for relativity

    hello!: my problem is about of a theorem mathematic,as I prove the following theorem? F(x)=F(a) + \sum^{n}_{i=1}(x^{i}-a^{i})H_{i}(x) good first start with the fundamental theorem of calculus: (for proof): F(x) - F(a) = \int^{x}_{a}F'(s)ds sustitution: s=t(x - a) + a...
  23. AnTiFreeze3

    Best Ways to Improve Mathematic Abilities?

    Forgive me if this is the wrong place to be posting this, but as far as I can tell, this is the most appropriate place to post my question that I can find. My main question is obviously the title of this thread, but I figured that it would be best for me to give you some background...
  24. O

    How finite element analysis differs from mathematic derivation in beam bending?

    So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...
  25. J

    Music What is music? is it 100% mathematic?

    I have been pondering what music actually is, why does a certain configuration of sounds increase dopamine/endorphin in our brain. What makes music feel good. Is it their mathematical order in the sounds so they follow mathematical rules or equations? Or is it something pshycological that...
  26. S

    Meaning of mathematic operator

    Homework Statement What is the difference between ≤ (less than or equal to) and "less than over equal to" (the operator is similar but there are 2 lines under the 'less than' operator) Homework Equations none The Attempt at a Solution I simply do not know the difference. And how to...
  27. D

    Mathematic Inductive Proof question

    Homework Statement Give a proof by Mathematical Induction of the following: For all integers n>=3, (n^2 - 3n + 2) is positive. Homework Equations The Attempt at a Solution Hey guys, this is a problem from my discrete mathematics study guide. Here's what I got so far: Proof: n-initial=3...
  28. T

    Two Discrete Mathematic Proofs I Need Help With

    Homework Statement Prove that at least one of 2*10500 + 15 or 2*10500 + 16 is not a perfect square. Can you say specifically which one is not a perfect square? Consider the proof that √2 is irrational. Could you repeat the same proof for √3? What about √4? Homework Equations n/a...
  29. B

    Free Math Software: Find Area Under Graphs

    do you guys know any free mathematical software that can help me find the area under a graph which can't be intergarted using just a level skills. i already checked autograph but it kinda sucks and i looked other forums but didnt find a thing about this.
  30. Y

    Is R1 an Equivalence Relation or Partial Order on Set M?

    R1 = {(p,q) | p-q is even}; R1 on set M = {1,2,3,4}; Ordering of M: 1,2,3,4 a) Write the relation R1 as a set of ordered pairs. Draw the arrow diagram and determine whether R1 are functions or not. Explain your answer. b) Hence, determine whether the relation R1 is an equivalence relation...
  31. B

    Question about mathematic courses I need

    I've read through a lot of different threads on the topic of prerequisite knowledge required to take a course in quantum physics and I was wondering about what mathematics I should take (I want to order the textbooks online) Ive done calculus and have finished a college physics textbook Now...
  32. C

    Programs Which classes to take to finish minor in mathematic sciences?

    So, I've decied to major in Computer Science w/ a minor in Mathematical Sciences; however, I'm in a dilemma. I need to choose 3 more classes (out of the list below; I've already chosen the other 4 classes) and I'm not sure which ones I should take to make myself more "marketable" and a better...
  33. D

    Math Degree in statistic and mathematic

    Hi! I'm on my way to get my bachelor in Statistic and mathematic with specialization in statistic...the thing is i heard a few people said that they have to go back to school because this field has no future...Now I'm kinda worry because I'm not sure if I'm in the right field. I like doing what...
  34. D

    The Simpsons mathematic geek received no attention

    I remember an episode of The Simpsons, where a mathematic geek received no attention of his fellow peers, so he shouted: PI IS EXACTLY THREE! I just couldn't help laughing:D OK, over to my recent low-leveled mathematics-discovery, regarding whether i is not equal to 1, -1 nor anything like...
  35. T

    What does these mathematic simbol meens?

    http://img120.imageshack.us/my.php?image=f5e97fb005d59328d3730e3qs9.png the two parallel lines symbol ?
  36. L

    Mathematic operations and structures in C

    Hello guys, I was wondering: say you have a structure: struct tag{ int a char b int b int c } how would you make int c equal to int a + int b for all variables of type struct tag? I have tried using pointers but it baffles me how you would make a global change in that all...
  37. R

    What is the Equation for Calculating Uncertainty in Velocity and Acceleration?

    Homework Statement Hi. I need to prove that these 3 eqns are the same. p \rightarrow q \vee r p \wedge \neg q \rightarrow r p \wedge \neg r \rightarrow q Homework Equations p \rightarrow q \equiv \neg p \wedge q The Attempt at a Solution p \rightarrow q \vee r p...
  38. U

    Mathematica Mathematica vs Maple: Which is Best for Maths?

    i hope i got this in the right forum...if not sorry i was in the market for a mathematical software that would be able to just about anything related to maths (differentiate, integrate, factorise, complete the square, give results in exact form, all the basics, etc.) i am familiar with...
  39. A

    The true result for A is -0.1762.

    Hi, here is my equation of basic mathematic.. I know it looks a bit huge but actually on the paper it isn't. In the equation is one mathematic mistake, I checked several times alone and I am not able to find it, I hope i can get some help and thank you: If I write like this '' L1 '' (without...
  40. N

    Which math software is recommended for advanced math classes?

    I am thinking about purchasing some math software so I can get a better understanding of the math I am learning. I will use it for my calculus 2 class, but once I am done with calculus I will surely use it for my Diff E, Linear Algebra, and Complex Variables classes too. Which program would...
  41. M

    Advanced Electromagnetic and Mathematic Concepts

    Hi All, From electromagnetic theories, with the Lorentz gauge condition for the magnetic vector potential, I get the following wave equation: 1/csquared * d2A/dt2 + del2 A= u0 j. in some literatures, they ignored the d2A/dt2 term and I don't know why they can do that...
  42. C

    Fundamental mathematic proofs

    Fundamental mathematic proofs... I know this may seem a slightly odd question, but are there any website or pdf files, etc, floating around of proofs of the basic pricipals and "tricks" of maths? eg - adding, subtraction, multiplication, division, fractional sums and products, percentages, etc...
  43. R

    How Do You Solve for X in This Equation?

    How to solve this mathematic?? Hello, Can anyone help me how to solve this? I wat to solve for X 0.0032 = (x/100 * 0.0556) + (y/100 * 0.0153) Should I do it like this? 0.0032 = (x/100 * 0.0556) + (100-x/100 * 0.0153) ... And how to solve it [?]