Mathematics Definition and 995 Threads

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. JohnPython

    Applied I need some textbooks about Mathematical models please

    Hi, I need some textbooks about Mathematical models, thanks:cool:
  2. chwala

    Solve the given problem involving logarithms

    Part (a) ##s=ab^t## ##\log s= \log a+ t\log b## Expression on the right hand side increases linearly with ##t##Part(b) ##s=120 ×1.15^t## ##\log s = \log 120+t\log 1.15## ##\log s =2.08+0.06t## From graph, y-intercept = ##2.08## ##m=\dfrac{2.45-2.08}{6-0}=0.06## Part (c)...
  3. D

    Will the Riemann hypothesis be solved by 2100?

    What do u think?
  4. chwala

    Solve the given problem involving functions: f(x)=|ax-b| and y=f(x)+c

    A bit confusing here; what i did, Using gradient, we have, ##m=\dfrac{7-1}{0-3}=-2## ##y=-2x+7## Since there is a Vertex, we have the other ##m_2=2## thus, ##y=mx+c## ##1=2×3 +c## ##... y=2x-5## ##a=2, b=-5, c=12## or##a=-2, b=5, c=2##
  5. Slimy0233

    Studying Self-Studying Physics in 8 months for a University Entrance Exam

    I am studying Physics to get into a University to study masters in India. But, I do realize how vital a role mathematics plays and I am studying Mathematical Methods for Physical Sciences by Mary L Boas for that. I have some background in Physics, I did study Physics in high school and...
  6. RChristenk

    Prove that these three ratios are equivalent

    I have the solution: ## \dfrac{2x-3y}{3z+y} = \dfrac{z-y}{z-x} = \dfrac {x+3z}{2y-3x} ## (1) ## \dfrac{2x-3y}{3z+y} = \dfrac{3(z-y)}{3(z-x)} = \dfrac {x+3z}{2y-3x} ## (2) ##= \dfrac{(2x-3y)-3(z-y)+x+3z}{(3z+y)-3(z-x)+(2y-3x)} ## (3) ##=\dfrac{x}{y}## My question is how is it possible to go...
  7. Slimy0233

    Studying How to self study Physics and Mathematics

    TL;DR Summary: I have heard detailed description of what to do when you study physics, but I don't know how to learn Physics in the first place, so this post tries to counter that. Here's How to Teach Yourself Physics and Math [Futurism] How To Self-Learn Physics: The Ultimate Guide How to...
  8. Charles Link

    So many people are unable to do simple algebra

    I find it interesting that so many know how to use all kinds of apps on their cell phones, but so few are able to do simple algebra any more. If you ask around, engineers not included, I think you would find very few people e.g. to be able to find the axis of symmetry of the parabola ##...
  9. Slimy0233

    Overcoming English Difficulty to Learn Physics

    I am an Indian and even though my English knowledge is somewhat better than that of an average Indian, there isn't a day I try to real highly technical books and fail to understand it at the first glance (or don't understand it at all). I understand why they use language which might seem...
  10. Abhikamya M S

    Schools Which colleges in India are best for physics and/or mathematics BSc MSc and PhD?

    In 12th and considering a career in research. Ik most of the collages ( IIT Kanpur, IISc Bangalore, IISERs etc ) but I am not sure of the research possibilities provided so if anyone can help out please do
  11. M

    Does 'rest' have a precise mathematical definition?

    Math qyuestion for AI (Skype) include an expression that x is resting on y (both straight line segments). AI insisted that x coincides with y, while my intent was only placing x on y. Does 'rest' have such a narrow definition?
  12. T

    A Separation of variables is possible only in 11 coordinate systems?

    I vaguely (strong word there because I can no longer remember the source, but the idea sticks in my head for 30 years now) recall reading (somewhere long forgotten) that method of separation of variables is possible in only 11 coordinate systems. I list them below: 1.Cartesian coordinates...
  13. S

    Solving this definite integral using integration by parts

    Using integration by parts: $$I_n=\left. x(1+x^2)^{-n} \right|_0^1+\int_0^{1} 2nx^2(1+x^2)^{-(n+1)}dx$$ $$I_n=2^{-n} + 2n \int_0^{1} x^2(1+x^2)^{-(n+1)}dx$$ Then how to continue? Thanks
  14. T

    I Understanding Vectors: Magnitude & Direction

    Good Morning (And apologies if this is not the right forum -- it is not a homework problem.) On the one hand, a vector is an arrow and a tail: it has magnitude and direction. It is used to describe direction, forces, acceleration, etc. However, there are more mathematical definitions: a...
  15. Euge

    POTW An Integral with Fractional Part

    Evaluate the integral $$\int_0^1 x\left\{\frac{1}{x}\right\}\, dx$$ where ##\{\frac{1}{x}\}## denotes the fractional part of ##1/x##.
  16. S

    What type of mathematics did you find the most difficult?

    Mathematics tends to be more progressive than any other field. But I've heard some people say that some math classes that they took were more difficult than the most advanced math classes that they took. For instance, I've heard people say that Calculus II is more difficult than Calculus III...
  17. S

    I What's the mathematics behind "spontaneous synchronization"?

    I was looking at this video, and have become quite interested:
  18. Theia

    Geometry Looking for a good book about trigonometry

    Hi all! I've never been studied the identities and such of secant, cosecant and cotangent. Yet I think, it would be useful to have them in my toolbox. Thus I'm asking, if anyone would know a reasonable book or other kind of material (paper or pdf) about trigonometry that has brief theory...
  19. J

    Other Math Olympiad Advice Please (I will be 13 years old next year in 9th grade)

    Hi! I am 12, and will be a 13 in 9th grade ( I skipped 6th grade). I have a curiosity for mathematics and have started preparing to take the AMC 10 and 12 exams. I enjoy solving the ingeniously crafted problems, as I share the sentiment of many math competitors of not being challenged by the...
  20. M

    Why Can We Take Limits of Both Sides? [Answered]

    For this, Does someone please know why we are allowed to take limits of both side [boxed in orange]? Also for the thing boxed in pink, could we not divide by -h if ##h > 0##? Many thanks!
  21. E

    Collatz conjecture brought me here

    These are the two tables I developed trying to untangle how the Collatz Conjecture operates, and this certainly helps clear the water a bit
  22. Fra

    A Comment on Nicolas Gisin "Intuitionistic Mathematics"?

    I noticed this https://www.physicsforums.com/forums/quantum-interpretations-and-foundations.292/ about Indeterminism in Physics and "Intuitionistic Mathematics" but it was already closed. I just wanted to add that, although the value of these ideas are aren't clear from abstract of quick...
  23. Photonico

    Other How to select one from these two books? (Physical Mathematics)

    Dear everyone, I'm an HDR student in Condensed Matter Physics. I want to enhance my math ability with the aim is learning physics. I found two books, they seem all fit my purpose. 1. Mathematical Physics 2nd by S.Hassani 2. Physical Mathematics 2nd by K.Cahill I want to choose one of them to...
  24. cwill53

    Quantum Workforce Elements, Toolbox for QIS Programs at Universities

    TL;DR Summary: Imagine you have infinite funds and cooperation to build a very ideal curriculum and student organization, both dedicated to quantum information science, at a university. What does this look like pedagogically? How would this be structured? What resources do students need access...
  25. E

    Exploring Mental Blocks in Mathematics: A Personal Perspective

    Since this is a "general lounge" area, I will assume this rather personal story is not out of line. I am 64 years old (relevance of my age should become clear shortly) and graduated from an Ivy League University in 1980 with a degree in Electrical Engineering. I also scored over 700 on my math...
  26. matqkks

    Introduction to pure mathematics

    TL;DR Summary: education, history I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis. What should I cover to make this an...
  27. John Bernier

    Towards a new theory of information kinematics

    The physical world is highly parallel; many things are happening side by side simultaneously. This is true not only at the macroscopic scales that we can see but as far as we know down to the subatomic scales. This is referred to as the principle of locality [1], which states that an object is...
  28. WMDhamnekar

    Stochastic mathematics in application to finance

    Get your friends and family to play this simple little game that illustrates a key aspect of stochastic mathematics in application to finance. Draw on a big sheet of paper a sequence of 30 squares and label them consecutively 0 (bankrupt), 1, 1, 2, 2, 3, 3, 4, . . . , 14, 14, 15...
  29. S

    Deciding between physics and mathematics

    I am not sure if this is the right place to post this, so if not sorry in advance. I am a second-year physics major, thinking of switching to mathematics. I have always been interested in both, but I could never be sure whether I could become a mathematician. Understanding physics was...
  30. J

    I Double Slit Experiment Mathematics

    Electrons are shot thru two slits separated by a distance s at a screen a distance ##z_0## away. The wave function for the particles is proportional to ## e^{ik \sqrt{(x-s/2)^2+z_0^2}} +e^{ik \sqrt{(x+s/2)^2+z_0^2}}## Taking the first one, we can manipulate the square root algebraically...
  31. F

    Insights Classification of Mathematics by 42 Branches

    Continue reading...
  32. A

    B What Math Is This? (Logic of Mathematics)

    Can someone please tell me what math is this (see below pic)? For example: algebra, calculus, etc.
  33. C

    Building a step by step course for different subjects in mathematics

    Hi, I mostly do Self study and I was wondering how to build up a course ie the.different levels from beginner to advanced in the fields of linear algebra, optimization (rbfs etc), statistics and probability? Suggestions of books with the various levels is welcome. Please help me out in this as...
  34. sergiokapone

    I Mathematics for dancing laser beam

    Is there a math that describes these shapes at least one frequency?
  35. N

    Please recommend a free pdf book about university-level mathematics for me

    Homework Statement:: Recommend PDF books Relevant Equations:: . Hi, I'm a second-year physics student and my uni doesn't have any study material in the syllabus. Only lectures. I want to learn more. Can you recommend to me a good mathematics pdf book that is about calculus? General topics...
  36. lucky31501

    Programs What courses would best benefit an Applied Mathematics degree?

    Hi everyone! I am looking for advice on what courses I should take to better flush out my degree/be more versatile. Currently, I am going into my sophomore year in Applied Mathematics. I originally wanted to change into a Math/CS degree, but it was full, so I had to settle with taking the...
  37. Darkside

    Algebra College Algebra, Mathematics & Trigonometry Textbooks

    Some textbooks I found online ( open source ) College Trigonometry 3rd Corrected Edition - STITZ ZEAGER OPEN SOURCE MATHEMATICS Precalculus 3rd, Corrected Edition - Lakeland Community College, Lorain County Community College A First Course in Linear Algebra - Robert A. Beezer Cheers.
  38. R

    B Mathematics involving a gravitational force

    It's been more than 60 years since I attended high school, and I am trying to learn and understand concepts in Newton's physics that were not taught and were not part of the school curriculum during the 1950's. It is my understanding that the current mathematics taught and used in our...
  39. The Bill

    Intro Math What were the first modern Discrete Mathematics and Precalculus texts?

    What was the first textbook for the modern syllabus of precaclulus which had "precalculus" in the title or subtitle? What was the first textbook for the modern syllabus of discrete mathematics which had "discrete," "discrete mathematics" in the title or subtitle? If you have personal...
  40. junyoung

    I Open interval or Closed interval in defining convex function

    The Korean textbook standard defines the convexity of the function as an open section. Many textbooks and university calculus textbooks define the convexity of the curve as an open section. However, some textbooks define convexity as closed sections. Do you think it is right to define the...
  41. XcgsdV

    Courses Is Pure Mathematics required to be a top-tier Physics student?

    Hey y'all, I'm starting college as a Physics major this fall and I started working through Steve Warner's Pure Mathematics for Beginners in my downtime because I love the math courses I've had, wanted to learn more about proofs and how those things came to be, and most importantly had nothing...
  42. atyy

    High Energy Mathematics for Physics by Adam Marsh

    Adam Marsh's Mathematics for Physics is available online. Subodh Patil recommends the algebraic topology section, and as a primer to Nakahara.
  43. matqkks

    Which Classical Mathematics Textbooks Should a Mathematician Possess?

    What are the classical mathematics textbooks for advanced and undergraduate level that a mathematician should possess?
  44. matqkks

    Where to Find Mathematics Textbooks from the 1920s-1980s?

    Where can I purchase old mathematics textbooks up to undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.
  45. matqkks

    Looking for old mathematics textbooks (high school to undergrad level)

    Where can I purchase old mathematics textbooks on Advanced level (16-18 year olds) or undergraduate mathematics? I am ideally looking for books from the 1920’s to 1980’s.
  46. shivajikobardan

    MHB How do I understand notational mathematics?

    I will try to explain what I mean. I understand how to calculate cartesian product. but I can't write the formula for cartesian product as shown below. Similarly, in other cases I understand what it is trying to say(the inituition) but I really don't understand a word written in it. I feel...
  47. manareus

    Estimating maximum percentage error using partial differentiation

    Attempt at question No. 1: ΔD = ∂D/∂h * Δh + ∂D/∂v * Δv ∂D/∂h = 3Eh^2/(12(1-v^2)) ∂D/∂v = 2Eh^3/(12(1-v^2)^2) Δh = +- 0,002 Δv = 0,02 h = 0,1 v = 0,3 ΔD = 3Eh^2/(12(1-v^2)) * Δh + 2Eh^3/(12(1-v^2)^2) * Δv Because the problem asked for maximum percentage error then I decided to use the...
  48. B

    B Distance between two points on Earth doesn't increase with altitude?

    Consider the following example: Point A has coordinates 45 lat, 0 long. Point B has coordinates 45 lat, 2 long. Both points are 5000 ft above sea level. The distance between them is X. Point C has coordinates 45 lat, 100 long. Point D has coordinates 45 lat, 102 long. Both points are at sea...
  49. S

    Ambitious, probably delusional guy wants to make a Kiselev manual

    Nice to meet you all! I am a college dropout self-studying math. Before dropping out, I flunked out my Calculus class even though I managed to pass my Precalculus class (I honestly don't know how). I realized that I was lacking a lot in Geometry and Trigonometry. My understanding of algebra is...
  50. Vividly

    Newton’s Principia of Mathematics

    Summary:: What kind of geometry/Math do I need to understand to read this book? Hey people! I would like to know what kind of geometry and/or math would I need to understand this book. I skimmed through it( The translated version by Florian Cajori) and seen that it gets technical with shapes.
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