What is Map: Definition and 441 Discussions

A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although most commonly used to depict geography, maps may represent any space, real or fictional, without regard to context or scale, such as in brain mapping, DNA mapping, or computer network topology mapping. The space being mapped may be two dimensional, such as the surface of the earth, three dimensional, such as the interior of the earth, or even more abstract spaces of any dimension, such as arise in modeling phenomena having many independent variables.
Although the earliest maps known are of the heavens, geographic maps of territory have a very long tradition and exist from ancient times. The word "map" comes from the medieval Latin Mappa mundi, wherein mappa meant napkin or cloth and mundi the world. Thus, "map" became a shortened term referring to a two-dimensional representation of the surface of the world.

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  1. M

    MHB Kernel of Linear Map $\theta$ in $\mathbb{F}_{q^n}$

    Hey! :o Let $q$ be a power of a prime and $n\in \mathbb{N}$. We symbolize with $Tr$ the map of the trace from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, i.e. $Tr:\mathbb{F}_{q^n}\rightarrow \mathbb{F}_q$, $\displaystyle{Tr(a)=\sum_{j=0}^{n-1}a^{q^j}}$. I want to calculate the dimension of the image...
  2. twoski

    How to Generate Semi-Organic Shapes for a 2D Map Generator in Dominions Game?

    Hello, I am working on a map generator for a game called Dominions. I plan to make it open source once it's functional. Maps in this game typically wrap vertically and horizontally, so the generator must create maps that seamlessly wrap on the X and Y axis. Typically (for even player counts)...
  3. J

    Writing: Input Wanted What Makes Great Lakes Earth So Geographically Unique?

    https://orig00.deviantart.net/1603/f/2018/163/d/8/great_lakes_earth_map_by_jdailey1991-dce7cbj.jpg Dark brown=mountains. Light brown=uplifts. Black=Igneous provinces still visible today at their original extent with no consideration of erosion. Let us say that, in the future, some scientists...
  4. A

    Python How to get pixel value from a color map?

    I have a python code where it generates two 1D arrays, plots them using scatter plot and then draws colorbar using normalization range. How can I find individual values at those individual pixel points? HC = data["HC"] OC = data["OC"] sample = y widthmm, heightmm = 171, 233 ratio =...
  5. alexi_b

    Map question involving vectors (find the angle)

    Homework Statement Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...
  6. J

    MHB Linear Map, T^p(x)=0, Show Linear Independence

    Problem: Suppose V is a complex vector space of dimension n, and T is a linear map from V to V. Suppose $x \in V$, and p is a positive integer such that $T^p(x)=0$ but $T^{p-1}(x)\ne0$. Show that $x, Tx, T^2x, ... , T^{p-1}x$ are linearly independent.During class my professor said it was "a...
  7. evinda

    MHB Find components of map with respect to basis

    Hello! (Wave) Let linear map $f: \mathbb{R}^3 \to \mathbb{R}^2$, $B$ basis (unknown) of $\mathbb{R}^3$ and $c=[(1,2),(3,4)]$ basis of $\mathbb{R}^2$. We are given the information that $cf_s=\begin{pmatrix} 1 & 0 & 1\\ 2 & 1 & 0 \end{pmatrix}$. Let $v \in \mathbb{R}^3$, of which the coordinates...
  8. G

    I Can Quadratic Forms Map Integers to Integers?

    Alright, so this might be a stupid question, but nevertheless, I ask. I am to consider whether the quadratic form ## P(x,y) = a x + b y + d xy ## can map the integers onto the integers. So through a change of basis, I re-express this as ## P'(u,v) = Au^2 + Bv^2 ## for rational A and B...
  9. jim mcnamara

    Smoke plume map of California fires

    https://www.cnn.com/2018/08/10/us/smoke-california-wildfire-reaches-nyc-wxc-trnd/index.html Reaches completely across the continent.
  10. W

    I Exponential map for Lie groups

    I’ve read about the exponential map that for Lie groups the exponential map is actually the exponential function. But the exponential map is based on the geodesic ODE, so you need Christoffel symbols and thus the metric. But usually nobody gives you a metric with a Lie group. So how can I get...
  11. ADDA

    UV Map View Plane: Calculate 2D Position?

    Would there be a way to take a uv map and compute the 2 dimensional position of a viewing plane or eye or camera, without the need to expand the parametric equation into three dimensions? In the above video the uv map in the background yellow is calculated first. Then only the bright portions...
  12. olgerm

    I Map possible values of a set with a condition to the naturals

    I want a way to map natural numbers to possible values of set A. It would also be helpful if you could tell me how many possible values are for set A(it depends of k). All that is known about set A is: Non of set A elements is subset to another element of A, but all elements of set A are proper...
  13. Baris Kalfa

    Demonstrating set properties of a map

    Hello, could you please help me regarding this question about a certain map (application). Homework Statement Demonstrate if A1 ⊂ A2 →ƒ(A1) ⊂ ƒ(A2) 2. Homework Equations ƒ:A→B is a map A1, A2⊂ A The Attempt at a Solution first assumed that (A1∪A2)⊆A ⇒ (ƒ(A1) ∪ ƒ(A2))⊆ ƒ(A) then if A1 ⊂ A2 ∴...
  14. wolram

    B New Topographic Map of Saturn's Moon Titan Reveals Liquid Flows

    Using the now-complete Cassini data set, astronomers have created a new global topographic map of Saturn's moon Titan that has opened new windows into understanding its liquid flows and terrain. https://www.sciencedaily.com/releases/2018/01/180106190439.htm I found this fascinating I hope others do.
  15. Jamz

    I Map from space spanned by 2 complex conjugate vars to R^2

    Hello, I would like your help understanding how to map a region of the space \mathbb{C}^2 spanned by two complex conjugate variables to the real plane \mathbb{R}^2 . Specifically, let us think that we have two complex conugate variables z and \bar{ z} and we define a triangle in the...
  16. PsychonautQQ

    A Why Does the Orbit Space of a Covering Map Not Necessarily Equal the Base Space?

    Suppose ##q: E-->X## is a covering map (not necessarily normal). Let ##E' = E/ Aut_{q}(E)## be the orbit space, and let ##\pi: E-->E'## be the quotient map. Then there is a covering map ##q': E' --->X## such that ##q' * \pi = q## where ##*## is composition of functions. I am confused why ##E'##...
  17. davenn

    NASA New moon map from NASA .... VERY zoomable

    this will blow your mind ! https://sservi.nasa.gov/articles/lroc-quickmap-try-it-out/ click on the blue colour "Quickmap" link in the first paragraphDave
  18. PsychonautQQ

    I Impossible to lift the identity map on the circle

    Suppose that L: ##S^1## ---> ##R## is a lift of the identity map of ##S^1##, where e is the covering map from ##R## to ##S^1##, where ##R## is the real numbers and ##S^1## is the circle. Then the equation e * L = ##Id_{S^1}## (where * is composition) means that 2*pi*L is a continuous choice of...
  19. F

    A Proving the Differential Map (Pushforward) is Well-Defined

    I am taking my first graduate math course and I am not really familiar with the thought process. My professor told us to think about how to prove that the differential map (pushforward) is well-defined. The map $$f:M\rightarrow N$$ is a smooth map, where ##M, N## are two smooth manifolds. If...
  20. W

    I Finding the Kernel of a Matrix Map

    Hi All, I am trying to see if there is a "nice" ( relatively straightforward) way of finding the solution/kernel of the map : ##f(A)=A^n -Id ## , where A is an ## k \times k ## matrix and ##n## is a positive integer. Question: what is the kernel of this map? Cranking out matrix coefficients...
  21. PsychonautQQ

    Proving conditions for a covering map to be a homeomorphism

    Homework Statement Let p: E-->B be a covering map. Let E be path connected and B be simply connected. Prove that p is a homeomorphism. Homework EquationsThe Attempt at a Solution I'm really struggling with this. Can anyone give me any insights? B is simply connected so any two paths with the...
  22. K

    How Can We Restrict the Function f(x)=x^3-x to Create a Bijective Function g?

    Homework Statement Let f: R->R and f(x)=x3-x. By restricting the domain and range of f appropriately, obtain from f a bijective function g. Homework Equations x3-x=(x+1)(x-1)x g(x): R->R The Attempt at a Solution we can find roots from the polynomial form (x+1)(x-1)x and restrict the domain...
  23. jack action

    B Map of Solar System: See How Far Away Planets Are!

    Isn't this the best map of the solar system you've seen? http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html It is so hard to imagine those distances.
  24. LLT71

    Schools Math "road map" for learning college math

    Hey people, I study engineering but our math is very poor here. We basically do high school maths with the addition of slightly complicated integrals. So here is the deal. As I want to be a better engineer I'm asking someone to give me specific ordered list of what math's I should attack next...
  25. I

    Show that the map is continuous

    Homework Statement Consider the map F: R^3 →R^2 given by F(x,y,z)= ( 0.5⋅(e^(x)+x) , 0.5⋅(e^(x)-x) ) is continuous. Homework EquationsThe Attempt at a Solution [/B] I want to use the definition of continuity which involves the preimage: ""A function f defined on a metric space A and with...
  26. M

    Linearly stable / non-linearly unstable map example

    Homework Statement [/B] Give examples of fixed points of vector fields and maps that are stable in the linear approximation but are nonlinearly unstable Homework EquationsThe Attempt at a Solution [/B] I was able to find an example in a vector field that, when the Jacobian is found and the...
  27. M

    A Velocity Map Imaging Spectrometer

    Can anyone explain the basic principal of VMI? If it is possible then please give some study material links with your reply.
  28. F

    MATLAB Matlab map representation problems

    Hi everybody. I am currently doing a metheorological study of Angola's climate. I can draw the country's shape without much trouble. >> worldmap angola >> load coastlines >> plotm(coastlat,coastlon) But once I have the shape drawn things start to go downhill. I have a vector with the...
  29. Andrew Whalen

    B How can we create a map of the universe?

    Hello Everyone, This is my first post, and I don't have any formal background in cosmology. I'm in the middle of reading a book called 'The Exploration of Outer Space' by Sir Bernard Lovell and I find myself falling in love with this topic! I have a question that has gnawed at my head for a...
  30. S

    A What Determines the Degree of the Gauss Map in Differential Geometry?

    If ##M^{2} \subset \mathbb{R}^{3}## is a surface with given normal field, we define the Gauss (normal) map $$n:M^{2} \rightarrow \text{unit sphere}\ S^{2}$$ by $$n(p) = \textbf{N}(p), \qquad \text{the unit normal to $M$ at $p$}.$$...
  31. L

    I Computing the Weingarten Map L by raising an index

    Hello, I have to prove that the Weingarten Map L for the unit sphere is + or - the identity "by computing the Lik in a coordinate patch and raising an index". S^2 : x(Φ,θ)=(sinΦcosθ, sinΦsinθ, cosΦ) I have computed the first (g) and the second (Λ) fundamental forms and I have found : L=g-1Λ=...
  32. rrw4rusty

    I need a 3D map of the universe out to 400 ly....suggestions?

    Hello, I'm a sci-fi author and need to plot a course with distances and galaxy (cluster and super cluster) stop overs between the Coma Wall, Earth and the Great Attractor. I've looked at a few online 3D universe maps and 2D maps but have not found anything ideal. Any suggestions? Thanks so...
  33. T

    I Explore the Immense Universe with the Incredible 3D Map | CS Monitor

    There are links in the article to more science-oriented reports. http://www.csmonitor.com/Science/2016/0715/Scientists-create-huge-3-D-map-of-universe-validating-Einstein-s-theories That would be a great use for some of those Virtual Reality goggles.
  34. H

    I Why a bijective map may not preserve area?

    Consider the following map ##f## that maps an annulus to a larger annulus: ##f: (r, \theta)\to(r+1, \theta)##. ##f## maps the annulus in the region ##1\leq r\leq2## to the annulus in the region ##2\leq r\leq3##. Clearly, the area is not preserved. Next, is the converse true? That is, must an...
  35. G

    A Mapping Tangent Space to Manifold - Questions & Answers

    Hi all, this might be a silly question, but I was curious. In Carroll's book, the author says that, in a manifold M , for any vector k in the tangent space T_p at a point p\in M , we can find a path x^{\mu}(\lambda) that passes through p which corresponds to the geodesic for that...
  36. F

    A Continuous map from one manifold to another

    I need a reminder. What numbers or functions characterize a map from one manifold to another? More specifically, is there a continuous function that goes from one manifold to another to another to another is some parameterized way? What is that called? I'm thinking of a manifold of spacetime...
  37. J

    Speculative; map of Lakes region w/ much higher water levels

    I remember this forum from years back as a good place to ask speculative science questions, so I figured I'd give you guys first dibs. Sorry if I put this thread in the wrong place. I'm doing some fantasy world-building, and I'm curious as to what the Great Lakes would look like at various...
  38. R

    MATLAB Create track map using Lateral acceleration & speed in Matlab

    Hi I was wondering if someone could help with creating a track map using lateral accel and speed. More specifically the steps to the maths needed to plot the coordinates. I know how to find the curvature radius but not sure what the next step is. Thanks
  39. H

    B Is Solving Schrodinger's Equation the Best Way to Approach Quantum Mechanics?

    Wondering what educators / researchers in the field think is the most important and logical flow of topics. The way I was instructed was solving Schrodinger's wave equation, SWE, for every possible problem that could be solved with a pen and paper in say 2 or 3 pages max. The problems were...
  40. 1

    A The fundamental group of preimage of covering map

    i: B to Y is an inclusion, p: X to Y is a covering map. Define $D=p^{-1}(B)$, we assume here B and Y are locally path-connected and semi-locally simply connected. The question 1: if B,Y, X are path-connected in what case D is path-connected (dependent on the fundamental groups)? 2 What's the...
  41. C

    Contour map of the function showing several level curves

    Homework Statement ƒ(x,y) = ln(x2+4y2) Homework Equations I'm not really sure but I solved for y The Attempt at a Solution
  42. W

    Metric for the construction of Mercator map

    Homework Statement The familiar Mercator map of the world is obtained by transforming spherical coordinates θ , ϕ to coordinates x , y given by ##x = \frac{W}{2π} φ, y = -\frac{W}{2π} log (tan (\frac{Θ}{2}))## Show that ##ds^2 = Ω^2(x,y) (dx^2 + dy^2)## and find ##Ω## Homework Equations...
  43. sa1988

    Prove a linear mapping of a polynomial function is a map

    Homework Statement The bane of all physicists... 'Proof' questions... So we have the mapping, Δ : P3→P3 Δ[P(x)] = (x2-1) d2P/dx2 + x dP/dx And I need to prove that this is a linear mapping Homework Equations Linear maps must satisfy: Δ[P(x+y)] = Δ[P(x)] + Δ[P(y)] and Δ[P(αx)] - αΔ[P(x)]...
  44. N

    Self organising map classifying everything to one coordinate

    Hey all,just coded this SOM based on the explination on the ai-junkie website, it seems to place all the input vectors in one single common coordinate, what am I doing wrong? I suspect its the training loop as that was the one part that the site was unclear about, Any help appreciated. static...
  45. J

    Karnaugh Map for Active Low Output Y*

    Hi All, I am given a canonical expression with active low output Y* Y*(A, B, C, D) = πM(1, 3, 4, 6, 9, 11, 14) I would like to use a karnaugh map to obtain the Product of Sum. However, I am confused because of the terms "active low". Is my truth table correct? A B C D Y* 0 0 0 0 1 0 0 0...
  46. O

    Understanding State Machines: Converting Logic Problems into K Maps

    So I was reading my book and I came across a table, I don't understand how they converted the problem into a table. They're designing a sequential logic machine and it looks like they made a K map of something, but I don't know what they used. Can anyone explain how the book did this...
  47. L

    Electric field from map of voltage potentials

    Homework Statement [/B] I recently retired and thought it would be fun to reread my old EM texts. I took Fields and Waves 35 years ago for my undergraduate electrical engineering degree, so I am more than a little rusty. This question is for my personal knowledge, not for a class, but seems to...
  48. Kelson Adams

    Use 3D laser scanning to map Outer Space?

    Mobile, airborne, and terrestrial 3D laser scanning gives an unprecedented amount of data to companies, organizations, and governments. However, I am wondering whether or not 3D laser scanners have ever been used in astronomy, astrophysics, and in astrocartography... If they haven't, I believe...
  49. Math Amateur

    MHB Affine Algebraic Sets - Properties of the map I - Dummit and Foote, page 661

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help...
  50. S

    Meaning of isomorphism/diffeomorphism ## f: R^n\to M^m##

    Can one define an isomorphism/diffeomorphism map ## f: R^n\to M^m## when ##n>m##? ##M## is a non-compact Riemannian manifold..
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