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Can anyone suggest me topics that connect maths with geology or geography or anything related to earth? Thank you.

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closed as too broad by mathematics2x2life, M Turgeon, AlexR, Nicholas R. Peterson, TMM Jan 28 at 0:00

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

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This has nothing to do with general topology –  Dennis Gulko Mar 13 '13 at 8:30
    
I'm not sure what for (probably to calculate depth of some layer), but geologists do calculate the distance between any two lines in $\mathbb{R}^3$. –  dtldarek Mar 13 '13 at 8:32
    
I know that it has nothing to do with general topology but there was no tag either I could think of. Thank you for choosing a good tag. –  Sawarnik Mar 13 '13 at 8:33
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@dtldarek Like cartography, Earth's orbit. –  Sawarnik Mar 13 '13 at 8:46
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Let me tell you right now, set theoretical geology has nothing to do with what you are looking for. –  Asaf Karagila Mar 13 '13 at 9:00

5 Answers 5

up vote 2 down vote accepted

Well, spherical geometry is one obvious application. Navier Stokes can help with any kind of fluid flow which has countless applications such as weather, turbulent flows in the atmosphere, shallow/deep water waves, and if you go deep enough assuming the dynamo theory then the core is a magnetized liquid in which case we have Navier Stokes combined with Maxwell's Equations giving us the ideal MHD equations. And since you said "anything related to Earth", the ideal MHD equations can also apply to the plasma trapped in the magnetosphere. This is by NO MEANS exhaustive. There are many MANY more examples, way too much to even summarize here. Any topic in a standard applied math syllabus (excluding things like pure abstract algebra/group theory) has an application related to something you would see at an AGU meeting. If you need a connection to a particular geophysical field or if you need an application for a particular math topic, then let us know and no doubt we'll find you at least one.

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Just a few more to consider:

  • Vector Calculus to work on problems related to mass/volume/density considering things like the amount of oceanic crust vs continental crust and their varying depths.
  • Markov chains and sedimentary sequences.
  • Differential equations and 1/2 life of radioactive decay. This also suggests equations considering residual heat from accretion (integration) vs heat from radioactive decay.
  • Algebra & systems of equations using Airy and Pratt isostacy equations.
  • Taylor series and temperature gradient as one bores into the Earth.
  • And since you mention geography... graph theory and map coloring problems.

Two books that I like, and which might be helpful to someone trying to connect Math and Geology are:

  • Davis, J.C., Statistics and Data Analysis in Geology, Wiley, 1986
  • Ferguson, J. Introduction to Linear Algebra in Geology, Chapman and Hall, 1994
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A very open-ended question. Look into general Geophyics to get started down the rabbit hole. http://en.wikipedia.org/wiki/Geophysics

There are other more geometric and trig applications used widely in the field of structural geology. Some examples include calculating degrees of rotation of bedding planes, displacement along faults, and locations of linear mineral deposits.

Also paleomagnetic problems, earthquake physics and seismology, geodesy, tomography. Pretty much everything quantitative in Earth Sciences.

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You might be better off asking someone who does geostatistics or exploration geophysics - I don't think people in mathematics proper often think about how their work connects to geology.

From knowing someone who works in geostatistics I've heard of Kriging, which seems like some fairly sophisticated statistics that was first invented in the context of geology.

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