# Geology with maths

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

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This has nothing to do with general topology –  Dennis Gulko Mar 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 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 at 8:33
@dtldarek Like cartography, Earth's orbit. –  Sawarnik Mar 13 at 8:46
Let me tell you right now, set theoretical geology has nothing to do with what you are looking for. –  Asaf Karagila Mar 13 at 9:00

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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