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Timelike Geodesics and Euler-Lagrange Equations
First things first: what are geodesics? Well, they’re basically just the shortest paths between two points in a curved space (like spacetime). And when…
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Solving Geodesic Equations in Riemannian Manifolds
If you don’t know what that means, don’t worry neither do most people. But let me break it down for ya: A Riemannian manifold…
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Decimal Arithmetic: Square Root
It’s the number you get when you take the square of another number (hence the name “square” root). For example, if we want to…
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Square Root of Negative Numbers
Yep, you heard us right. We know what you’re thinking: “But wait, isn’t a square root always positive or zero?” First off, let’s clarify…
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Solving Equations
Look no further than solving equations! That’s right, this is not your typical algebra class. We’re talking about real-life applications of math that will…
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Metrics of Positive Scalar Curvature and Connections with Surgery
Don’t worry if you don’t know what any of those words mean, because we’ll break it down for ya in a way that won’t…
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Invariance Theory and its Applications in Mathematical Analysis
No worries, though, because I’m here to break it down for you in the most casual way possible. To kick things off, what is…
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Kazdan and Warner’s Trichotomy Theorem
Now, before we dive into the details of this theorem, let’s first clarify what “trichotomy” means in math speak. Essentially, it refers to a…
