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Category Archives: Extra
What is Curvature? (II)
[ Background required: rudimentary vector calculus. ] The aforementioned definition of curvature is practical but a little aesthetically displeasing. Specifically, one seeks a definition which is independent of the parametrization of the curve. The advantage of such a definition is … Continue reading
What is Curvature? (I)
[ Background required: calculus, specifically differentiation. ] In this post, we will give a little background intuition on the definition of curvature. One possible approach is given in wikipedia, ours is another. Note that this is not IMOrelated (my apologies … Continue reading
Pick’s Theorem and Some Interesting Applications
[ Background required: none. ] A lattice point on the cartesian plane is a point where both coordinates are integers. Let P be a polygon on the cartesian plane such that every vertex is a lattice point (we call it a lattice polygon). … Continue reading
Posted in Extra
Tagged arithmetic, farey sequences, ford circles, geometry, intermediate, lattice points, pick's theorem
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Matrices and Linear Algebra
Background recommended : coordinate geometry Here I thought I’d give an outline of linear algebra and matrices starting from a more axiomatic viewpoint, instead of merely giving rules of computation – the way it’s usually taught in school. The materials … Continue reading
Number Theory and Calculus/Analysis
Background required: modular arithmetic, calculus. Once in a while, I’ll post something which offers a glimpse into more advanced mathematics. Here’s one. Example 1 For starters, we know from basic algebra that . Let’s see if there’s a corresponding result … Continue reading
Posted in Extra
Tagged advanced, analysis, calculus, extra, notes, number theory, padic
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