Here is a list of 25 possible topics that serve as great math IA ideas. And keep in mind that in a math IA, it is more important to pick a topic that genuinely motivates you to display personal engagement than to pick something that sounds harder but does not resonate with you.
25 Unique Math IA Ideas
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Arc lengths from integration techniques
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Architecture and mathematics: the golden ratio
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Bertrand paradox and probabilities
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Cat’s cradle and the mathematics of knots
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Chaos theory and the logistic map
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Chess and the eight Queens puzzle
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Conditional probability and the Monty Hall problem
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Describing the vibrations of drums with Bessel functions
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Dirac delta function and its applications
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Elliptical geometry: when the sum of the angles of a triangle does not equal 180º
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Euler’s identity: complex numbers and mathematical beauty
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Fourier transformations
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Fractals in nature
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Markov chains and random walks
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Modular arithmetic: when 2+2 is not always equal to 4
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Möbius strip: the strange world of non-orientable surfaces
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Simpson’s paradox and the strange outcomes of misused statistics
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Special functions: error function and normal distributions
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Surprising ways of finding Pi: Gaussian integral and the Leibniz Formula
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The Koch snowflake: fractals and the tessellation of plane
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The Mandelbrot Set: when fractals meet complex numbers
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The Logistic function and its applications (population growth, neural networks, or linguistics)
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The Gambler’s ruin: how beneficial chances are never beneficial in the end
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The wave equation: how differential equations can be used to find the shape of a music note.
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Topology: when a coffee mug and a donut are one and the same