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Mathematics Foundations

Algebra, calculus, and the language of science.

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  1. 1

    Pythagorean Theorem

    Beginner
    a2+b2=c2a^2 + b^2 = c^2

    In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

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  2. 2

    Quadratic Formula

    Beginner
    x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    Solves any quadratic equation ax² + bx + c = 0 by finding its roots.

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    Mathematics
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  3. 3

    Euler's Identity

    Intermediate
    eiπ+1=0e^{i\pi} + 1 = 0

    Connects five fundamental constants—e, i, π, 1, and 0—in one breathtaking equation.

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  4. 4

    Taylor Series

    Intermediate
    f(x)=∑n=0∞f(n)(a)n!(x−a)nf(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n

    Any smooth function can be approximated as an infinite sum of polynomial terms around a point.

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  5. 5

    Bayes' Theorem

    Intermediate
    P(A∣B)=P(B∣A) P(A)P(B)P(A|B) = \frac{P(B|A)\, P(A)}{P(B)}

    Updates your belief about A after observing evidence B—rational reasoning under uncertainty.

    Formal Sciences
    Probability
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