📐 Constructibility Criterion A real number $\\alpha$ is constructible if and only if $[\\mathbb{Q}(\\alpha):\\mathbb{Q}]$ is a power of $2$. From: gal-morandi Learn more:

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📐 Abel There is no formula that expresses the roots of the general fifth-degree polynomial equation in terms of the coefficients using only addition, subtraction, multiplication, division, and the extraction of $n$th roots. That is, the general quintic is not solvable by radicals. From: gal-edwards Learn more:

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📐 Kummer Theory Let $F$ be a field containing a primitive $n$-th root of unity. The abelian extensions $E/F$ of exponent dividing $n$ are in bijection with subgroups of $F^\\times / (F^\\times)^n$. Explicitly, $E = F(\\sqrt[n]{a_1}, \\ldots, \\sqrt[n]{a_r})$. From: gal-weintraub Learn more:

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🎮 Interactive: Continuity Explorer Test functions for continuity at a point. Understand the epsilon-delta definition visually. From: Real Analysis Try it:

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📖 Simple Root of $F(X)$ The polynomial $t$ in the roots is a simple root of its equation $F(X)$ if the polynomials $t, \\phi_1 t, \\phi_2 t, \\ldots$ obtained by distinct permutations of the roots are all numerically distinct (when actual root values are substituted). In modern language, this means $F(X)$ has no repeated roots. From: gal-edwards Learn more:

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Interactive courses covering the mathematics that powers modern technology, from foundational algebra to the cryptography securing the internet.