I am looking for a list of the most frequent Greek letters used in high school and college textbooks or some other corpora. I've realized my students don't know Greek letters and I would like to teach them starting from the most used letters. My interest is in high school, mainly.
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asked Jan 13 at 1:10
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6$\begingroup$ My bet is $\pi$. But seriously, just give them a sheet with the entire Greek alphabet for reference, and point them out if and when they come up. It highly depends on what math class it is. $\alpha, \beta, \gamma$ for angles in geometry, upper case $\Sigma$ for sums in combinatorics and probability. In Analysis you might need many $\varepsilon$'s ... $\endgroup$– Torsten SchoenebergJan 13 at 6:56
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$\begingroup$ Textbooks at which level of studies? $\endgroup$– TommiJan 13 at 7:41
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$\begingroup$ Let me reverse the question: is there any Greek letter which is not used in mathematics? :-) $\endgroup$– DominiqueJan 13 at 9:26
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8$\begingroup$ @Dominique .. D.L. Knuth claimed somewhere in Computers and Typesetting that upsilon $\upsilon$ is not used in mathematics. But he was wrong: it is used for the Hewitt realcompactification. I have a nice check for $2.56 from him for pointing that out. $\endgroup$– Gerald EdgarJan 13 at 10:23
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2$\begingroup$ Please update the question to indicate if you are talking about high school or college level. $\endgroup$– Amy BJan 13 at 14:01
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1 Answer
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It strongly depends on field. Everybody uses $\pi$ and $\Sigma$ appears in many fields as the summation sign. In elementary statistics you're likely to see $\sigma$, $\mu$, and $\chi$. In geometry and trigonometry $\theta$ is often used, and sometimes $\phi$ or $\psi$. In calculus, $\Delta$, $\epsilon$, and $\delta$ are ubiquitous. In elementary physics $\omega$, $\lambda$, $\Omega$, and $\rho$ have common uses. Beyond those, you often see $\alpha$, $\beta$, $\gamma$, $\tau$, $\Gamma$, $\Lambda$, $\Pi$, and sometimes $\eta$, $\zeta$, $\nu$, $\xi$, $\kappa$, $\Theta$, $\Phi$, $\Psi$, and $\Xi$. The variants $\varphi$, $\varepsilon$, and $\vartheta$ are common.
It is less common to see the letters that are indistinguishable from Latin letters, namely A, B, E, Z, H, I, K, M, N, O, P, T, X (Alpha, Beta, Epsilon, Zeta, Eta, Iota, Kappa, Mu, Nu, Omicron, Rho, Tau, Chi), and $\iota$, $\omicron$, $\upsilon$, and $\Upsilon$ seem to be rare as well. The variants $\varsigma$ and $\varpi$ are uncommon, although $\varpi$ shows up in number theory.
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2$\begingroup$ And the script pi $\varpi$ is used in astronomy for "perihelion". $\endgroup$ Jan 13 at 10:17
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5$\begingroup$ In some countries, you will see iota $\iota$ used for $\sqrt{-1}$ instead of $i$. $\endgroup$ Jan 13 at 10:25
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1$\begingroup$ Some students find it very hard when they don’t know the names of some of the letters. $\endgroup$– SimdJan 15 at 6:40
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$\begingroup$ @Simd When teaching the letters, teaching their names is a must. Of course this doesn't help a student who hasn't been taught a letter and encounters it in a text. I, for example, ran across $\varpi$ in a classic article of Hardy and Littlewood, but for several years had no idea that it was a variant of the lowercase pi. Torsten Schoeneberg's suggestion to distribute a reference sheet would help with that, as long as it included names and variant forms. Stackexchange sites are nice because anyone can view the LaTeX source and learn the names that way. $\endgroup$ Jan 15 at 13:39
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$\begingroup$ iota is used in category theory for a kind of injection (en.wikipedia.org/wiki/Inclusion_map) $\endgroup$ Jan 15 at 19:52