I am not the most math-affine person, but passable. What breaks me every time is greek letters in formulas, or one letter in both cases(upper/lower). I cannot seem to remember even the most basic formulas if they contain greek characters (an exception being alpha, beta, delta, pi, epsilon and gamma, perhaps because i learned these at a younger age). I can read and write them all, but formulas containing them won't stick and are much harder to understand/work with 'at a glance'. Lower case char vs. same char in upper case also trips me up, as the case info tends to vanish from my recollection.

As the latin alphabet contains more than enough characters to tackle most questions, i surmise that greek characters are in use because that way you can express more things simultaneously without overlapping meaning. However that pro for me pales in light of the con that i cannot recall the formulas.

Rewriting formulas did the trick, but i am still holding out hope that i am not alone with this affliction, and that there is ready-made literature out there that caters to my inability. I did not know whether to post this here or in the Physics stack (Thermodynamics lit is driving me up the walls) but my guess was that there is some overlap in readership anyways.

Tldr: I'm looking for university level (though introductory) Calculus and Thermodynamics literature with one-case, no-greek character set in English or German; or equivalent literature that has the ideas contained in the formulas spelled out long-form (e.g. 'The sine of the difference of the temperature ..')

Edit: To quote Paul Sinclair, from his answer below: " The Law of Sines that Hagen von Eitzen quotes is not "$\frac a{\sin A} = \frac b{\sin B} = \frac c{\sin C}$". But rather that "in a triangle, the ratio of a side to the sine of its opposing angle is the same for all three sides" " - My problem is not that i try and memorize ' lower case a divided by the sine of upper case A ... ' but that i cannot, at a glance, divine the meaning of that formula, and neither can i recreate that formula (actually it's a bad example, because i am, as stated, ok with the use of alpha, beta and gamma, probably because i learned them in some formative phase in school; So those could have been used here and made the formula better for me, as it would have done away with the upper case characters...).

I am aware that greek, fat, cursive, etc. are a great help to many others out there, and that there can be meaning encoded, etc. . I'd just like a text book that either has formulas completely rendered as the ideas they represent, or as formulas in one-case only Latin. Please refrain from 'walk it off'-comments and 'that's math, man'-comments. I walked it off, got a degree, am functional. I'd just like to read maths literature, for fun, without having to rewrite and annotate every single formula.

  • $\begingroup$ idk if you'll get what youre asking for because greek letters are a part of math .Its everywhere. $\endgroup$ – The Integrator Jun 18 '18 at 15:27
  • $\begingroup$ Read TeX source code! E.g., on MSE just press the "edit" buttons, and voilà: Everything can be read in plain ASCI text. $\endgroup$ – Christian Blatter Jun 18 '18 at 15:33
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    $\begingroup$ The alphabet, case, font, etc. are in fact means to improve the way we convey meanings and contexts to be seen 'at a glance'. The formula $$ \frac a{\sin u}=\frac b{\sin v}=\frac c{\sin w}=\frac{abc}d=2r$$ needs a lot of explanation ($u$ is the angle opposite side $a$ in a triangle $ABC$ - oops: a triangle $efg$ - and $v$ is the angle oppsite $b$ and $w$ the angle opposite $c$ adn $d$ is the area of the triangle even though we maybe called it $q$ a few formulas earlier because we needed $d$ for something else, and $r$ is the radius of the circumscribed (or was it inscribed?) circle. $\endgroup$ – Hagen von Eitzen Jun 18 '18 at 15:41
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    $\begingroup$ Greek characters are so ubiquitous in math or science writing it would be a mistake to skip over them. If it helps to know the names of the characters, just take a look at, e.g., en.wikipedia.org/wiki/Greek_alphabet once in a while and you'll get it. There's also nothing wrong with re-writing the formulas using Roman characters while you are learning, except it can be time-consuming. $\endgroup$ – Jair Taylor Jun 18 '18 at 23:49
  • $\begingroup$ To the 'walk it off' commenters: i have been able to read and write all greek letters, upper and lower, usual and alternate for going on twenty years. Hagen von Eitzens formula above i have gone through once, and can now reproduce. Had there been greek characters i'd now be lost. ----- To the 'that's how math is' commenters: i know, i said as much in the question, that's exactly the problem. The resultant problems from transcribing into single-case Latin are far outweighed by the benefits, for me. I just hoped there might be enough of this inability out there to have fomented a few textbooks. $\endgroup$ – bukwyrm Jun 19 '18 at 8:38

This is not an answer to your question per se, as I do not know of any books that do as you ask. As The Integrator says, these letters are everywhere.

But I suspect that part of your problem is how you are approaching mathematics. If I am wrong about this, I apologize for wasting your time. But it appears that you have fallen into the trap of thinking of mathematics as a bunch of formulas to be memorized. And apparently your memory works phonically rather than visually, so $x$ and $X$ and $\mathbf X$ are hard to differentiate. That you keep thinking about them as the lower case letter $x$, the upper case letter $X$ and a bold un-italicized upper case $\mathbf X$, instead of as a point $x$ in a topological space $X$ from a family $\mathbf X$ indicates that in your memorization you are concentrating on the symbols instead of what they stand for, and what the formula actually means.

To be sure, memorization is a useful skill in mathematics. But mathematics is no more about this than literature is about memorizing dictionaries. Logophiles know many interesting words and concepts, but it takes different skills to string them together into a great novel. Similarly, in mathematics, memorizing formulas and algorithms will get you past many tests, but leave you woefully unprepared to figure out, for example, where the center of the landing gear axle is when the oleo extension is a given amount (a calculation that I've had to automate).

  • Knowing that "$6 + 9 = 15$" is really useful, but recognizing that it means when you join $6$ objects with $9$ other objects, the resulting count will be $15$ objects, is better.
  • Knowing that $A = \frac 12bh$ is good, but knowing that the area of a triangle is half its base times its height is better. And better yet is to know that if you take a copy of the triangle, turn if over and join it to the original along a common side, you get a parallelogram with the same base and height, and cutting off a right triangle from one side and moving it to the other of the parallelogram converts it into a rectangle of the same base and height, so that the area is the product of base times height, is even better yet. Because then if you have trouble remembering "$A = \frac 12bh$", you have the whole road map for why it is true to remind you.
  • The Law of Sines that Hagen von Eitzen quotes is not "$\frac a{\sin A} = \frac b{\sin B} = \frac c{\sin C}$". But rather that "in a triangle, the ratio of a side to the sine of its opposing angle is the same for all three sides".

The best advice I can give you is stop memorizing letters and start memorizing ideas.

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    $\begingroup$ Lovely answer. I hope the OP appreciates it. You could add to it in a way that brings it closer to his question by noting that we use typographical conventions to remind us of ideas. In geometry, Latin letters often stand for lengths, Greek ones for angles. The mathbb font gives is $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$ for common important sets of numbers. And so on. $\endgroup$ – Ethan Bolker Jun 18 '18 at 23:55
  • $\begingroup$ It is a lovely text, i wholly endorse the expressed ideas. It is not an answer, as Paul Sinclair already suspected: Imagine a blind person asking for audiobooks of Math. Neither the information that math ideas can be easily expressed using just a few squiggles on paper, nor the information that reading is a lot faster than listening are wrong, but they are not helping, either. I know greek characters, i can read them, write them, pronounce them. I just can't USE them in formulas. If there are books that exclusively go: 'Sum of all values, divided by number of values', i'd love it, too. $\endgroup$ – bukwyrm Jun 19 '18 at 9:09
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    $\begingroup$ @bukwyrm - I included the apology at the start because I knew I was picking up on a few vague clues and extrapolating for causes behind them. But I figured it was worth writing up in case I did hit close. I'm sorry I couldn't be of more help. From your comment, it doesn't sound like you truly understood my point (you need to concentrate on the ideas, not the notations and algorithms), but this may just be talking past each other, and I don't want to waste your time or mine by going back and forth on that. I hope you can find an approach that works for you. $\endgroup$ – Paul Sinclair Jun 19 '18 at 14:49
  • $\begingroup$ Thanks for your time, Paul! $\endgroup$ – bukwyrm Jun 19 '18 at 20:10

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