I read the first 10 pages of the pdf. I'm not sure who you think your target audience is, but this book doesn't seem to serve any of them.
You gloss over huge sections of algebra, and in doing so, ignore incredibly common mistakes that students make. Take a look at the top of page 9, 6 \sqrt{x} - 7 = [...]. You solve that out, but give no reason as to why you got rid of the 7 first, the 6 second, and the radical third. This is not an easy concept, nor is it an academic distinction.
Math might be easy for you, but it probably isn't for your target audience. You're assuming entirely too much about what your readers will know.
Beyond that, some of your math (and math history) has flaws.
"So this is what number meant during the whole middle ages. The notion of 2.5 goats didn’t make any sense to the people of those days. They would have been totally confused by the menu at Rotisserie Romados which offers 1/4 of a chicken."
This is entirely untrue. Even most illiterate peasants knew the basics of fractional parts in the middle ages. 2.5 goats didn't make sense, but 2.5 stone of barley did. The church prohibited usury, but lending still happened, so they had some knowledge of percentages as well. Despite the fall of Rome and the horrible loss of knowledge that followed, math wasn't completely lost. In 725, monks knew enough mathematics to predict the date of Easter (based on the lunar cycle, mind you) years in advance. And math flourished in medieval Islam.
Heck, if my memory serves, fractions were invented in Ancient Sumer, ~4000 years earlier.
"We can move a function f to the left by h units by subtracting h from x and using that as the input argument:
g(x) = f(x − h)."
This actually translates the function to the right. This is also where I stopped reading.
I really want this to be good. I love finding wonderful new resources for teaching mathematics. I'm sure you put a serious effort into the text. But I fear your no bullshit guide is just going to scare the shit out of its readers.
The Bible, for example, uses fractions. In Lev. 5:16 - "He must make restitution for what he has failed to do in regard to the holy things, add a fifth of the value to that and give it all to the priest, who will make atonement for him with the ram as a guilt offering, and he will be forgiven."
But I'm with pflats' judgement. I see text like "Indeed, on computers systems which don’t have a hardware multiplication circuit, every time you write ab the computer will repeatedly add the number a for a total of b iterations." and wonder first, won't the target audience be confused by "hardware multiplication circuit", and second, is this actually true? I'm pretty sure they use shift-and-add.
Or, there's a use of "=" to say that "a/b = ... = one bth of a" then on the same page there's a triple bar "≡" used for the same thing. Will your target audience understand the notation shift?
The language "It is worth clarifying what" and "It is interesting to note that" and "We will now illustrate how the equations of kinematics are used to solve physics problems" are part of the same stultifying language you complain about. There's a bunch of places where you can simplify text like "the expression 5×32 +13 is to be interpreted" to "the expression 5×32 +13 is interpreted" -- the "to be" is useless. And the voice changes from "we get" to "you get".
Why is x<sup>-1</sup> different from f<sup>-1</sup> ? That is, the first is 1/x and the second is the function inverse. As far as I see, you don't explain that those "-1"s mean different things. Nor do you say that "f" is another type of variable naming pattern, which describes a functions.
Suppose your student wants to actually do the Moroccan example as an experiment. It will fail, because of air friction. Yet friction isn't brought up here. Newton's laws are not intuitive, because we are used to a world which is full of friction, and frictional forces aren't easy to describe. But the text assumes that the clarity of Newton's laws will be self-apparent, even if it doesn't match expectations.
The Moroccan example also uses "44.145[m]". Who measures their balcony height down to the millimeter? The precision was chosen so the answer would be exactly 3[s], but other examples aren't that fussy. In any case, the answer should be 3.00". Significant figures are hard for students to understand, and I don't see any guidance that a fall of 44 meters should not be answered 2.9950690022496134[s], even if that's what the computer gives.
Finally, good on you for using SI for the file size instead of base 210 units. However, [Mb] is megabit, not megabyte. You should use [MB].
Traditional Jewish sources would translate that as 25%. It does say one-fifth, but it's a fifth in the sense that you pay 125%, and 25% is one fifth of what you pay. There have been shifts in a lot of mathematical concepts over time and that's just one example. For instance, at some points in history people did use fractions, but favored using one in the numerator - 3/5 would have been expressed as 1/2 plus 1/10.
My goal was to find counter-examples to the phrase "The notion of 2.5 goats didn’t make any sense to the people of those days. They would have been totally confused by the menu at Rotisserie Romados which offers 1/4 of a chicken."
"The fraction one-fifth is likewise common (Lev. 5:16; 22:14)." "In ritual observances the fraction one-tenth occurs frequently (Num. 28)." "The term pi shenayim originally meant two-thirds but subsequently came to signify "twice as much" (II Kings 2:9)."
As for the translation, I used NIV. Some others will actually say 20% for that quote.
This comment highlights the benefits of editors in the traditional publishing industry. The publishing process may seem full of painful disincentives, but there are many non-obvious benefits to following its subscribed protocol. One of them is that you do not publish books, especially instructional ones, containing glaring errors.
There was an article on HN recently that mentioned the fact that most of a book's marketing is its reputation. This makes sense because you can't form a full opinion of a book until after you've read it, so buyers of the book are heavily influenced by the opinions of others who have already finished it. Nobody is going to shell out money for a book that they hear contains even a FEW glaring errors.
People hold books to such high standards because once you put your words into print, you cannot change them. There is no real-time editing of books. So people assume you have put the proper amount of preparation, thought, and diligence into your writing and editing. This is very difficult to do by yourself.
That said.... I do want to emphasize that the "traditional publishing industry" generally refers to the producers of hard-copy books. With the industry moving toward a digital future, real-time editing is becoming possible. I think we will see a move toward "crowdsourced" editing of for-profit books, not so much in the way that Wikipedia edits its content but more in the way that video games fix their bugs. We may start to see "beta releases" of digital books for early adopters. At the cost of reading what amounts to a rough draft, you will be able to access the content early, so long as you report any errors you find. I think on the whole this is a very positive change that will increase the world's general knowledge.
So I'm a very big fan of your first attempt at creating this book. I think the errors pflats points out are important to consider, but certainly nothing to discourage you. Don't let this criticism stop you from your pursuit. You are on a very good track.
You are right about the history, though I was specifically talking about the usage of the word "number" not about whether people knew about fractions. I won't dig up the reference, now, but I read in a history of Calculus treatise somewhere that Newton was the first who started using the word "number" in its present sense: any quantity including integers, rationals or irrationals.
If a complete copy of the pdf is not available you might want to make a draft wip copy available for purchase. If the feedback in this thread is any indication I think a lot of good will come out of it. (You may also want to honor Knuth by paying people who bought the wip pdf and spotted mistakes :)
This historical issue about the nature of a "number" also caught my eye. (In the PDF: "Before Newton, the word number referred only to the natural numbers...".)
Of course, the notion of irrational numbers dates (at least) back to the classical Greeks (the proof-by-contradiction that root-2 is irrational is ancient and elementary, and will be known to some of your intended audience). In the Greek era, there was debate about the status of the irrationals, but sophisticated Greeks were well-acquainted with rational numbers. The statement in the PDF seems to ignore this.
Summary: I think this statement of yours is dubious to begin with, and in any event would have to be so qualified and referenced that its value to a novice is nil.
I , too, would love a list of 'casualized' textbooks. I was interested in the premise of this, but the flaws i've caught thus far (the newton/natural number thing got me too) have made me lose confidence in the rest of the book.
"The Idiot's Guide to [Math Subject]" have all been really useful to me for my college courses. Well-written, detailed, and understanding of common mistakes, I would highly recommend them.
I didn't have the energy to respond to your comments in detail earlier so I will do that now.
> You gloss over huge sections of algebra
What do you have in mind?
> give no reason as to why you got rid of the 7 first, the 6 second ... third.
I think it is fine as is + math operator precedence //is// discussed.
> So this is what number meant during the whole middle ages.
You guys were all up on my case with the "number" thing. I took a Phil. of Math class at some point and learned that the pre-Newton notions of a numbers (referred to as "arithmoi" to indicate that they are distinct from the modern notion) was principally about the integers. Rationals were treated as separate objects (ratios) and irrationals like √2 were known only through geometrical arguments. I am sure bankers of Venice knew how to calculate too, but the point remains that Newton did something very special when he started using the word "number" to mean Real numbers: a concept which subsumes ints, floats and transcendental numbers. That being said, you and @mturmon are right that the wording could be better. Will fix / clarify.
You gloss over huge sections of algebra, and in doing so, ignore incredibly common mistakes that students make. Take a look at the top of page 9, 6 \sqrt{x} - 7 = [...]. You solve that out, but give no reason as to why you got rid of the 7 first, the 6 second, and the radical third. This is not an easy concept, nor is it an academic distinction.
Math might be easy for you, but it probably isn't for your target audience. You're assuming entirely too much about what your readers will know.
Beyond that, some of your math (and math history) has flaws.
"So this is what number meant during the whole middle ages. The notion of 2.5 goats didn’t make any sense to the people of those days. They would have been totally confused by the menu at Rotisserie Romados which offers 1/4 of a chicken."
This is entirely untrue. Even most illiterate peasants knew the basics of fractional parts in the middle ages. 2.5 goats didn't make sense, but 2.5 stone of barley did. The church prohibited usury, but lending still happened, so they had some knowledge of percentages as well. Despite the fall of Rome and the horrible loss of knowledge that followed, math wasn't completely lost. In 725, monks knew enough mathematics to predict the date of Easter (based on the lunar cycle, mind you) years in advance. And math flourished in medieval Islam.
Heck, if my memory serves, fractions were invented in Ancient Sumer, ~4000 years earlier.
"We can move a function f to the left by h units by subtracting h from x and using that as the input argument: g(x) = f(x − h)."
This actually translates the function to the right. This is also where I stopped reading.
I really want this to be good. I love finding wonderful new resources for teaching mathematics. I'm sure you put a serious effort into the text. But I fear your no bullshit guide is just going to scare the shit out of its readers.