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.
I applaud the idea, but I think this book needs some serious work before it is suitable for your intended audience.
For example, in Section 1.1 you explain how to go about solving the equation x^2 - 4 = 45, a topic which (I would venture) most 16 year olds should be comfortable with.
Then in Section 1.2 you, out of nowhere, introduce set-theoretical ideas and notation. Even seemingly innocent notation like
{0, 1, 2, 3, ...}
to denote the natural numbers can be confusing for someone who hasn't seen it before. In this case it's clear that the dots are supposed to indicate "continue in the obvious way". But then you write
Q = { -1.5, 1/3, 22/7, 0.125, ... }
in which the dots, presumably, mean something different. Then, at the bottom of the page, you suddenly start using the notation "∈" to denote set membership, as in
if x,y ∈ N, then (x+y) ∈ N.
First, what does this weird "∈" symbol mean? Second, what does it mean to write "x,y ∈ N"? Is that x∈N and y∈N? Or is it some special object "x,y" that is ∈N? Or is it two statements, "x" on its own, and "y∈N"?
The next couple of paragraphs contain both historical and mathematical inaccuracies (can you really always divide two rational numbers to get another rational number?). I'll stop there.
Like I say, I applaud what you're trying to do. I think you have a noble aim. But if the preview is anything to go by, your textbook in its current form is falling short of that aim.
> For example, in Section 1.1 you explain how to go about solving the equation x^2 - 4 = 45, a topic which (I would venture) most 16 year olds should be comfortable with.
> Then in Section 1.2 you, out of nowhere, introduce set-theoretical ideas and notation.
Is there any decent "crowd editing" solution? Or at least, "crowd suggested edits" solution?
Smart people know the math and the grammar and can correct those errors, or improve diagrams, or tweak the wording. People with weak math can say where they get confused; where things ramp up too quickly or where things take too long to get going.
Errors in a book like this are especially dangerous for someone like me. Dunning Kruger and all that - I wont know enough to know what I don't know, or to know what I've learnt is not quite correct.
> even seemingly innocent notation like {0, 1, 2, 3, ...}
I think that would be OK. There is a fine line between having to define everything and just using the math and letting the reader pick up on their own.
> set membership, as in if x,y ∈ N, then (x+y) ∈ N.
Yeah that was non-sense. It definitely didn't belong so early on in the book. Several people emailed me about this and it has been fixed in print/pdf versions now.
Yes, and it's pretty easy to prove. Multiplying any rational number by the inverse of another gives you a new rational number. (Zero doesn't have an inverse).
A rational number is a number that can be represented as one integer divided by another. Take two rational numbers, A = a/b, and B = c/d. If B has an inverse, then A/B = a/b * d/c = ad/bc. ad and bc are both integers, so A/B is rational.
My point was that you can only divide one rational by another to produce a new rational if the denominator is nonzero.
This is not what it says in the book, so there's potential for a newbie to get confused (and anyone reading the book in order to learn from it is, by definition, a newbie).
Oh, then that seems like a pretty pedantic worry. You can't divide by zero in any context; even children know that. It's such an obvious exception that it didn't even occur to me that's what you thought was wrong with the statement.
Given the definition "The definition of a rational number is a number that can be expressed as the quotient of two integers where the denominator is not 0."
Let N be the set of all integers and Q be the set of all rational numbers.
Trivially 0 is in the set N, 5 is in the set N
by the definition 0/5 is in Q. Therefore 0 is in Q. QED.
I appreciate the goal and the bold tone. I volunteer time to tutor middle and high school kids in math. It would be nice to have a fresh approach available, and a hard copy or four would be nice.
Would it be possible to create a version without the 'bullshit' language? Outside of the cover there are two 'bullshits' in the first chapter. It doesn't bother me but I don't think the directors of my program or parents would be very happy about it.
I'm sure the kids would like it but in a program such as ours, adding unnecessary friction to the relationship with parents is not a good idea. The older kids are spending time in our program that could be used to work jobs to help support their family (and it is a real pressure on these kids and families), so anything that threatens that is a non-starter.
Just to clarify and since the author is being cool and replying to individual comments...
The reason I asked about a 'clean' version is this: we serve kids from relatively low-income households. The goal is to increase high school graduation rates and college attendance. This is a long-term goal that conflicts with short-term needs. Often times it might be better to have a 13-17 year old boy or girl go to work with a family member, instead of spending time being tutored or participating in athletics.
In this situation, I can't send a kid home with this book if they want to check out the new approach. I love profanity and curse more than I should, but there are certain situations and audiences where it's not appropriate. Perhaps much of the audience for this book could use a cleaner approach.
I am definitely going to do a cleaned up version with less attitude. I will start by cleaning up the examples. The theory sections are mostly OK. Please send me an email so I can keep you updated on that front.
For v4.0 of the book, I am thinking of making it customizable. Before you order the book, you will be able to adjust the level of "attitude" with a slider.
I hesitated to post this, since I think clearer, shorter, better written textbooks are an admirable goal, and I keep a (short) list of good text books I have found over the years. But based on the preview on the website, I'm going to keep referring those who ask me to Gelfand's wonderful basic math texts instead (Algebra, Method of Coordinates, Functions and Their Graphs, Trigonometry -- anyone who wants further pointers to these, private message me).
There are also some howlers in the preview text, such as "after thinking very hard the mathematicians were able to classify all the different number like objects into sets" and then lists the naturals, integers, rationals, reals, and complex numbers. Except that these are nested subsets of each other, not disjoint, and the four normed division algebras are the reals, complexes numbers, quaternions, and octionions, so if you're going to talk about all the number like objects without including those last two, you're off the mark.
I haven't seen the physics sections, but I will say that teaching physics is actually remarkably difficult. I tend to recommend 1960s editions of Halliday and Resnick (not the recent ones!), though I will probably switch to recommending Karl Wiemann's work (http://c21.phas.ubc.ca/).
I absolutely agree that mechanics and the differential and integral calculus should be taught together, though. They don't make any sense without each other.
"after thinking very hard the mathematicians were able to classify all the different number like objects into sets"
Granted I am only going from the quote but I see nothing in there that indicates he considers them disjoint. Given most people have seen the Euler diagram of numbers since grade school i think the default interpretation would be correct. Could be clarified but not a howler.
quaternions, and octionions,
Considering the intended audience I do not see what purpose that would serve beyond intimidating the audience with how clever he is. Counter productive. This is just intro physics - the places where quaternions might be useful are just not there. And in the cases where introducing the terms actually served a purpose one would be better served by just going with the neater geometric algebra framework.
There are some helpful suggestions in some posts but it would be nice if people swapped their easily flabbergasted expert tones for a more helpful one. He has a vision and has begun acting on it. Has a good start with lots of potential. No one gets it just right from the outset.
> Given most people have seen the Euler diagram of numbers since grade school i think the default interpretation would be correct.
This kind of assumption is one reason so many textbooks suck so much. This assumption is not true for me. I don't know why you'd assume it would be true for "most people."
Indeed, stating that these objects result from some classification of all number-like objects seems misleading at best: Most mathematicians would, just as one example, certainly consider p-adic numbers as number like objects.
It would be better to point out what really matters in the hierarchy N, Z, Q, R, C:
Everybody will accept that N is an interesting object for counting.
Z is the quotient group of N under addition, more elementary: In Z you can compute arbitrary differences of elements of N, and it is the smallest "reasonable" such object.
Similarly, Q is the quotient field of Z, i.e. "the smallest reasonable object containing Z that allows division of non-zero elements".
R is the completion of Q under a natural metric (i.e., "fills the gap on the number line of Q"), and therefore allows one to have a reasonable notion of limits and calculus.
C finally is the algebraic closure of R, so that every non-constant polynomial has a root in C.
Thus, these objects are all constructed from the natural numbers to satisfy certain "niceness" properties.
Of course, it would take quite some space to explain this in a very elementary fashion. So perhaps it is instead better to simply refrain from such a statement in a textbook aiming for shortness above all, or at least make sure that any statement in this direction is substantiated and supported by a suitable reference to a place where your readers can learn more.
A textbook that gains conciseness from vague statements and half-truths would seem to be much worse than a textbook of twice the length that explains its content well.
My choice was to cover N,Z,Q operationally -- as in what you can do with them. Everyone knows about +,-,/ and so I think it makes sense to connect with this previous knowledge of the reader rather than get into the formality of sets and set containment. I stand by my choice.
> normed division algebras are the reals,
> complexes numbers, quaternions, and octionions,
Can you see why I would not want to talk about quaternions and octionions in a chapter which is meant to introduce math to people who have math phobia?
> these are nested subsets of each other, not disjoint,
>
Everybody can see why you wouldn't want to do that, but there's no point in lying or, if you prefer, selectively informing. Complex numbers and quaternions will be equally mysterious to the true novice; there's nothing intrinsically scary about the words.
> I tend to recommend 1960s editions of Halliday and Resnick (not the recent ones!)
I'm curious why. I remember reading the second edition back in 1998. Recently, I got one of the new editions (8th) but the new ones seem too verbose. What went wrong?
In textbook publishing, it's very important to put out a new edition every year or two. Otherwise your sales will disappear, since everyone will buy the book used. For a book like Halliday and Resnick that's been around since the 1960s, it doesn't take a very large number of people selling theirs to satisfy the demand of all current physics students.
So you put out a new edition in which you shuffle all the exercises so that students can't do their homework, and you have someone mess with the text and the formatting to make it look like a real change. You add glossy pictures, because you get a much bigger visual impact from changing the pictures than from actually changing content.
For an old book, this is a problem because often the authors are dead or retired, or think the book is just fine. Now you have to find someone who would like his name added to a classic text who will sign off on the job. Today it's Halliday, Resnick, and Crane. For Arfken's old mathematical methods for physics text, it was Weber.
Thanks for pointing to Gelfand. I'd never heard of him. Intriguing that University of Chicago assigns these texts. (Heads up— there's no contact info in your profile).
Personally looking forward to the ebook coming out! I was actually just this morning going through and signing up to a bunch of mathematics related Coursera courses. For those interested, quite a few are starting soon:
I would adjust the tone for the "I am in Arts" section. Saying "I think you have math issues" is not the kind of welcome you want to give to people who do, in fact, have math issues.
I like the end, where you emphasize that math is a great exercise in abstract thinking and modeling. But I would start with something more neutral saying something like, "Many people had suboptimal experiences with math in school because it was often presented well, and some teaching styles don't work for some people. And some may have just always found other things more interesting. However, my goal with this book was to make math more accessible and interesting to many people by presenting material in more a more intuitive manner and emphasizing the core skills of abstract thinking and mathematical modeling of the real world."
That's definitely not perfect, but it's something to start with. Try to imagine that you're someone who never found math all that interesting and always thought that literature or history or art was far more interesting and meaningful, and that possibly you had some bad experiences with math and got the idea that you're not good at it. Now try to imagine what might trigger those bad feelings about math and turn you off to a book, versus what might make you decide to give it a chance. If you don't trust your ability to imagine this way, try to find a close friend who is in this situation and will be honest with you.
I disagree. Looking at the title, & reading over the preview of the book, I think that the concise, anti-politically correct tone the author uses is one of his best selling points. After all the book is titled "no bullshit". And there's already plenty of texts that use ostensibly comforting words to artists.
There is a difference between being somewhat edgy and improper ("no bullshit") and actively working against one's aims by including copy that is confrontational and discouraging to the most insecure segment of one's audience ("you have a math problem; you need therapy"). Those whom it does not bother might appreciate this continuation of his tone, but it is horribly damaging with the audience that it claims to target.
I have some experience encouraging groups who tend to be less sure of their abilities in an academic subject to study that subject and am friends with many people who are much more involved in these efforts, and I know that being confrontational is counterproductive and that you have to be very careful about how you suggest to them that they have a "problem", even if you are telling them that they can overcome that problem. You want to stay positive and show empathy toward their struggles, emphasizing that the struggles are not any failing or inherent shortcoming on their part and are very common.
PS: I know a lot of people who say that they absolutely hate math because they think, for some reason, that they are not good at it. You should consider giving math another try. Math is not just about algebra ...
I like the abrasive comment "you have issues", but it is better to stay positive rather than point fingers. Everyone has issues ;)
I would have to disagree with the general statement that "textbooks suck". Stewart's calculus ("the violin book") is really a great textbook, and it's used very widely. Serway Jewett is a superb Physics textbook. The examples, in particular, are excellent (sometimes humorous or intriguing.)
Also, textbooks are long. But most courses don't use the entire textbook. I took 3 math courses and 2 physics courses in first year using those two textbooks and we didn't use every section, nor did we have to read every page.
I think having example problems which have stood the test of time (more than 20 years for those 2 textbooks, I think) is worthwhile.
I'm taking the Serway and Jewett physics right now, and I actually hate it. Their explanations of tricky concepts kind of suck. For example, it doesn't even try to explain why a hot gas is less ordered than a cool one (it's the same amount of information, the same number of real numbers, right?). I only got a vague understanding after scouring Wikipedia and later portions of the chapter. Stewart is pretty decent though, AFAICT.
This book looks very interesting, and one that I want to buy, but I'm going to hold off on buying it at the moment because (based on the comments in this thread and the preview) it sounds incomplete. Any chance of you selling a work in progress version so that we can help out (akin to the Manning Early Access Program)?
I actually clicked "Buy Now" before I realized this was a physical textbook and cancelled. To me, it's almost inexcusable to market this sort of text to this type of audience and not have a digital copy.
Shouldn't the barriers to entry be much lower for the author to get this out electronically?
I see that the author is responding to comments here, so if you're like me and will buy it if it comes out electronically, please let him know in the comments that he can count on your purchase.
Assuming you're interested in even compensating yourself for the time you're spending on this, I wouldn't go too low. Maybe base price of $19, and free when you order the physical book? That would still give you some wiggle room to do sales and give discounts to people who ask. Many people will happily pay that much, and if you were to go as low as, say, $9 (closer to 8 after transaction fees), that's really not that much, and you'll need to sell a lot to really make money and be able to keep doing this.
Hi Ivan, glad to hear it. You can count on my purchase.
Regarding pricing, yeah, you probably want to go cheaper than your print version. Maybe $19 or $9, depending on how much profit you are expecting to make on the physical copies.
To be honest, you're probably best off a/b testing the price, as it can be very surprising how consumers will react to various price points. I've seen situations were significant price hikes result in much higher sales, presumably because of the implied value of the product.
Please listen to this guy's suggestion of making the price for both only marginally higher than the price for the Print version alone. One of the quickest ways to kill my interest in in purchasing a book is by expecting someone to pay a non-trivial amount of money for a digital copy after they just purchased a hard copy at full retail.
As far as pricing the ebook alone, I think it should be somewhere around 14.99 to 19.99.
If it helps, I am probably a good example of your target customer. I didn't take my education seriously until I was out of high school for a few years, and now I find myself trying to catch up with all of the stuff I should have learned when I was younger.
If it were a one-off download, it probably wouldn't be. But I quite like the system O'Reilly uses: $5 for an ebook if you own the dead-tree version, because you can download it as many times as you like, in all different formats, and they maintain it with errata updates etc. for life.
The lifetime ability to download the most-current version of a book in any current format is, IMO, worth a few dollars more than a free but unmaintained ebook in what may very easily become a legacy format within a few years.
Good point. Every book should come with a free digital copy, but unfortunately the standard practice seems to be to offer a trivial discount when purchasing both.
The digital copy offers something the physical copy doesn't, e.g. portability. Some people might be willing to pay an incremental sum for this added benefit.
1) If a book is interesting and its priced around 15$, I would purchase it no question asked.
2) I hope you can release a EPUB/Mobi version of the book in the future and make it available to people who bought the PDF.
3) This might be pushing it but if someone has purchased the ebook and wants to get the paperbound after certain period of time, it would be sweet if you can offer major discount on paperbound for those people (look at Oreilly for an example)
4) Similarly offer ebook version of the book with the paperbound copy, almost every publisher does it these days.
For what it is it seems pretty reasonably priced as it is. I wouldn't drop the price too much.
Also you mention formats in another comment. It'd be nice to have a choice. ePub is easier to read on some devices, but then PDF is easier to mark up (I'm thinking Goodreader) later on, which is nice for this sort of thing. Anyway, once you have an ebook version that's another sale from me :)
If you scroll through his comments, you'll see many instances of him telling people to charge more for things and explaining some of this stuff news.ycombinator.com/threads?id=patio11
I'm not great with math, so seeing your take on it is exciting. I think $29 for the print copy is a good price, and $19 for the PDF (and I wouldn't go much lower than that).
I think after a few iterations of this book, this should be a real money maker for you.
BTW, the language is a bit strong, and may distract from the message. I have two daughters in University but I won't buy your book for them until the language is toned down. There are probably others like me as well. Worth considering.
I'm not a big fan of that picture. We're trying to
compute f'(400), judging by the text (scroll down a bit on the first
page). What the image suggests, afaict, is that f'(400) that can be
computed as the limit [f(x+h) - f(x-h)]/2h with x=400 and h -> 0 (in
the picture, we see the case h=80). At least the graphic appears to
connect the two somehow.
Nothing to that effect is mentioned in the text... just the cookbook
recipe 'at^n becomes ant^{n-1}'. So why is there even a triangle here?
Two things are fishy here. The limit and the triangle.
The limit: Taking the aforementioned limit for the derivative is
rather weird. If the function is differentiable, you'll get the right
result, namely f'(x). If you consider the limit for the function x ->
|x| at x=0 e.g., you'll get a limit as well, even though that function
is not differentiable.
The triangle: I would expect it to connect the three points
[x-h,f(x-h)], [x+h,f(x-h)], [x+h,f(x+h)]. Instead, we get three points
whose X-coordinates match the ones I mentioned with Y-coordinates that
are chosen to have the slope of the triangle match the slope of the
function. Why? (If this were about the mean-value theorem... but it's not!)
So what I'm left with is a plot with a triangle, no text that explains
any of that, and nothing I can make of it myself.
> I'm not a big fan of that picture. We're
> trying to compute f'(400),
>
Well, technically speaking, you are not supposed to talk about derivatives in the picture answer. I am just trying to connect the notion of "download rate" with the "slope of the file size function".
The triangle with the hypotenuse touching the function (tangent line) is a way to compute the slope from the graph. As such the actual size of the triangle is not important -- so long as it helps you compute the rise-over-run.
So to answer your question -- the triangle is not meant to illustrate the derivative calculation. Indeed, it would be quite difficult to show an infinitely small triangle ;)
I teach college biology, and I've never seen a textbook in my discipline that wasn't written in a soporific and meandering style. Some are worse than others, but I've never seen a textbook I thought was good.
If I needed to fill a gap in my knowledge or learn a new subject I would never resort to a textbook until I had exhausted every other available option.
That may well be true in your discipline, but there are some excellent, concise texts in undergraduate mathematics. For example, Apostol's Calculus or Spivak's Calculus on Manifolds. Not the most accessible texts by a longshot, but not your average Pearson or Wiley drivel either.
likewise, the explanation for how the concepts flow together. drawing these connections is usually the last step for me in the "a-ha" moment, and too few resources explain the connections between concepts really well. khan academy being a strong exception.
Helena Curtis wrote a wonderful college level intro textbook as of 1980 when I last used it, but the publisher (Worth) let it die after she retired (which also pretty much killed them as I recall).
I'm sure halo knows there are other browsers. Remarking that a website is unreadable in a widely-used browser is a legitimate comment that doesn't deserve snark.
I don't think that there is a need for the liberal use of swearing in a mathematics book ("shit" appears 5 times in your sample PDF alone, two of which are in the title). In my opinion, it makes it sound very amateur and unprofessional.
> "Check this shit out:"
Could be "Consider this example:"
> Now get ready for some crazy shit. Using your...
Now for something even more interesting. Using your...
> that there is a need for the liberal use of swearing in a mathematics book
You are right that there is no //need//, but I find that a little swearing goes a long way to make the student who is scared of the subject feel more comfortable. "This is not a math book", they will think -- this is informal narrative like a blog post.
A cleaned up version is in the works. ETA March because I have to finish Linear Algebra and E&M first.
random idea - consider making some examples/sections from the book also available as an IPython notebook. IPython+matplotlib+numpy+scipy is a perfect quartet for getting some ideas across in an interactive, intuitive way. best of all the reader doesnt have to setup anything. just include some URLs in your book.
Why this is on Hacker News, while the download rate in his example would follow f(t)=k\cdot t^2? Mine only follows f(t)=C+k\cdot rand().
We need better, deeper, broader understanding of math and physics. This fast food-styled stuff is really not for us. Why? Think you're going into approximated algorithms without knowing the wonderful essentials of constant e? Think you're going into pattern recognition without a throughout understanding of linear/quadratic/etc systems?
A thick textbook only to charge you $150? That sounds like "6-pack abs the quick way" advertisement... XD
A thick textbook only to charge you $150? That sounds
like "6-pack abs the quick way" advertisement... XD
Have you been to college recently? I'm in college right now, and I absolutely believe it. Maybe it's not quite that simple, but only because the publishers are being slightly more devious. College textbooks are a racket.
I received my undergrad education in China. We've got some really good math textbooks, and they're very cheap. Yes I know textbooks in English are very expensive. But during my PhD education I mainly rely on free resources. (For example, Vazirani has written some very comprehensive materials about math and algorithms, search for it. If I don't remember it wrong, somebody posted his algorithm book a month ago on HN)
On the other hand, for what purpose would you like to choose a book that you call "racket"? If forced by your school, then it's done, no choice. If it's your willpower to learn something, why don't do some mining and research first before diving into a pile of junk? :-)
I actually got away without the book for my first semester of physics, but basically yes, it's forced by the school. That's why they can get away with a racket.
Ivan, could you share a little about your toolchain writing this book? There's been a lot of traffic on HN around self publishing and I think it would be of interest.
OK, so I have a blog post in the works but since that is taking too long I will say a few words here briefly. Basically I use:
dokuwiki | dokutexit | sed (cleanup) | pdflatex
DokuWiki is a file-system based wiki which I run on localhost. Each section is one .txt file. To generate the book I made a master file which includes all necessary sections. The plugin dokutexit then produces the .tex output. Dokutexit does a good job, but I still there is some cleanup necessary (via sed). I also do some manual touchups by adding the front matter / back matter stuff (via \input{subfile.tex}) and then pdflatex does its magic.
The latex document class is extbook -- the regular book class does not have the 9pt option.
@READERS Sorry for inflicting upon you the 9pt font. I know it is tiny, but look at how small and portable the book is now ;)
____
I am still researching how to generate .epub and .mobi form latex files. If anyone has pointers to articles which discuss this, I would be very interested to hear. PM me, or post them here so that everyone can learn. (plasTeX? MathJax? MathML?)
I would buy it, but it appears you don't have an ebook version? I can't really keep physical books because they take up too much space (small apartment).
As a high school student with final math exams coming up soon, large gaps in my mathematical knowledge and a bunch of useless textbooks, I went for the "buy now" button just after reading the "I will teach you everything you need to know about equations, functions, vectors, limits, derivatives, integrals, forces, accelerations and optics" tagline.
Then I saw that there is no e-book option. It's 2013. Get with the times.
Same here - I was excited to see this kind of book, as I'm trying to improve my maths knowledge and the conciseness and structure of Ivan's book was attractive, but no eBook option stopped me right there.
While we're on the topic of exams, I've recently came across the following book[1] that deals specifically with doing better in maths heavy exams - you might want to have a look whether it's something that can help you in your exams:
An ebook being cheaper isn't a big deal for me, since my view is the price more to do with the content than the format. For other people it does seem to be more significant though. Maybe it should be the price of the physical book less the costs of printing/binding/etc. such that you get the same amount of money in the pocket at the end? (I don't know if that's how it works, having never published a book!)
PDF is good for PC viewing and will work on pretty much everything, though EPUB and Kindle formats will make things better on e-readers and phones/tablets since they support re-flowable content, but I guess would probably require more work on your part to support.
Please please please do an ePub version. PDF is great for reading on a computer, but an ePub is miles better on an iPad. I'll buy a digital copy if it comes in ePub, but not if it's only PDF.
Excellent - I'd be willing to spend around $20 - PDF is my preferred format (iPad and Desktop PC), but agree with notdrunkatall, why not offer all three.
On page 126 it is implied that if a person collides with two objects, the object with the most momentum will do that person the most harm.
This is nonsense. I am likely to survive being hit by a car at 10 mph, but I will certainly be killed if I'm hit by a 1 kg projectile travelling at 2000 m/s, even though it has less than half the momentum.
Sounds like a fascinating book. I'll be purchasing it as soon as the ebook is available.
Note: I didn't even know this book existed ten minutes ago, but now I'm annoyed that I have to wait until tomorrow for the ebook version. Sometimes my demand for instant gratification shocks even me.
I was just discussing writing this same exact book for/with my wife. Se^(2^(x))^e does not interest her. The standard in my past has been mathematics books that use equations that do not/rarely occur in nature. The concepts are priceless, but the problems/solutions do not use common integers.
Breaking a problem down six times to actually start applying the principle I am learning is my largest downfall. It makes me lose interest in the subject at hand. I would rather understand and be able to reference the concepts.
Like many others, an ebook would be more delightful. Yet, I may buy the paperback this weekend.
Nice! I'd buy ebook when it's out. BTW, I also recommend "The Joy of x: A Guided Tour of Math, from One to Infinity" (http://www.stevenstrogatz.com/the_joy_of_x.html). This amazing book rekindled my interest in Mathematics. Now, I've got a couple of math books in my 'to-read' list.
I am a big fan of "choose your own adventure" kind of books, and I will try to do something with that soon.
For the physics part, I also have a simple physics game engine which is in the works. Instead of answering questions about different //points// of the motion the user would have to specify the js function which describes the entire motion. There will be not "grades" just test suites your code has to pass ;)
What do you have in mind exactly when you say "interactive book"?
I was thinking of graphs and equations where you could test different values, see how the outcome varies. When you learn with a graphic/equation you can manipulate, the experience stays with you
If you make this promising book available in eBook format you are guaranteed at least a few sales from HN readers, and indeed very likely from many other readers who prefer digital books over paper books.
I would advise that you make the digital copy of the book available as soon as possible—I am an interested buyer as well.
Based on the comments I've read and reading a bit of the preview - I am curious as to how polished this version is. I'm hesitant in buying the paperback copy especially, if there are errors.
Otherwise, this looks incredible. Exactly what I've wanted when wanting to learn math!
This is the third iteration of the book, so I think I have gotten the typos-per-page down to an almost non-existant level. I am sure there are some left, but it is definitely not a first draft.
From the example it looks like he doesn't connect the graphical answer to the calculus answer or to the obvious answer. I really hope he actually explains it in the book, because physicists are notoriously bad at being mathematically correct.
Thx for the feedback. I am just added the following paragraph to clarify.
It is important to see the connections between the three different ways of finding the answer: the intuitive notion of download speed that we are all familiar with, the graphical notion of slope and the more abstract calculus notion of function derivative.
I meant that I hope you explain elsewhere in the book why these notions are related. Too often in physics people just accept how things work out without understanding why mathematically. For instance, the whole point of introducing limits is to make the "obvious/graphical" answer of "download speed" rigorous, but students rarely make that connection regardless of how many times the professor or textbook reiterates it (most likely because they don't read the textbook or go to class to begin with).
Do you in your book mention that calculating the exact download speed is impossible (and why this is the case)? Do you mention that the download speed one sees in their web browser is an approximation via a limit? These are the kind of important connections that get lost in the bullshit and the calculations.
Only read a few pages, but I would eliminate a lot of the introductory formalism. Most people don't need to be confused by the different sets of numbers, or common uses of variable names, or how to alter the shape of functions.
Agreed! I am pleasantly surprised that someone else is doing this! I have been drawing "concept maps" for myself for the knowledge they taught in high school and undergrad school. I have always thought I was the only one to draw such things :) I am a very visual person and these maps help me memorize stuff but also understand how everything fits together.
I did not know it. It would be nice if one could travel through graphs by just clicking on nodes, expanding other neighboring nodes, etc. Too bad it seems to only allow browsing up to 2 nodes away from the central node...
formal notation and esoteric naming conventions is _exactly_ the bullshit i was expecting to be left out. i'm not sure this will actually work for the audience it was intended for.
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.