Edit: Cutting out all the "bullshit" seems to make it hard for a "busy adult" to easily learn the concept, but it actually seems like a good resource to improve your knowledge which you simply forgot.
For the part of noBS I'm through I appreciate the get-to-the-point explanation and amusing (thought highly opinionated) examples. I don't think there's much you can do better when you are teaching standard concepts and notation; it will always look foreign at first.
Looking at the sample, I agree with you. Condensed ≠ easy to understand. Honestly, a lot of the graduate texts I deal with look easier to understand. In my opinion, every single concept should be introduced with physical analogies if one wishes a reader with no maturity in the subject to actually understand. Then again if the author is going for "no-bullshit" this could serve as a good reference for someone who just needs a quick easy to understand reference.
Looking at the sample, I agree with you. Condensed ≠ easy to understand. Honestly, a lot of the graduate texts I deal with look easier to understand. In my opinion, every single concept should be introduced with physical analogies if one wishes a reader with no maturity in the subject to actually understand. Then again if the author is going for "no-bullshit" this could serve as a good reference for someone who just needs a quick easy to understand reference.
To my eyes it's a quick overview of some linear algebra basics, the only complex thing possibly being notation (but I would assume and hope the book builds up to it while also building intuition).
That looks fine to me. He's talking about reducing a matrix to reduced row echelon form, and gives a pretty clear example. If you're giving yourself 4 pages on linear algebra, there's not much better you can do.
That said, you're not going to learn linear algebra in four pages. No royal road, and all that.
Finishing the applications chapter has been a massive time sinkhole! I wanted to make a survey of all the cool things you can do once you have the tools of linear algebra under your belt, but it's proving to be too much (Chapter 8 is getting almost as long as the rest of the book).
In the coming weeks I'll be going over the latest draft and I might do a scope-cut, in order to get it done more quickly. In summary I'd say end-of-April for "dev close" and then probably a month for the final editing with my editor, so June 1st for official release.
Exactly my thought - this looks like a good review for people who breezed through this stuff in high school or college. Speaking as someone who was never able to get this stuff (not for lack of trying) back then, this guide uses the same obtuse language and carries the same "if this explanation isn't immediately understandable then you probably aren't cut out for this" tone that I hated back then too.
I bought the book, because $29 for a math/physics book is cheap and if I learn one single thing from it I'm going to get many many times that amount back.
Anyways: point being, flipping through the book, it is decided not like that image you posted. It's mostly casual prose with lots of diagrams.
To be fair, you were looking at the super-condensed linear algebra tutorial, which is meant to be a condensed pre-exam review for students and not as a standalone tutorial. The actual book starts off much more smoothly and introduces concepts step by step
(see http://cnd.mcgill.ca/~ivan/miniref/noBSguide2LA_preview.pdf for a preview).
The "onboarding" in the math/phys book (No bullshit guide to math and physics) is even smoother. About 1/3 of the text is a review of high school math topics, which helps to establish a solid foundation understanding mechanics and calculus. (see http://minireference.com/static/excerpts/noBSguide_v5_previe... for a PDF preview.)
You are absolutely right though, many of the readers who have written to me over the years are adults who used the book to review what they learned at university. The compactness works well for that.
I'm definitely going to look into this. Even with working on a second degree in Engineering Mechanics, I've found that I have forgotten a considerable amount of information I learned earlier in my degree (likely replaced by the overwhelming information in CS). I would love to brush back up on those areas, if only to overcome my fears of mechanical inadequacy. Without constant application, material as complex as mechanics can simply slip away, so having a book like this that hits on the high notes would be fantastic.
I think that's part of the alleged "bullshit", pretty stories that distract from the actual material.
Then again, similar methods like in Learn You A Haskell For Great Good seem to work on me. I do wonder how much time I spend trying to understand the jokes and references.
Sure, but why this book? I mean, it seems like a nice review guide and all (though probably too terse for someone trying to learn the material for the first time), but what about it is catching peoples' attention?
If I post about Tom Moore's fantastic "Six Ideas that Shaped Physics" textbook series (http://www.physics.pomona.edu/sixideas/), which is based on a career's worth of experience and many of the best ideas from the active field of Physics Education Research, is that also a front page link? (I'm teaching my Modern Physics course out of two of those volumes this semester, and the students seem to really like it.)
It fits in you (man) purse, yet covers the equivalent of 2000+ pages in mainstream textbooks. Also, it covers both calculus and mechanics in an integrated manner (something not usually done). Finally, it's (arguably) fun to read.
RE price: I would price the book less, but Amazon discounts the book like mad, so if I want to keep any semblance of respectability (i.e. above $20) I have to price it at $39. I also setup a 40% discount on lulu for today to match/beat the amazon discount.
Yep. If you email me a proof of purchase (e.g. lulu receipt) I'll be happy to hook you up with the ebooks.
I really want people to read the print version---it is so much better than the PDF, because you can flip through it, refer back to previous sections, and most-importantly the small size (5.5" x 8.5") makes the book look un-intimidating.
This is not what he was referring to as bullshit. What he was calling bullshit is putting flowery stories around problems. E.g., "A train is traveling from Dusseldorf to Amsterdam..."
x(t) is not bullshit just because you don't understand it. It's a mathematical function. x is the function, t is time. Meaning that you can give the function the time you're interested in and the function can tell you the motion of the object. I'd imagine the text goes on from there to explain how you obtain the function based on the sentence you quote.
The website lists prerequisites to reading the book, perhaps you don't meet them?
From reading the website it seem like an HR person or fireman could read this book and understand mechanics which is bullshit. Even your explanation would confuse them "x is the function?", "What function does x serve?", "How the fuck would I give an 'x' the time?"
If you need to use a guide, then it is B.S.
No shortcuts to taking classes, doing practice problems, and tests.
The main ting the modernworld offers is some nifty animations to illustrate these equations. We didnt have such in my day.
"Linear algebra is the math of vectors and matrices."
"The matrix-vector product is used to define the notion of a linear transformation"
This is BS.
* First: Linear Algebra actually is the math of linear transformations.
* Second: No sane mathematician would define linear transformations in terms of matrices.
Vectors and matrices are only one way to model linear transformations; They help beginners to imagine linear algebra; But often, refraining from using coordinates delivers a much clearer picture.
Maybe this should be called the "No BS guide to passing your engineering math tests".
I'm guessing you're reading the short tutorial, which starts off with some computational aspects of LA.
As soon as I introduce linear transformations (a few sections later) I make an update to this statement turning it into "linear algebra is all about vectors and linear transformations."
What "math" means to people outside of math--including physicists and engineers--is completely different from what "math" means to people inside math. We really ought to have a different word for the two fields. Even "applied math" doesn't cut it, because most applied mathematicians still think like mathematicians, and it ain't like the rest of us.
What mathematicians don't see is that when they rail against the kind of concrete, heuristic definitions that non-mathematicians use for parts of mathematics, is that it isn't just that we don't care that there is a better, more general, more abstract, more justifiable definition out there, it's that we can't understand them so they aren't useful to us, even a little bit. You may as well try explaining Shakespeare to your dog: it'll frustrate you and annoy the dog, who is perfectly happy to use Shakespeare for his intended purpose, which is to say, chewing on the edges of the "Complete Shakespeare" for entertainment.
That's an overstatement, but the gulf between the mathematician's mind-set and the mind-set of physicists and engineers is still far wider than most mathematicians appreciate, and it really would be valuable to have a different word for what physicists and engineers do when we "do math", because it is not "math" the way you mean it.
That's an overstatement, but the gulf between the mathematician's mind-set and the mind-set of physicists and engineers is still far wider than most mathematicians appreciate, and it really would be valuable to have a different word for what physicists and engineers do when we "do math", because it is not "math" the way you mean it.
I don't think that's true, at least in areas where physicists or engineers are actually going to be trying to use the relevant math. I think the difference is mostly in norms of written presentation. In physics, the concrete motivating example is often seen as an important thing to present; in math, it seems more typical to polish your definitions until they're as minimal and general as can be and start the presentation there. This often obscures the more concrete examples, but I've found plenty of times that if you read or talk to mathematicians in informal settings they can be pretty good about the examples that motivate the ideas.
Could you recommend a book for me so I can get deeper understanding?I'm a college student(software engineering). I love linear algebra,I passed it easly in my first semester, and I've done my studying and problems on Khan Academy.org .
From a math perspective some definitions could be "cleaner" but as a first/second round it gives a very good perspective on linear algebra.
Some of the good stuff:
* The general theme is "direct sum decomposition".
* Determinants are delayed as much as possible. (There are many good reasons to do this.)
* Eigenvalues are not computed using the characteristic polynomial but the other way around; This reflects the algorithmic side: For performance reasons a computer usually calculates the char.polynomial using the eigenvalues and not by using determinants.
> Vectors and matrices are only one way to model linear transformations; They help beginners to imagine linear algebra; But often, refraining from using coordinates delivers a much clearer picture.
They also make for a handy model when mapping them in to computer systems. It's hard to know from those quotes how things are actually presented in the material, but an emphasis on matrix & vector view of the world is really not a bad idea that I wish was more prevalent in math education.
While, like most people here, anything that claims to disrupt the textbook industry gets me excited on instinct, even a cursory glance shows some major issues with this that leaves me questioning whether someone who hasn't taken these classes could do well.
An example from the first chapter.
> By the way, before we continue our discussion, let it be noted: the
equality symbol (=) means that all that is to the left of = is equal to
all that is to the right of =. To keep this equality statement true, for
every change you apply to the left side of the equation, you
must apply the same change to the right side of the equation.
What is a change, and why do I have to do it to both sides? Is deleting all the exponents on both sides a valid change as long as I do it to both sides? What about dividing both sides by 0? This is a woefully inadequate explanation of manipulating equations. Maybe that's the bullshit that's been taken out, but I consider it fundamentals which often trip a person up later due to missing knowledge, and where I most commonly hear the phrase "Well you never told me I couldn't..." come out of a struggling student's mouth.
These sorts of fundamentals are glossed over or not mentioned throughout, though. For instance, both in and after the section on integration, the fact that \int (f+g) = \int f + \int g. No explanation or limitation is placed on that information. If I can do that, can't I also write \int (f/g) = \int f / \int g ? These are common tripping points for many.
I actually have this book but haven't read it yet. As someone who joined the web startup world when I was 14 and never went back to school, I need to work on my math skills. I believe strongly in building knowledge by layers (start with a simple overview, work you way towards the core of the subject) rather than going in for the detail right away.
Would you say this book does the former well and just doesn't cover the details very well, or is the book somehow flawed?
I think it's one thing to say "Where and how you can apply these we can discuss in more detail later, but for now assume that you can do x, y, and z only" and another to omit details altogether to later correct (if corrected at all) or leave what's available to inference.
From my reading and skimming of the samples provided, I wouldn't call this book a "simple overview" as I would call it something that's so concerned with getting to what appears to be the result/goal of a class like high school physics, but misses the real point. For instance, the purpose of a high school class many might take to be to learn how to take derivatives and integrals and apply them to a few common types of problems. After all, that's what you spend your time building up to, and what final exams on the class cover, so that's the point, right? But to the contrary, the skills and problem solving you get from doing those things in more rigor, with the details fully fleshed out instead of glossed over, and with motivation properly explained, is the real purpose.
In short, what I think this book will do is teach to the test, where the test is a template final exam from the type of course it purports to cover. But as we are all well aware, exams are not always proxies for whether you learned the whole of the material. Based on the depth of information provided, I'd say if your goal was to pass that class for your GED and never touch the information again and never try to apply it outside of the small template given by the textbooks, maybe it's useful. If you want practical knowledge that you can apply in a variety of situations and use to continue your education past this point, you're going to be missing a lot of very important details.
Thanks for reviewing the book. It's interesting that you came away with conclusion that I aim to teach-to-the-test, which is in fact diametrically opposite to my intent.
My main purpose with this book is to communicate to students the power of using mathematics to model the real world. For this reason I made a great effort to show the connections between the tools of calculus and the different modelling techniques in physics. E.g. I make sure this reasoning is understood:
by covering it in Chapter 2, Chapter 4, and again in Chapter 5.
True there are some sections that are written more in a you-need-to-know-this-because-its-going-to-be-on-the-exam (e.g. integration techniques, and series convergence tests), but that's just the nature of these topics.
I'd love to see a table of contents, as it'd make it much easier to judge the breadth of the subject matter.
One concern I have is I didn't see much that looked like discrete/finite math. That compounds the mistake made by too many math curriculums. In particular, statistics and probabilities rule our world these days (and seem destined to do so only more in the future), yet so many people never even get a basic education in them.
Note: the aim of the book is to cover mechanics (Physics 101) and calculus (I and II). There is a second tome in the works that will cover optics, waves, E&M, and vector calculus.
Can't look a gift horse in the mouth, but I'm not sure of the intended use case for such a guide. Normally you need a pretty formal foundation in Physics to get much value from it, which is why I hopped on the discrete math picture (lots of people do programming without any need for a formal math education).
My mental muscle for math has definitely atrophied since graduating with an engineering degree. I’ve been looking for a nice way to exercise it, and this looks like something that can get me there.
For a more in-depth discussion of physics, I’ve found the Feynman Lectures [1,2] to be quite enjoyable. It’s a long read (I’ve only finished the first book) but it is very thorough.
It looks like 'no bullshit' in the sense of a heavily compressed primer using a lot of notation. I think that is very useful if you're in the right frame of mind. i.e. if you're happy with notation, and you want to refresh, or pick up something just directly from the undiluted concepts. Say, if you haven't looked at linear algebra for 5 years but suddenly need to use it for something, a text like this is going to be great. Or maybe as almost a syllabus/framework for connecting together concepts while you're doing a course.
But I'm not sure it justifies the level of branding/rhetoric on the webpage. If you think mathematics is hard, an introduction to a linear algebra section which starts like this isn't going to change your mind:
> Linear algebra is the math of vectors and matrices. Let n be a positive integer and let R denote the set of real numbers, then R^n is the set of all n-tuples of real numbers. A vector v E R^n is an n-tuple of real numbers. The notation “E” is read “element of S”...
Lol... in a previous version of the tutorial, I was using informal language to define vectors as "arrays of numbers," which attracted a lot of negative comments on HN because it wasn't mathematically precise enough.
Note the LA book is "Tome II" in the series, and assumes you've read the "Tome I" (no BS guide to math & phys), which means the reader would be equipped to understand more formal math descriptions.
But yeah... try giving an explanation for what a vector is that is both: (1) understandable and (2) mathematically precise.
"A vector is a composite quantity that has a magnitude and a direction. If something has a direction component and/or a magnitude component, it can be represented by a vector, and if something is a vector, we can ask for its direction or its magnitude (or both.)"
Cool. That works well, if a bit geometrical. I'm going to think about rewording the intro in this way.
However, I'd still have to introduce the notion of "coordinate vector" somehow, which begs for the word "tuple" or array, neither of which the right choice.
What I've described is the concept of a vector. You will have to determine the notation, and in setting the notation, and ordered list of basis vector coefficients is most commonly called a tuple, which is a generalization of ordered pair / triple / quadruple, etc.. (Though 'tuple' doesn't usually imply ordered.)
The reason 'array' doesn't really work is that arrays are generally understood to be homogeneous in type, while tuples are usually Cartesian products. So if you are using a Cartesian coordinate system, tuple is the ideal term.
I think the emphasis I would put on all this is variety. All of these books are like different shapes and sizes of tools that you're using to pry open an understanding of the subject. At certain moments you'll want one sort of tool, and at different moments you'll want another. Maybe, on a particular topic, you want to read a chatty, informal explanation, and then you'll want something heavily summarized to nail things in place. Then you might want something really rigorous if you need to go into a lot of detail. Or it might be useful to have a text that scatters explanation of the concepts in amongst the steps to solve practical examples. All of these approaches have value.
When I was learning Maths and Physics one of the major conclusions was that there was not enough variety in the material which was available, so when you hit a brick wall, part of the skill was developing an acceptance that you would hit your head against the wall repeatedly until something sank in. Which is inherently frustrating.
FWIW I think it's also inevitable that a higher level summary has some kind of slightly leaky abstractions in order to give people a feel for what's going on. I don't see why Maths is any different from Chemistry, or other sciences, in the sense that you need to teach it progressively, at least to some degree. You talk first to a Chemistry student about covalent and ionic bonds, you don't start immediately on Quantum Mechanics and Orbital Theory.
Try something like "you can think of a vector as an array of numbers. More precisely, [formal definition here]'. If you give somebody an analogy it gives them something to 'hang their thoughts on', if you know what I mean; you read the formalism and try to correlate it back to the analogy.
Of course,an analogy is not an equivalence, so there will necessarily be exceptions. You can follow that up with something like "be careful not to assume X from the array of numbers idea; the formal defition states Y, which precludes that". Well, you get the idea.
I'd say the standard UGRAD-level physics and calculus textbooks (Serway, Giancoli, Stewart) are full of BS. Do you really need to read 1000+ pages to learn calculus?
Textbooks after first-year university are normally much better and bullshitfree. Graduate textbooks are usually solid.
Also, there are many free textbooks out there that are essentially bullshit free, e.g. Calculus Made Easy by Silvanus P. Thompson available at http://www.gutenberg.org/ebooks/33283
Each chapter is independent, the text has a thorough index and covers most everything. Few errors, well-illustrated, nicely-sized and pleasant on the eyes. Most easy to read math book ever.
As an analog from the electronics field, look at the Forrest Mims notebook series. That is a superb example of how to take something insanely complex and converting it to no bullshit.
The example I saw on the website looks like just another dry math textbook. I've seen high school math books with more color and engaging concepts than this.
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[ 0.21 ms ] story [ 199 ms ] threadBTW, here's a link to a PDF version of the book preview http://minireference.com/static/excerpts/noBSguide_v5_previe... (137pp, 6MB) in case flipping through low resolution .jpgs isn't your thing ;)
http://cl.ly/image/150V0z3T2b0g
In contrast to that, I found https://openstaxcollege.org/books a really awesome resource for learning physics (on an easy level)
Edit: Cutting out all the "bullshit" seems to make it hard for a "busy adult" to easily learn the concept, but it actually seems like a good resource to improve your knowledge which you simply forgot.
That said, you're not going to learn linear algebra in four pages. No royal road, and all that.
Finishing the applications chapter has been a massive time sinkhole! I wanted to make a survey of all the cool things you can do once you have the tools of linear algebra under your belt, but it's proving to be too much (Chapter 8 is getting almost as long as the rest of the book).
In the coming weeks I'll be going over the latest draft and I might do a scope-cut, in order to get it done more quickly. In summary I'd say end-of-April for "dev close" and then probably a month for the final editing with my editor, so June 1st for official release.
Anyways: point being, flipping through the book, it is decided not like that image you posted. It's mostly casual prose with lots of diagrams.
To be fair, you were looking at the super-condensed linear algebra tutorial, which is meant to be a condensed pre-exam review for students and not as a standalone tutorial. The actual book starts off much more smoothly and introduces concepts step by step (see http://cnd.mcgill.ca/~ivan/miniref/noBSguide2LA_preview.pdf for a preview).
The "onboarding" in the math/phys book (No bullshit guide to math and physics) is even smoother. About 1/3 of the text is a review of high school math topics, which helps to establish a solid foundation understanding mechanics and calculus. (see http://minireference.com/static/excerpts/noBSguide_v5_previe... for a PDF preview.)
You are absolutely right though, many of the readers who have written to me over the years are adults who used the book to review what they learned at university. The compactness works well for that.
https://www.khanacademy.org/math/multivariable-calculus
Then again, similar methods like in Learn You A Haskell For Great Good seem to work on me. I do wonder how much time I spend trying to understand the jokes and references.
If I post about Tom Moore's fantastic "Six Ideas that Shaped Physics" textbook series (http://www.physics.pomona.edu/sixideas/), which is based on a career's worth of experience and many of the best ideas from the active field of Physics Education Research, is that also a front page link? (I'm teaching my Modern Physics course out of two of those volumes this semester, and the students seem to really like it.)
"Six no bullshit ideas that shaped physics" Boom! front page.
It's a math textbook. There are thousands of them. What makes this one so special? The fact that it says, "No B.S."? It has a fancy webpage?
It looks pretty standard, and isn't even very cheap.
It fits in you (man) purse, yet covers the equivalent of 2000+ pages in mainstream textbooks. Also, it covers both calculus and mechanics in an integrated manner (something not usually done). Finally, it's (arguably) fun to read.
RE price: I would price the book less, but Amazon discounts the book like mad, so if I want to keep any semblance of respectability (i.e. above $20) I have to price it at $39. I also setup a 40% discount on lulu for today to match/beat the amazon discount.
I really want people to read the print version---it is so much better than the PDF, because you can flip through it, refer back to previous sections, and most-importantly the small size (5.5" x 8.5") makes the book look un-intimidating.
This is exactly the type of bullshit that confuses people. To a regular person what the fuck is x(t)?
x(t) is not bullshit just because you don't understand it. It's a mathematical function. x is the function, t is time. Meaning that you can give the function the time you're interested in and the function can tell you the motion of the object. I'd imagine the text goes on from there to explain how you obtain the function based on the sentence you quote.
The website lists prerequisites to reading the book, perhaps you don't meet them?
From reading the website it seem like an HR person or fireman could read this book and understand mechanics which is bullshit. Even your explanation would confuse them "x is the function?", "What function does x serve?", "How the fuck would I give an 'x' the time?"
This is BS. * First: Linear Algebra actually is the math of linear transformations. * Second: No sane mathematician would define linear transformations in terms of matrices.
Vectors and matrices are only one way to model linear transformations; They help beginners to imagine linear algebra; But often, refraining from using coordinates delivers a much clearer picture.
Maybe this should be called the "No BS guide to passing your engineering math tests".
As soon as I introduce linear transformations (a few sections later) I make an update to this statement turning it into "linear algebra is all about vectors and linear transformations."
What mathematicians don't see is that when they rail against the kind of concrete, heuristic definitions that non-mathematicians use for parts of mathematics, is that it isn't just that we don't care that there is a better, more general, more abstract, more justifiable definition out there, it's that we can't understand them so they aren't useful to us, even a little bit. You may as well try explaining Shakespeare to your dog: it'll frustrate you and annoy the dog, who is perfectly happy to use Shakespeare for his intended purpose, which is to say, chewing on the edges of the "Complete Shakespeare" for entertainment.
That's an overstatement, but the gulf between the mathematician's mind-set and the mind-set of physicists and engineers is still far wider than most mathematicians appreciate, and it really would be valuable to have a different word for what physicists and engineers do when we "do math", because it is not "math" the way you mean it.
I don't think that's true, at least in areas where physicists or engineers are actually going to be trying to use the relevant math. I think the difference is mostly in norms of written presentation. In physics, the concrete motivating example is often seen as an important thing to present; in math, it seems more typical to polish your definitions until they're as minimal and general as can be and start the presentation there. This often obscures the more concrete examples, but I've found plenty of times that if you read or talk to mathematicians in informal settings they can be pretty good about the examples that motivate the ideas.
From a math perspective some definitions could be "cleaner" but as a first/second round it gives a very good perspective on linear algebra.
Some of the good stuff:
* The general theme is "direct sum decomposition".
* Determinants are delayed as much as possible. (There are many good reasons to do this.)
* Eigenvalues are not computed using the characteristic polynomial but the other way around; This reflects the algorithmic side: For performance reasons a computer usually calculates the char.polynomial using the eigenvalues and not by using determinants.
Edit: I see someone else linked to it in this comment thread.
They also make for a handy model when mapping them in to computer systems. It's hard to know from those quotes how things are actually presented in the material, but an emphasis on matrix & vector view of the world is really not a bad idea that I wish was more prevalent in math education.
An example from the first chapter.
> By the way, before we continue our discussion, let it be noted: the equality symbol (=) means that all that is to the left of = is equal to all that is to the right of =. To keep this equality statement true, for every change you apply to the left side of the equation, you must apply the same change to the right side of the equation.
What is a change, and why do I have to do it to both sides? Is deleting all the exponents on both sides a valid change as long as I do it to both sides? What about dividing both sides by 0? This is a woefully inadequate explanation of manipulating equations. Maybe that's the bullshit that's been taken out, but I consider it fundamentals which often trip a person up later due to missing knowledge, and where I most commonly hear the phrase "Well you never told me I couldn't..." come out of a struggling student's mouth.
A few sections later I define "change on both sides" more formally as "applying a function".
Would you say this book does the former well and just doesn't cover the details very well, or is the book somehow flawed?
From my reading and skimming of the samples provided, I wouldn't call this book a "simple overview" as I would call it something that's so concerned with getting to what appears to be the result/goal of a class like high school physics, but misses the real point. For instance, the purpose of a high school class many might take to be to learn how to take derivatives and integrals and apply them to a few common types of problems. After all, that's what you spend your time building up to, and what final exams on the class cover, so that's the point, right? But to the contrary, the skills and problem solving you get from doing those things in more rigor, with the details fully fleshed out instead of glossed over, and with motivation properly explained, is the real purpose.
In short, what I think this book will do is teach to the test, where the test is a template final exam from the type of course it purports to cover. But as we are all well aware, exams are not always proxies for whether you learned the whole of the material. Based on the depth of information provided, I'd say if your goal was to pass that class for your GED and never touch the information again and never try to apply it outside of the small template given by the textbooks, maybe it's useful. If you want practical knowledge that you can apply in a variety of situations and use to continue your education past this point, you're going to be missing a lot of very important details.
My main purpose with this book is to communicate to students the power of using mathematics to model the real world. For this reason I made a great effort to show the connections between the tools of calculus and the different modelling techniques in physics. E.g. I make sure this reasoning is understood:
by covering it in Chapter 2, Chapter 4, and again in Chapter 5.True there are some sections that are written more in a you-need-to-know-this-because-its-going-to-be-on-the-exam (e.g. integration techniques, and series convergence tests), but that's just the nature of these topics.
You've heard the expression "let's get busy"? Well this is a textbook that gets biz-zay. Consistently and thoroughly.
this: http://www.amazon.com/Mathematics-Physical-Sciences-Robert-L...
and this: http://www.amazon.com/Further-Mathematics-Physical-Sciences-...
One concern I have is I didn't see much that looked like discrete/finite math. That compounds the mistake made by too many math curriculums. In particular, statistics and probabilities rule our world these days (and seem destined to do so only more in the future), yet so many people never even get a basic education in them.
Note: the aim of the book is to cover mechanics (Physics 101) and calculus (I and II). There is a second tome in the works that will cover optics, waves, E&M, and vector calculus.
Can't look a gift horse in the mouth, but I'm not sure of the intended use case for such a guide. Normally you need a pretty formal foundation in Physics to get much value from it, which is why I hopped on the discrete math picture (lots of people do programming without any need for a formal math education).
For a more in-depth discussion of physics, I’ve found the Feynman Lectures [1,2] to be quite enjoyable. It’s a long read (I’ve only finished the first book) but it is very thorough.
[1] http://www.feynmanlectures.caltech.edu/ [2] http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/...
[0] http://www.amazon.com/dp/0486409163/ (Mathematics: Its Content, Methods and Meaning)
But I'm not sure it justifies the level of branding/rhetoric on the webpage. If you think mathematics is hard, an introduction to a linear algebra section which starts like this isn't going to change your mind:
> Linear algebra is the math of vectors and matrices. Let n be a positive integer and let R denote the set of real numbers, then R^n is the set of all n-tuples of real numbers. A vector v E R^n is an n-tuple of real numbers. The notation “E” is read “element of S”...
Note the LA book is "Tome II" in the series, and assumes you've read the "Tome I" (no BS guide to math & phys), which means the reader would be equipped to understand more formal math descriptions.
But yeah... try giving an explanation for what a vector is that is both: (1) understandable and (2) mathematically precise.
However, I'd still have to introduce the notion of "coordinate vector" somehow, which begs for the word "tuple" or array, neither of which the right choice.
The reason 'array' doesn't really work is that arrays are generally understood to be homogeneous in type, while tuples are usually Cartesian products. So if you are using a Cartesian coordinate system, tuple is the ideal term.
http://en.wikipedia.org/wiki/Tuple#Type_theory
I think the emphasis I would put on all this is variety. All of these books are like different shapes and sizes of tools that you're using to pry open an understanding of the subject. At certain moments you'll want one sort of tool, and at different moments you'll want another. Maybe, on a particular topic, you want to read a chatty, informal explanation, and then you'll want something heavily summarized to nail things in place. Then you might want something really rigorous if you need to go into a lot of detail. Or it might be useful to have a text that scatters explanation of the concepts in amongst the steps to solve practical examples. All of these approaches have value.
When I was learning Maths and Physics one of the major conclusions was that there was not enough variety in the material which was available, so when you hit a brick wall, part of the skill was developing an acceptance that you would hit your head against the wall repeatedly until something sank in. Which is inherently frustrating.
FWIW I think it's also inevitable that a higher level summary has some kind of slightly leaky abstractions in order to give people a feel for what's going on. I don't see why Maths is any different from Chemistry, or other sciences, in the sense that you need to teach it progressively, at least to some degree. You talk first to a Chemistry student about covalent and ionic bonds, you don't start immediately on Quantum Mechanics and Orbital Theory.
Of course,an analogy is not an equivalence, so there will necessarily be exceptions. You can follow that up with something like "be careful not to assume X from the array of numbers idea; the formal defition states Y, which precludes that". Well, you get the idea.
Textbooks after first-year university are normally much better and bullshitfree. Graduate textbooks are usually solid.
Also, there are many free textbooks out there that are essentially bullshit free, e.g. Calculus Made Easy by Silvanus P. Thompson available at http://www.gutenberg.org/ebooks/33283
"... Textbooks after first-year university are normally much better and bullshitfree. Graduate textbooks are usually solid."
Amen!
To that end I recommend
"Mathematics Of Physics And Modern Engineering - Second Edition by I. S. Sokolnikoff and R. M. Redheffer
http://www.amazon.com/Mathematics-Physics-Engineering-Stephe...
Each chapter is independent, the text has a thorough index and covers most everything. Few errors, well-illustrated, nicely-sized and pleasant on the eyes. Most easy to read math book ever.
The example I saw on the website looks like just another dry math textbook. I've seen high school math books with more color and engaging concepts than this.