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No bullshit guide to math and physics

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Re: No bullshit guide to math and physics

#131

Post by madhadron »

cosmikduster wrote: post #87
madhadron wrote: post #48

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 poin…

> 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.

Re: No bullshit guide to math and physics

#132

Post by MattSayar »

serf wrote: post #107
walexander wrote: post #72

Earlier quoted context omitted.

Since you seem to be informed about the books out there that are attempting what the OP's book is, what would you suggest in place of it? Seems like even with the problems you've listed, it might still fit a niche that I haven't seen filled very well.

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.

Re: No bullshit guide to math and physics

#133

Post by Dove »

chris_wot wrote: post #111
crntaylor wrote: post #103

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,…

can you really always divide two rational numbers to get another rational number? I'll not give a formal proof, but intuitively the answer is surely "yes"!

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.

Re: No bullshit guide to math and physics

#134

Post by cabalamat »

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.

Re: No bullshit guide to math and physics

#135

Post by v-yadli »

DIFF wrote: post #118
chris_wot wrote: post #114

Earlier quoted context omitted.

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.

0 \in N, 5 \in N => (0/5) \in Q. Therefore 0 \in Q. QED.

Watch out for your proof. Q is constructed as a field with + and x only. The availability of the inverse operator is not well documented :-D

Re: No bullshit guide to math and physics

#136

Post by DanBC »

crntaylor wrote: post #103

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,…

> 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.

Re: No bullshit guide to math and physics

#137

Post by crntaylor »

Dove wrote: post #133
chris_wot wrote: post #111

Earlier quoted context omitted.

can you really always divide two rational numbers to get another rational number? I'll not give a formal proof, but intuitively the answer is surely "yes"!

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).

Re: No bullshit guide to math and physics

#138

Post by andrewflnr »

v-yadli wrote: post #94
andrewflnr wrote: post #78

Earlier quoted context omitted.

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) O…

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.

Re: No bullshit guide to math and physics

#139

Post by ivansavz »

pflats wrote: post #39

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 thir…

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.

Re: No bullshit guide to math and physics

#140

Post by ivansavz »

crntaylor wrote: post #103

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,…

> 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.

More on set notation: http://cnd.mcgill.ca/~ivan/miniref/set_notation.pdf

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