I've had very hit or miss experiences with old (very old) books on math and physics. I'm dangerously close to graduating with an undergrad degree in math and physics, so I wasn't entirely unprepared to tackle such books (I hope).
On one hand, I picked up Newton's Principia, and frankly I found it incomprehensible. From what I understand, his mathematical notation is entirely different from what we use today, and a lot of his reasoning is hidden in impenetrable text or absurd geometric diagrams. If you wanted to learn classical mechanics, there are several more modern books that would serve you better.
On the other hand, I've read some things by Euler and a few 19th century mathematical papers, and I found them clear and readable. Euler apparently popularized a lot of mathematical notation, so I suspect works subsequent to him would be a lot easier for a modern reader to understand.
You've hit on my pet peeve here. I HATE it when people tell stories that unilaterally paint teachers as villains. All I get out of your post is a smug polemic against some teacher you had a grudge against AS A CHILD.
I think it's true that most public school curricula don't serve advanced students well. I've had a lot of experience with that; I'd been repeatedly identified as "highly gifted" as a kid, and that repeatedly resulted in absolutely nothing happening. None of my teachers were adequately prepared to instruct me. I got into petty confrontations like that with my teachers all the time, and I can say with hindsight that I instigated every single one. It's true, they didn't know how to handle me because I was "gifted", but I also tried my hardest to be an annoying little shit.
This is a complicated issue. Sometimes there's really an incompetent teacher, and sometimes there's an ignorant parent or spoiled student raising a shitstorm. Often, it's both.
Wrong. When there is a continuous range of outcomes, a probability of zero doesn't mean "this event is impossible." A probability _density_ of zero, however, would mean that.
Actually, if you've got some basic knowledge of ordinary differential equations, Stogatz has a very readable text on non-linear differential equations and how fractals naturally arise as the stable solutions of chaotic systems.
I call shenanigans. All I see are some ill-defined pseudo-mathematical terms casually being tossed around. This is exactly the kind of hand-wavey, pop-sci explanation that appeals to string theory enthusiasts. I'm not saying Palmer's ideas are without merit (and conversely I'm not saying they have merit), but just because an explanation is appealing it doesn't make it scientific.
The minute you try to make scientific research into a commodity like this, you will kill all scientific research.
Do you think 19th century physicists had iPhones in mind when they were creating rudimentary batteries and experimenting with electromagnetism? Do you think Maxwell only published his famous paper so he could enable the creation of hybrid cars? Could anyone have predicted digital computers? Hell, could the inventors of digital computers have predicted modern desktops?
No. Simply no. There is no better way to turn a student off of math than to make them work SAT problems ad nauseum. It's so far removed from what an undergrad pursuing a degree in math will learn.
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I've had very hit or miss experiences with old (very old) books on math and physics. I'm dangerously close to graduating with an undergrad degree in math and physics, so I wasn't entirely unprepared to tackle such books (I hope).
On one hand, I picked up Newton's Principia, and frankly I found it incomprehensible. From what I understand, his mathematical notation is entirely different from what we use today, and a lot of his reasoning is hidden in impenetrable text or absurd geometric diagrams. If you wanted to learn classical mechanics, there are several more modern books that would serve you better.
On the other hand, I've read some things by Euler and a few 19th century mathematical papers, and I found them clear and readable. Euler apparently popularized a lot of mathematical notation, so I suspect works subsequent to him would be a lot easier for a modern reader to understand.
You've hit on my pet peeve here. I HATE it when people tell stories that unilaterally paint teachers as villains. All I get out of your post is a smug polemic against some teacher you had a grudge against AS A CHILD.
I think it's true that most public school curricula don't serve advanced students well. I've had a lot of experience with that; I'd been repeatedly identified as "highly gifted" as a kid, and that repeatedly resulted in absolutely nothing happening. None of my teachers were adequately prepared to instruct me. I got into petty confrontations like that with my teachers all the time, and I can say with hindsight that I instigated every single one. It's true, they didn't know how to handle me because I was "gifted", but I also tried my hardest to be an annoying little shit.
This is a complicated issue. Sometimes there's really an incompetent teacher, and sometimes there's an ignorant parent or spoiled student raising a shitstorm. Often, it's both.
Wrong. When there is a continuous range of outcomes, a probability of zero doesn't mean "this event is impossible." A probability _density_ of zero, however, would mean that.
Actually, if you've got some basic knowledge of ordinary differential equations, Stogatz has a very readable text on non-linear differential equations and how fractals naturally arise as the stable solutions of chaotic systems.
I call shenanigans. All I see are some ill-defined pseudo-mathematical terms casually being tossed around. This is exactly the kind of hand-wavey, pop-sci explanation that appeals to string theory enthusiasts. I'm not saying Palmer's ideas are without merit (and conversely I'm not saying they have merit), but just because an explanation is appealing it doesn't make it scientific.
The minute you try to make scientific research into a commodity like this, you will kill all scientific research. Do you think 19th century physicists had iPhones in mind when they were creating rudimentary batteries and experimenting with electromagnetism? Do you think Maxwell only published his famous paper so he could enable the creation of hybrid cars? Could anyone have predicted digital computers? Hell, could the inventors of digital computers have predicted modern desktops?
That's actually exactly the opposite of a falsifiable hypothesis.
No. Simply no. There is no better way to turn a student off of math than to make them work SAT problems ad nauseum. It's so far removed from what an undergrad pursuing a degree in math will learn.