>I think you aren't buying very good math books then.
Just to follow up. A comment[0] on the book `Discrete Mathematics and Its Applications by Kenneth H. Rosen`
`I'm convinced that math gurus are incapable of teaching math.
Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping that they'd profit from the thefts, but although their business plan included a Phase 1 ("Steal underwear") and a Phase 3 ("Make a profit"), Phase 2—the connective tissue—was just "?".
Rosen and others like him fail to grasp how much "?" connective tissue they're leaving out when they "teach" math. He'll describe a math concept using almost-but-not-quite human language, then—oh, there's always a "then" with these books—the math gymnastics begin. Math teachers can't resist the gymnastics, can they? No, they really can't. At some point they lose their ability to see how much they assume other people know, and when that happens they cease being effective at teaching. This describes almost every math teacher I've had, and it definitely describes almost every math textbook that I've read. Rosen's book isn't the worst math textbook that I've read, but it's still pretty awful.
Seriously, corner cases and extreme mind-bending problems don't help people learn math; giving students time to grasp concepts before baffling them with bullshit does. This is why math schools like Khan Academy are amazing and college/university level math courses are not. This stuff can be taught, but not like this.`
I strongly agree with this argument. I had this book in my undergrad and I felt barely learning anything and just kept getting drowned in the way the content was written. I switched to a different text in a few weeks and it became an easy subject. The difference was more intuitive examples and gradual difficulty in exercises and less of the proof is left for the reader as an exercise.
Just to follow up. A comment[0] on the book `Discrete Mathematics and Its Applications by Kenneth H. Rosen`
`I'm convinced that math gurus are incapable of teaching math.
Whenever I encounter math textbooks like this one, I'm reminded of Underpants Gnomes on South Park. For the unwashed: Underpants Gnomes stole underwear from the residents of South Park hoping that they'd profit from the thefts, but although their business plan included a Phase 1 ("Steal underwear") and a Phase 3 ("Make a profit"), Phase 2—the connective tissue—was just "?".
Rosen and others like him fail to grasp how much "?" connective tissue they're leaving out when they "teach" math. He'll describe a math concept using almost-but-not-quite human language, then—oh, there's always a "then" with these books—the math gymnastics begin. Math teachers can't resist the gymnastics, can they? No, they really can't. At some point they lose their ability to see how much they assume other people know, and when that happens they cease being effective at teaching. This describes almost every math teacher I've had, and it definitely describes almost every math textbook that I've read. Rosen's book isn't the worst math textbook that I've read, but it's still pretty awful.
Seriously, corner cases and extreme mind-bending problems don't help people learn math; giving students time to grasp concepts before baffling them with bullshit does. This is why math schools like Khan Academy are amazing and college/university level math courses are not. This stuff can be taught, but not like this.`
I strongly agree with this argument. I had this book in my undergrad and I felt barely learning anything and just kept getting drowned in the way the content was written. I switched to a different text in a few weeks and it became an easy subject. The difference was more intuitive examples and gradual difficulty in exercises and less of the proof is left for the reader as an exercise.
[0] https://www.goodreads.com/book/show/1800803.Discrete_Mathema...