Discrete Mathematics: An Open Introduction [pdf] • Hacker News Board

Re: Discrete Mathematics: An Open Introduction [pdf]

#41

Post by redczar » Tue, Jun 10, 2025, 5:47 PM UTC

defrost wrote: post #38

redczar wrote: post #37

Earlier quoted context omitted.

It is quite obvious that you have not taught mathematics at a non specialized high school. You think the experience you and 3 other people each of whom got a Ph.D. at a good university in science and/or philosophy is somehow normative. You think this book could be taught to 15 year olds to anything more than a very small number of people is insane. Please go spend time in a classroom as a mathematics teacher before a…

Twelve, not three, in my first year university math 100 class, I gave three typical examples of the twelve. It was almost the only university in the state at that time, two others opened in the year or so prior and these were (at the time) free universities for any that got a sufficient TAE score (high school exam for tertiary entrance). All in all many more people were educated in mathematics or in their particular…

..not a claim I made, please stop strawmanning.

What you’ve been saying is based on your experience (very limited). The essence of your beliefs are that you and 12 other people could have done this book on high school therefore it should be a class in high school. Though you have no evidence that high schools have the resources to give a class that very few people are qualified to take. The distribution of qualified students is such that each individual high school will on average have very few students capable of taking such a class.

You went to high school and university and tutored some people. Therefore you know much more than me on what is appropriate to teach high schoolers. I just have 30 years of experiece teaching college level mathematics. Your arguements are compelling and I now agree with you.

Re: Discrete Mathematics: An Open Introduction [pdf]

#42

Post by vidro3 » Tue, Jun 10, 2025, 6:14 PM UTC

Having just done a discrete math course the best resource has been Kimberley brehms videos on YouTube which follows very closely to a textbook though I can't recall the author at the moment

Re: Discrete Mathematics: An Open Introduction [pdf]

#43

Post by rak1507 » Tue, Jun 10, 2025, 10:19 PM UTC

chongli wrote: post #39

rak1507 wrote: post #32

Earlier quoted context omitted.

You definitely don't need to know any of that background to be able to arrive at the answer. To fully understand everything maybe, but all it takes is: a = x^1 + x^4 + x^7 + ... = x(1 + x^3 + x^6 + ...) = x/(1-x^3) a + a^3 + a^5 + ... = a(1 + a^2 + a^4 + ...) = a/(1-a^2) Substitute + simplify. I don't think this is beyond a (fairly smart) elementary school student.

The question doesn’t ask for an answer, it asks for a proof. You can’t just write a bunch of algebra and call it a day. You have to justify all of your arguments.

There aren't really any complicated arguments being made, so I don't think a proof would be that involved.

Re: Discrete Mathematics: An Open Introduction [pdf]

#44

Post by fc417fc802 » Wed, Jun 11, 2025, 12:27 AM UTC

defrost wrote: post #36

redczar wrote: post #34

Earlier quoted context omitted.

Length + depth determines the appropriateness of a book at a given level. They go hand in hand and my comment was about this book. Not 1 or 2 chapters of it and not 1 or 2 chapters of it dumbed down a bit.

Again, while part of the book might be presented in a high school courses I took, a number of students that took such courses would read the entire book out of interest. I'm unsure how you were taught but we in Australia frequently had textbooks that were only partially taught in high school, leaving the rest as untested and for interest. This, as I'm sure you follow, means it would be fine as a text book despite onl…

I'll chime in as someone from the US who attended a public school and took a calculus class that used a university level text and did exactly as you described. Color me surprised when I arrived at university only to encounter that same book in use for the calculus course sequence.

The person you're engaging with here clearly has an overly generalized view of the US educational system (and is overly confident in it). It's not surprising that there's a bit of variance - the place is rather large after all.

Re: Discrete Mathematics: An Open Introduction [pdf]

#45

Post by fc417fc802 » Wed, Jun 11, 2025, 12:41 AM UTC

redczar wrote: post #41

defrost wrote: post #38

Earlier quoted context omitted.

Twelve, not three, in my first year university math 100 class, I gave three typical examples of the twelve. It was almost the only university in the state at that time, two others opened in the year or so prior and these were (at the time) free universities for any that got a sufficient TAE score (high school exam for tertiary entrance). All in all many more people were educated in mathematics or in their particular…

..not a claim I made, please stop strawmanning. What you’ve been saying is based on your experience (very limited). The essence of your beliefs are that you and 12 other people could have done this book on high school therefore it should be a class in high school. Though you have no evidence that high schools have the resources to give a class that very few people are qualified to take. The distribution of qualified…

The irony of you making this comment in a thread about math. 12 per year out of a population of 2 million in a remote, thus likely under served, thus likely under performing region.

My own experience is a rate closer to 1 per 35 in a reasonably well off region within the US.

Re: Discrete Mathematics: An Open Introduction [pdf]

#46

Post by Dropbysometime » Wed, Jun 11, 2025, 2:37 PM UTC

anthk wrote: post #13

Another CC book on discrete Math it's Gentle Introduction to the Art of Mathematics.

60 year old. still having trouble with math. Thank for this topic and both simple pdf.

Re: Discrete Mathematics: An Open Introduction [pdf]

#47

Post by [deleted] » Thu, Jun 12, 2025, 3:19 AM UTC

fc417fc802 wrote: post #45

redczar wrote: post #41

Earlier quoted context omitted.

..not a claim I made, please stop strawmanning. What you’ve been saying is based on your experience (very limited). The essence of your beliefs are that you and 12 other people could have done this book on high school therefore it should be a class in high school. Though you have no evidence that high schools have the resources to give a class that very few people are qualified to take. The distribution of qualified…

The irony of you making this comment in a thread about math. 12 per year out of a population of 2 million in a remote, thus likely under served, thus likely under performing region. My own experience is a rate closer to 1 per 35 in a reasonably well off region within the US.

[deleted]

Re: Discrete Mathematics: An Open Introduction [pdf]

#48

Post by redczar » Thu, Jun 12, 2025, 3:25 AM UTC

fc417fc802 wrote: post #45

redczar wrote: post #41

Earlier quoted context omitted.

..not a claim I made, please stop strawmanning. What you’ve been saying is based on your experience (very limited). The essence of your beliefs are that you and 12 other people could have done this book on high school therefore it should be a class in high school. Though you have no evidence that high schools have the resources to give a class that very few people are qualified to take. The distribution of qualified…

The irony of you making this comment in a thread about math. 12 per year out of a population of 2 million in a remote, thus likely under served, thus likely under performing region. My own experience is a rate closer to 1 per 35 in a reasonably well off region within the US.

You clearly have not taught mathematics at either the college level or the high school level. But your experience carries a great deal of weight. You are correct. I’ve taught mathematics at Purdue University, Florida State University, University of Kansas, various community colleges and in a prison. I don’t know what I’m talking about. The book in question should be a course at every high school. Each high school will certainly have enough students who can take such a course to justify having the course.

By the way, don’t look up what an outlier is and don’t forget that your anecdote is, in fact, data.

Re: Discrete Mathematics: An Open Introduction [pdf]

#49

Post by fc417fc802 » Thu, Jun 12, 2025, 3:55 AM UTC

redczar wrote: post #48

fc417fc802 wrote: post #45

Earlier quoted context omitted.

The irony of you making this comment in a thread about math. 12 per year out of a population of 2 million in a remote, thus likely under served, thus likely under performing region. My own experience is a rate closer to 1 per 35 in a reasonably well off region within the US.

You clearly have not taught mathematics at either the college level or the high school level. But your experience carries a great deal of weight. You are correct. I’ve taught mathematics at Purdue University, Florida State University, University of Kansas, various community colleges and in a prison. I don’t know what I’m talking about. The book in question should be a course at every high school. Each high school wil…

Indeed, I have not. Nor do I need to in order to make simple observations that contradict your claims. You are representing that something which is already widely put into practice is infeasible. A strange hill to die on.

The amusing thing is that if your claims weren't framed as an absolute they'd likely be correct. But when you attempt to make sweeping generalizations about the entire country you will almost invariably be wrong regardless of the topic at hand.

I'll also note that intentionally misattributing claims to me is neither in good faith nor in keeping with HN guidelines.