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Discrete Mathematics: An Open Introduction [pdf]

discrete.openmathbooks.org

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Re: Discrete Mathematics: An Open Introduction [pdf]

#11

Post by dr_kiszonka »

redczar wrote: post #4
WhitneyLand wrote: post #2

Think this would be a great course for high school or even middle school. No plug and chug that makes it a grind, plus a great intro to proofs and deeper mathematical thinking.

I taught mathematics for 30 years at the college level. This is a college level textbook and it is not appropriate for either high school or middle school. Very few students at that level would be able to understand this material.

I need to develop more intuition and maturity to understand a few relatively math-heavy engineering methods and ML/DL papers. Would you have any recommendations for not very bright college students? Perhaps something similar to Calculus Made Easy? Also, have you ever taught math using software like Mathematica or SageMath? (I graduated from college a long while ago and don't really have the bandwidth to solve problem sets by hand. I never enjoyed it or learned much from it.)

Re: Discrete Mathematics: An Open Introduction [pdf]

#14

Post by anthk »

redczar wrote: post #4
WhitneyLand wrote: post #2

Think this would be a great course for high school or even middle school. No plug and chug that makes it a grind, plus a great intro to proofs and deeper mathematical thinking.

I taught mathematics for 30 years at the college level. This is a college level textbook and it is not appropriate for either high school or middle school. Very few students at that level would be able to understand this material.

Discrete Math it's far easier than Calculus with infinitesimals, limits and curves everywhere.

As a programmer with Lisp experienc but not HS-er, I'd say that any kid learning Python would be at home with Discrete Math, or most Elementary kids playing RPG's/JRPG's at home.

Re: Discrete Mathematics: An Open Introduction [pdf]

#15

Post by McUsr »

redczar wrote: post #7
vouaobrasil wrote: post #6

Earlier quoted context omitted.

Not so sure. There are quite a lot of bright high school students that could indeed understand it. Maybe not in general but for a special interest group for sure. The local university had a group covering stuff like this and I found it to be very fun as a high school student, and there were at least 5 people that I went to school with that could easily handle this material (and I didn't go to some special school, eit…

[flagged]

You're right I think.

Though some High school kid with interest might grasp the parts he/she is interested in.

There is a big lap from there to "Could be taught in High School".

The sheer amount of work is the main obstacle in addition to the lack of specialization in the courses is one of the obstacles I think, apart from the obvious one which is the lack of foundational skills.

Re: Discrete Mathematics: An Open Introduction [pdf]

#16

Post by briangriffinfan »

redczar wrote: post #7
vouaobrasil wrote: post #6

Earlier quoted context omitted.

Not so sure. There are quite a lot of bright high school students that could indeed understand it. Maybe not in general but for a special interest group for sure. The local university had a group covering stuff like this and I found it to be very fun as a high school student, and there were at least 5 people that I went to school with that could easily handle this material (and I didn't go to some special school, eit…

[flagged]

You're so sarcastic I have no choice but to believe you.

Re: Discrete Mathematics: An Open Introduction [pdf]

#18

Post by chongli »

vouaobrasil wrote: post #6
redczar wrote: post #4

Earlier quoted context omitted.

I taught mathematics for 30 years at the college level. This is a college level textbook and it is not appropriate for either high school or middle school. Very few students at that level would be able to understand this material.

Not so sure. There are quite a lot of bright high school students that could indeed understand it. Maybe not in general but for a special interest group for sure. The local university had a group covering stuff like this and I found it to be very fun as a high school student, and there were at least 5 people that I went to school with that could easily handle this material (and I didn't go to some special school, eit…

Unless you’re talking about an elite private school where 5 student class sizes are the norm, no, a discrete math course is not appropriate for high school students.

I took an intro discrete math course in second year of university (at a school which is easily top 5 in math and engineering in my country) and I along with most of my peers struggled intensely with it, despite all of us having completed the proof-heavy courses in first year.

On the other hand, I routinely work with high school students who are unable to multiply a pair of single digit numbers without a calculator.

Re: Discrete Mathematics: An Open Introduction [pdf]

#19

Post by defrost »

redczar wrote: post #7
vouaobrasil wrote: post #6

Earlier quoted context omitted.

Not so sure. There are quite a lot of bright high school students that could indeed understand it. Maybe not in general but for a special interest group for sure. The local university had a group covering stuff like this and I found it to be very fun as a high school student, and there were at least 5 people that I went to school with that could easily handle this material (and I didn't go to some special school, eit…

[flagged]

Just for interest.

We covered part of this material to a similar level in high school in Australia in the early 1980s along with Calculus, probability and statistics.

In the math II/III streams ("advanced" for those wanting to do Enginering, Medicine, STEM, hard trades courses that need a grasp of math, etc).

This was a public high school in a remote area BTW, which I attended pretty much straight off an outback cattle station.

It's my understanding the US doesn't tackle any of this, nor Calculus, until undergraduate university.

Other countries address similar material (eg abstract algebra) in high school.

The full text is a bit OTT for high school (as I experienced it in Australia), but a good chunk wouldn't have been out of place, I and many of my peers would have happily read it as an extra curicular interest.

Re: Discrete Mathematics: An Open Introduction [pdf]

#20

Post by chongli »

anthk wrote: post #14
redczar wrote: post #4

Earlier quoted context omitted.

I taught mathematics for 30 years at the college level. This is a college level textbook and it is not appropriate for either high school or middle school. Very few students at that level would be able to understand this material.

Discrete Math it's far easier than Calculus with infinitesimals, limits and curves everywhere. As a programmer with Lisp experienc but not HS-er, I'd say that any kid learning Python would be at home with Discrete Math, or most Elementary kids playing RPG's/JRPG's at home.

Here’s a sample problem from discrete math when I took it in university:

For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd number of parts, and each part is congruent to 1 modulo 3. Prove that:

    |Cn| = [x^n] (x - x^4)/(1 - x^2 - 2x^3 + x^6)
Where [x^n] indicates the coefficient of the x^n term in the formal power series generated by the rational function (rational representation of the ordinary generating function).

I doubt many elementary school students would be able to solve problems like this.

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