4 ms·

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 mathe

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.

redczar 1y ago
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.
- vouaobrasil 1y ago
  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, either).
  - redczar 1y ago
    [flagged]
    - McUsr 1y ago
      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.
    - briangriffinfan 1y ago
      You're so sarcastic I have no choice but to believe you.
    - defrost 1y ago
      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.
      - cess11 1y ago
        Ninth grade introduced me to algebra and my 'technical' high school program spent a lot of resources teaching calculus and algebra. I also opted into all the other math courses they had, doing discrete math, complex numbers and stochastic math. I didn't have points to put into taking it but the school also offered a course on modern physics, teaching stuff like field equations and quantum mysteries. One of my adolescence girlfriends left Russia after fifth grade and had an introduction to both algebra and some discrete math there.
      - redczar 1y ago
        I’m speaking from the perspective of the U.S. I still contend though that the vast majority of people ages 12 - 18 are incapable of learning this book. Note that I’m talking about this book as it is in it’s totality. This book includes counting principles in it so one can always claim that aspects of this book can be taught to people between ages of 12 - 18. We do teach people how to count at a young age. The subject matter is such that one can introduce concepts from this book in grades 7 - 12 but not at the depth the book covers them. Calculus is taught in most high schools in the U.S. but very few students take calculus in high school.
        defrost 1y ago
        > the vast majority of people ages 12 - 18 are incapable of learning this book. Sure. That doesn't prevent it being a high school text taught in some high school streams though. Math I was taught to bulk of upper school students in Australia (in years 11 and 12), Math II/III was taught to those students interested in STEM at a university, Math IV was remedial math to bolster the poorer math students that didn't exactly pick up primary school math. Again, it's similar in depth to how I was taught math in high school and how my peers were taught in high school, but I guess we were more math orientated than others. * What makes it not a high school text (for advanced high school students here) is length rather than depth, while a breadth of math subjects were introduced along with concepts such as proof, reasoning, various notations, etc it was uncommon for a single subject such as discrete mathematics to be dealt with at great length, perhaps a third of the material presented here at a similar depth would be more common (again, for some high school students, not all high school students). * eg: https://profiles.imperial.ac.uk/j.gauntlett https://profiles.imperial.ac.uk/j.gauntlett , https://mysite.science.uottawa.ca/tschmah/ https://mysite.science.uottawa.ca/tschmah/ , https://hpi.uq.edu.au/profile/388/dominic-hyde https://hpi.uq.edu.au/profile/388/dominic-hyde are three of the people in my very small (12 in total) first year university math class who all had texts not disimilar to this in their senior math streams at their various high schools at the same time I attended high school. The entire group of twelve are not dissimilar.
  - deleted 1y ago
    [deleted]
  - chongli 1y ago
    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.
- dr_kiszonka 1y ago
  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.)
  - throwaway81523 1y ago
    Unfortunately the best way to develop intuition is to solve problem sets :). And for ML to make sense, understanding some probability theory might be more important than understanding calculus. In math heavy papers you'll need calculus and linear algebra too, but it's going to be hard to understand them without a fair amount of prior study. I took lots of math classes and wrote out problem sets, and I still can't read many of those papers.
- anthk 1y ago
  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.
  - chongli 1y ago
    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.
    - rak1507 1y ago
      Why not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.
      - chongli 1y ago
        And the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets). There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.
        rak1507 1y ago
        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.
- WhitneyLand 1y ago
  I meant more the subject itself rather than this particular textbook, but I’m curious about your opinion in general. I came to this opinion after taking it in college and not recalling very much in the way of needed prerequisites, but maybe this is a selective memory… What are some of the biggest things needed beyond algebra?

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.

redczar 1y ago

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.

vouaobrasil 1y ago
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, either).
- redczar 1y ago
  [flagged]
  - McUsr 1y ago
    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.
  - briangriffinfan 1y ago
    You're so sarcastic I have no choice but to believe you.
  - defrost 1y ago
    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.
    - cess11 1y ago
      Ninth grade introduced me to algebra and my 'technical' high school program spent a lot of resources teaching calculus and algebra. I also opted into all the other math courses they had, doing discrete math, complex numbers and stochastic math. I didn't have points to put into taking it but the school also offered a course on modern physics, teaching stuff like field equations and quantum mysteries. One of my adolescence girlfriends left Russia after fifth grade and had an introduction to both algebra and some discrete math there.
    - redczar 1y ago
      I’m speaking from the perspective of the U.S. I still contend though that the vast majority of people ages 12 - 18 are incapable of learning this book. Note that I’m talking about this book as it is in it’s totality. This book includes counting principles in it so one can always claim that aspects of this book can be taught to people between ages of 12 - 18. We do teach people how to count at a young age. The subject matter is such that one can introduce concepts from this book in grades 7 - 12 but not at the depth the book covers them. Calculus is taught in most high schools in the U.S. but very few students take calculus in high school.
      - defrost 1y ago
        > the vast majority of people ages 12 - 18 are incapable of learning this book. Sure. That doesn't prevent it being a high school text taught in some high school streams though. Math I was taught to bulk of upper school students in Australia (in years 11 and 12), Math II/III was taught to those students interested in STEM at a university, Math IV was remedial math to bolster the poorer math students that didn't exactly pick up primary school math. Again, it's similar in depth to how I was taught math in high school and how my peers were taught in high school, but I guess we were more math orientated than others. * What makes it not a high school text (for advanced high school students here) is length rather than depth, while a breadth of math subjects were introduced along with concepts such as proof, reasoning, various notations, etc it was uncommon for a single subject such as discrete mathematics to be dealt with at great length, perhaps a third of the material presented here at a similar depth would be more common (again, for some high school students, not all high school students). * eg: https://profiles.imperial.ac.uk/j.gauntlett https://profiles.imperial.ac.uk/j.gauntlett , https://mysite.science.uottawa.ca/tschmah/ https://mysite.science.uottawa.ca/tschmah/ , https://hpi.uq.edu.au/profile/388/dominic-hyde https://hpi.uq.edu.au/profile/388/dominic-hyde are three of the people in my very small (12 in total) first year university math class who all had texts not disimilar to this in their senior math streams at their various high schools at the same time I attended high school. The entire group of twelve are not dissimilar.
- deleted 1y ago
  [deleted]
- chongli 1y ago
  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.
dr_kiszonka 1y ago
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.)
- throwaway81523 1y ago
  Unfortunately the best way to develop intuition is to solve problem sets :). And for ML to make sense, understanding some probability theory might be more important than understanding calculus. In math heavy papers you'll need calculus and linear algebra too, but it's going to be hard to understand them without a fair amount of prior study. I took lots of math classes and wrote out problem sets, and I still can't read many of those papers.
anthk 1y ago
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.
- chongli 1y ago
  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.
  - rak1507 1y ago
    Why not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.
    - chongli 1y ago
      And the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets). There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.
      - rak1507 1y ago
        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.
WhitneyLand 1y ago
I meant more the subject itself rather than this particular textbook, but I’m curious about your opinion in general. I came to this opinion after taking it in college and not recalling very much in the way of needed prerequisites, but maybe this is a selective memory… What are some of the biggest things needed beyond algebra?