Today I completed my planning for my summer course for math teachers "Computer Science for Math Teachers"
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Today I completed my planning for my summer course for math teachers "Computer Science for Math Teachers"
But I'd love to know of any additional topics I ought to include. Main goal is to get the rest of the math faculty comfortable enough with code that they use it in a natural way as one of many problem solving techniques and teach this to our students.
When my lesson plans have a CS component other math teachers often skip it just because they don't feel comfortable.
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Today I completed my planning for my summer course for math teachers "Computer Science for Math Teachers"
But I'd love to know of any additional topics I ought to include. Main goal is to get the rest of the math faculty comfortable enough with code that they use it in a natural way as one of many problem solving techniques and teach this to our students.
When my lesson plans have a CS component other math teachers often skip it just because they don't feel comfortable.
I'm going to mostly teach them in python. Our "final project" will be building a class of objects for vectors. I think this will work well since math teachers already know all about vectors.
I will emphasize that looking up how to do things when programming is normal. I don't expect them to be able to "cold code" most of them can already read and write pseudo code for things like iteration and functions.
There is just a small gap when it comes to classes, and seeing code as a tool.
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I'm going to mostly teach them in python. Our "final project" will be building a class of objects for vectors. I think this will work well since math teachers already know all about vectors.
I will emphasize that looking up how to do things when programming is normal. I don't expect them to be able to "cold code" most of them can already read and write pseudo code for things like iteration and functions.
There is just a small gap when it comes to classes, and seeing code as a tool.
Example: "How many three-digit integers contain at least one 2?"
Elegant permutation solution:
9*10*10 - 8*9*9 = 252
It's also fun to write a program:
three_digit=[]
for i in range(100,1000):
if "2" in str(i):
three_digit.append(i)
print(len(three_digit))It's a less trivial problem if you make it: "How many three-digit EVEN integers contain at lest one 2?"
(but it's still trivial in code. Just add "and i%2==0")
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Example: "How many three-digit integers contain at least one 2?"
Elegant permutation solution:
9*10*10 - 8*9*9 = 252
It's also fun to write a program:
three_digit=[]
for i in range(100,1000):
if "2" in str(i):
three_digit.append(i)
print(len(three_digit))It's a less trivial problem if you make it: "How many three-digit EVEN integers contain at lest one 2?"
(but it's still trivial in code. Just add "and i%2==0")
I think one ought to be able to bounce in and out of both ways of seeing the problem seamlessly.
Use brute force to verify your theory. Use theory to make better brute force.
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F myrmepropagandist shared this topic
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Example: "How many three-digit integers contain at least one 2?"
Elegant permutation solution:
9*10*10 - 8*9*9 = 252
It's also fun to write a program:
three_digit=[]
for i in range(100,1000):
if "2" in str(i):
three_digit.append(i)
print(len(three_digit))It's a less trivial problem if you make it: "How many three-digit EVEN integers contain at lest one 2?"
(but it's still trivial in code. Just add "and i%2==0")
To start a popular and annoying tangent to this conversation... this is EXACTLY the sort of problem LLMs are terrible at solving. (unless they have been fed multiple correct versions of the solution)
The LLM will tell you a numerical answer with all the confidence of a god and it will be totally wrong. This understandable if you think about the way that these responses are generated, but to me this alone shows the limits of the system.
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To start a popular and annoying tangent to this conversation... this is EXACTLY the sort of problem LLMs are terrible at solving. (unless they have been fed multiple correct versions of the solution)
The LLM will tell you a numerical answer with all the confidence of a god and it will be totally wrong. This understandable if you think about the way that these responses are generated, but to me this alone shows the limits of the system.
@futurebird And really, a limit of human psychology that unless you're really really deep in your soul understanding how it works, the confidence will absolutely convince you,
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To start a popular and annoying tangent to this conversation... this is EXACTLY the sort of problem LLMs are terrible at solving. (unless they have been fed multiple correct versions of the solution)
The LLM will tell you a numerical answer with all the confidence of a god and it will be totally wrong. This understandable if you think about the way that these responses are generated, but to me this alone shows the limits of the system.
@futurebird I tried it on a local LLM and it followed the reasoning: determine how many 3 digit numbers there are, use complementary counting for numbers without a 2, and subtract one from the other. I suppose it might appear on its training set, or it might have generalise from similar problems.
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@futurebird And really, a limit of human psychology that unless you're really really deep in your soul understanding how it works, the confidence will absolutely convince you,
I think because this is the kind of problem that a computer can be used to solve with great confidence and accuracy people just assume that LLMs are doing what I've done in writing a program to literally count all of the numbers that meet the condition.
It's not an absurd error to make... but the LLM is doing no such thing!
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Today I completed my planning for my summer course for math teachers "Computer Science for Math Teachers"
But I'd love to know of any additional topics I ought to include. Main goal is to get the rest of the math faculty comfortable enough with code that they use it in a natural way as one of many problem solving techniques and teach this to our students.
When my lesson plans have a CS component other math teachers often skip it just because they don't feel comfortable.
@futurebird What are your thoughts on teaching them eg. Haskell? To me, Lambda Calculus feels like a natural gateway between math and programming
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@futurebird I tried it on a local LLM and it followed the reasoning: determine how many 3 digit numbers there are, use complementary counting for numbers without a 2, and subtract one from the other. I suppose it might appear on its training set, or it might have generalise from similar problems.
It reproduced text that someone else wrote that walked through the reasoning. It didn't follow it at all.
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I think because this is the kind of problem that a computer can be used to solve with great confidence and accuracy people just assume that LLMs are doing what I've done in writing a program to literally count all of the numbers that meet the condition.
It's not an absurd error to make... but the LLM is doing no such thing!
@futurebird i have noticed that in newest versions of chat-GPT it can indeed write a python program, run it, and give you the results. They charge extra for that capability. also still no guarantees the program it writes is correct
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@futurebird i have noticed that in newest versions of chat-GPT it can indeed write a python program, run it, and give you the results. They charge extra for that capability. also still no guarantees the program it writes is correct
So, they've added python to it to some degree do you think? That's interesting.
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So, they've added python to it to some degree do you think? That's interesting.
@futurebird it refers to it as “analysis”, it has special specific UI in which you can examine the python program and its output, and optionally download it to run on your own machine- a little like how it presents ui for other external services like image search results, image generation, image description- the llm itself doesn’t do those things but makes it seem like it is
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@futurebird What are your thoughts on teaching them eg. Haskell? To me, Lambda Calculus feels like a natural gateway between math and programming
None of our students uses Haskell, and it's just a bit obscure. These are just math teachers who never program anything most of the time. I'm picking python since they will see it most often and it might work its way into their lessons because of that.
(I will implement Haskell education for the math teachers when I start teaching the fifth graders Dvorak ... )
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@futurebird it refers to it as “analysis”, it has special specific UI in which you can examine the python program and its output, and optionally download it to run on your own machine- a little like how it presents ui for other external services like image search results, image generation, image description- the llm itself doesn’t do those things but makes it seem like it is
Well now I've got to try this too. I always try each new thing to understand it.
I mainly use LLMs to clean up my speech-to-text narration or to format lecture notes into lesson plans. They're good when I provide **all** the content, and decent at shortening and clarifying text. That said including the time needed to proofread the output it is only slightly faster than doing it from scratch.
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Example: "How many three-digit integers contain at least one 2?"
Elegant permutation solution:
9*10*10 - 8*9*9 = 252
It's also fun to write a program:
three_digit=[]
for i in range(100,1000):
if "2" in str(i):
three_digit.append(i)
print(len(three_digit))It's a less trivial problem if you make it: "How many three-digit EVEN integers contain at lest one 2?"
(but it's still trivial in code. Just add "and i%2==0")
@futurebird Is 8*9*4 just a typo, or are you checking to see how alert we are?
9 × 10 × 10 – 8 × 9 × 9 = 252 (correct)
9 × 10 × 10 – 8 × 9 × 4 = 612 -
@futurebird Is 8*9*4 just a typo, or are you checking to see how alert we are?
9 × 10 × 10 – 8 × 9 × 9 = 252 (correct)
9 × 10 × 10 – 8 × 9 × 4 = 612Thanks!
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@futurebird it refers to it as “analysis”, it has special specific UI in which you can examine the python program and its output, and optionally download it to run on your own machine- a little like how it presents ui for other external services like image search results, image generation, image description- the llm itself doesn’t do those things but makes it seem like it is
@bri_seven @futurebird
Presumably constraining the LLM output to valid python programs at the sampling stage, potentially giving a misleading impression about its capability -
I think one ought to be able to bounce in and out of both ways of seeing the problem seamlessly.
Use brute force to verify your theory. Use theory to make better brute force.
@futurebird one thing I've always appreciated in the intersection between coding and computer-science/mathematics is, when you can use a naïve approach initially, to get answers fast; but then have to switch to a more sophisticated algorithm to have any hope of scaling. I'll see if I can come up with some specific examples…
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@futurebird one thing I've always appreciated in the intersection between coding and computer-science/mathematics is, when you can use a naïve approach initially, to get answers fast; but then have to switch to a more sophisticated algorithm to have any hope of scaling. I'll see if I can come up with some specific examples…
Back in the day when computers were rare, if I had to show people who were completely new to coding one simple thing you could program super-easily if you weren’t too worried about efficiency, and then refine to get better scaling, I always took them through a few versions of listing the prime numbers up to N.
