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Siegfried · 12-17-2022, 06:43 PM

My fondness for HP calculators started in the mid-80's when I was allowed to use my father's HP15C after my TI30 had developed a key bounce that made it unusable. I used it throughout senior high school and made good use of the solver that allowed me to double-check on my symbolic algebra solutions as well as the complex number functions. My teachers were probably unaware of the HP15C's capabilities and rules on allowed calculators were yet to be written.

I have to admit, however, that I never progressed much beyond high school mathematically as the only math I needed for university was statistics and whatever programming I did was on home computers and DOS PCs.

Years later I still don't have much need for calculating anything more complicated than percentages or an occasional sine or cosine but this didn't stop me from buying a HP15C (I lost mine when I forgot it at work) as well as some of the other HP calculators I had found interesting as a teenager.

While their quality hardware quality is nice to behold I would really like to use them rather than just dusting them off or sorting them and beyond basic maths.

I have had a look at Valentin Albillo's challenges but found that at least those I looked at require a level of mathematical understanding that far exceeds what I learned in high school (minus what I forgot since) and I drop out when a solution requires a Taylor series or some other mathematical wizardry.

I would appreciate any ideas / links where to find simpler programming challenges that can be solved with a RPN calculator and high school maths or that lead onward from there in an instructional way.

Thanks!

John Keith · 12-17-2022, 07:02 PM

Our member pier4 recently posted this thread which has some interesting puzzles. They are probably best solved with advanced programmables such as the HP48 or the HP-71B but some of them could probably be solved with 4-level stack calculators.

SteveC · 12-18-2022, 02:39 AM

I wanted my kids to understand both the time value of money and the value of investing. Handing them each an HP 12C and walking them through several examples was a great way to help some kids become much less mathematically challenged. The oldest and his wife bought a house in their early 20s with that knowledge. Practical examples are the best way to become more math literate. New buttons on the calculator are like new levels in a game. The FV button on the 12C shows the growth on one's Roth IRA and the value of those early contributions.

Allen · 12-18-2022, 03:11 AM

The best I've found is Project Euler. Mos, if not all of the first 20 problems can be done on a HP calculator. Honestly if you want to up your math game to read VA's excellent challenge, you will likely need to pick up some basic Python or other scripting language.

If you prefer books, over websites, I have a collection of those.

Best Among them:

Algorithmic Puzzles
A friendly introduction to number theory (not about puzzles, but quite invaluable)
Concrete mathematics
How to Solve it

but where to start?

Allen · (This post was last modified: 12-18-2022 03:44 AM by Allen.)

(12-18-2022 03:11 AM)Allen Wrote: but where to start?

If you look at a "standard" progression of engineering classes in high school you will see:

Pre-algebra
Algebra
Geometry
Algebra II (matrix algebra) and Trigonometry
Calculus I

Then in college:
Calculus I (college level)
Calculus II
Calculus III (incl vector calculus)
Differential Equations
Linear Algebra (college matrix algebra)
Complex Analysis

Although Many Computer Science / Mathematics programs branch into other areas after Calculus 1 or 2:

Boolean Logic
Discrete math (concrete math)
Number Theory
Abstract Algebra
Topology
Combinatorics / Graph Theory

(If you like web-based classes, MIT open Course ware and Kahn Academy, and Corsera offer these classes for free or very little.)

Introduction to Algorithms (related book: Into to Algorithms)
Mathematics for Computer Science (online text)

Much of computer science, can be understood with these basic concepts, but learning how to apply mathematical tools to the analysis of data structures if often necessary to understand how to solve more advanced programs. (Caution: many of the Project Euler Problems are WELL above the normal undergraduate level maths listed above. Somewhere between 40 and 50% difficulty, the level jumps to MS and or upper level math/CS kind of solutions.)

Knuth's Magnum Opus: The art of computer programming is the sine quo non, but it is possible that not one living person other than the author fully understands the material in this 5+ volume set. Buy volume 1 used on some used book site and start there.

johnb · (This post was last modified: 12-26-2022 04:46 PM by johnb.)

I must heartily concur with Allen about the value of MIT's Open Courseware.
It is a collection of free (Open Source) books and guides and quizzes and tests.

If you are diligent, you could use them to go so far as to put yourself through the complete series of college engineering mathematics. Or just pick and choose the parts that interest you most and skip/skim the things you find most difficult and least rewarding.

I used these to help get my daughter through a calculus class where her instructor was a difficult person: a brilliant mathematician but a miserable excuse for a teacher/mentor.

I've also gone through them myself to maintain my skills as well as just for fun. (Even though I'm a software engineer, I find I only need calculus about once every 4-5 years or so. Or discrete math, or statistics, i.e. just long enough NOT using it to have to brush up every single time.)

Here's one man's opinion (mine) on the difficulty vs. fun of each topic Allen listed.

Absolutely necessary groundwork:

Pre-algebra
Algebra
Geometry

Necessary for most other topics below:

Algebra II and Trigonometry

Now for my very strong opinions:

Calculus I, II, III -- difficult for most people. Very useful for solving problems where 1 or more "something's" are happening continuously. Try learning it a bit: you'll either be fascinated by it or else completely put off. Physics beyond the high school level uses this heavily.

Differential Equations -- "very fancy calculus" :-)

Linear Algebra (college matrix algebra) -- much easier than calculus. Very useful for computer graphics, or for solving "sets" of problems. For example, you might have a problem where you have 3 things you need to spend your money on, and finding the "cheapest" or the "best" solution for any one of those means you can't afford cheapest or best on the other 2. What's the optimal mix of spending for all three things?

Complex Analysis -- useful for electronics. Not too hard if you found Trig easy. Kind of cool because it lets you solve things you couldn't otherwise.

Boolean Logic -- very easy, and if you work with computers you'll be surprised at how much of it you already know.

Discrete math -- lots of Sigma signs here. More difficult than matrix math or boolean logic. A toss-up whether it's harder than complex analysis or vice versa. It's the opposite of calculus: all values are though of as discrete chunks not continual smooth curves. Just like calculus, however, you'll either love this stuff and use it a lot, or hate it and decide to skip. It's very good for proving that nobody can improve on some particular algorithm.

Number Theory -- absolutely fascinating! Are there MORE irrational numbers (numbers that cannot be expressed as a fraction, like the square root of 2) than rational numbers? Is there more than one kind of infinity? Is there any true difference between an ordinal (this is the 11th thing in the list) and a cardinal (there are 14 things in the list)? You'll start thinking very concretely about some very abstract things!

Abstract Algebra -- haven't really dipped my toes in this yet.

Topology -- cool beans. You can prove a coffee cup is topologically identical to a doughnut. I have barely scratched the surface of this, though, because the proofs become very high-concept as you start wading through.

Combinatorics / Graph Theory -- another difficult subject that you'll either find a great use for and love it, or immediately hate it.

Now I'll bet that a lot of people vehemently disagree with my very subjective opinions above. Someone here may have even found easy all the things I found difficult, yet struggled with the things I found easy. Then there are those natural mathematicians who just absorb all this with ease. Also those brave souls who recognize the value and power of mathematics and are NOT naturally inclined, but chose to fight through it anyway!

Hope this helps!!

johnb · 12-18-2022, 07:34 AM

Oh, Oh, Oh!

I didn't notice the first time through that Allen also recommended George Polya's excellent book, "How to Solve It."

Polya was a brilliant, world-class mathematician who delighted in making mathematics accessible to his less mathematically-inclined students. I would have loved to have had him as a professor!

This book is a MUST READ!

If you like it, and you start learning more math, you might also like his book series, "Mathematics and Plausible Reasoning."

floppy · 12-18-2022, 11:30 AM

Have a look there: no RPN so far (a chance for you to introduce RPN there). https://rosettacode.org/wiki/Rosetta_Code
So far, I am wondering what people are trying to think mathematically with such a very limited calculator, except creating programs which should be documented in such link above for comparison purpose with other language (like comparison of latinum with more modern languages like Korean). For me, using it is a kind of YOGA. But as soon more deep activities has to be done, I move to for example the graphical https://www.desmos.com/calculator/ (however they are several mathematical tools online mathematica etc.).
At the end I am counting the "output". For what I have done few use of HP calculator. For a YOGA "session"? fine. Else for what? challenging what?

Allen · 12-18-2022, 04:59 PM

@ johnb
I agree 100% with your assessment.. I find I'm using calculus only occasionally, but the number theory is fascinating, partly because it's so practical. ( e.g. Chinese Remainder Theorem).

For Calculator work, I think it's also very practical to study integer factorization- even for small numbers (e.g. less than 10**12) this can be very instructive, and all of these can be implemented in some fashion on a RPN Calculator.

( previous forum post about similar algorithms )

A very approachable (undergrad accessible) book on the topic: Cryptanalysis of Number theoretic Ciphers

Here's some of the "low hanging fruit" from Project Euler:

5% Difficulty

10% Difficulty

Harald · (This post was last modified: 12-18-2022 05:13 PM by Harald.)

(12-18-2022 03:11 AM)Allen Wrote: The best I've found is Project Euler. Mos, if not all of the first 20 problems can be done on a HP calculator.

That looks interesting.
Is there anything like it at a much more basic level?
My youngest son is 5 years old now and not in school yet. He is asking me to give him mathematical challenges almost every day. His level now exceeds the second grade math his older sister is currently doing.
I am worried he will get bored as school, but I still would like to feed his curiosity. Any recommendations?

He sometimes surprises me. When he was three my wife was discussing a dice with my daughter. The question was how many corners does a dice have. She said 6. And was corrected it has six sides. A bit of guessing followed. Then from the background a little voice was raised, looking up from the toys "oh come on, it's 8!"

A couple of days ago I asked what is the middle between the largest two digit number and smallest one digit number.
I was thinking he would take one as the smallest one digit number. He was silent for a while. Then said "that doesn't work", 99 is odd. While discussing why it didn't work it became clear he used 0 as the smallest one digit number and so wanted to divide 99 by two. A few seconds later it became clear to him he wasn't limited to natural numbers and argued "if it was apples,I could cut one in half. So 49 and a half"

I have only his sister to compare with, but to me that seemed like an awful lot of thinking for a 5 year old.

Cheers,
Harald

Valentin Albillo · 12-18-2022, 11:50 PM

.
Hi, Siegfried,

(12-17-2022 06:43 PM)Siegfried Wrote: My fondness for HP calculators started in the mid-80's when I was allowed to use my father's HP15C [...] I have had a look at Valentin Albillo's challenges but found that at least those I looked at require a level of mathematical understanding that far exceeds what I learned in high school (minus what I forgot since) and I drop out when a solution requires a Taylor series or some other mathematical wizardry.

Thanks for your interest in my challenges and for having had a look at some of them, but I think that you didn't look far enough. Smile

Lest people reading your post might get the utterly wrong idea that my challenges are far too complicated and/or require superior math abilities or "math wizardry", let me assure everyone that's far from being the general case.

Some of my challenges do indeed requiere some math knowledge, such as my recent still-running SRC #012 - Then and Now six-pronged thread (three parts posted so far: Probability, Root, Sum) but there are dozens that do not require any complex math abilities, just the basics or even no math at all, e.g. when dealing with the functionality of HP calculators or RPN stack-handling techniques.

Also, my challenges have the unique advantage that they are specific for HP vintage calculators (featuring many for your HP-15C) and all of them include my original solutions in genuine RPN code for the specific machines, plus state-of-the-art solutions posted by dozens of forum member, plus very extensive comments. That you won't find anywhere else, not Project Euler, not anywhere.

All of my challenges are described and can be downloaded from my site, section HP Calculator Challenges, which is further subdivided in subsections Short & Sweet Math Challenges, The Regular Challenges and Semi-Regular Columns. The ones that would probably fit best with what you desire are mostly located in The Regular Challenges subsection, for instance:

HP Challenge VA101 - A Little HP-15C Challenge

HP Challenge VA102 - A little classical RPN challenge

HP Challenge VA104 - Little HP-15C challenge for the weekend

HP Challenge VA105 - Two little RPN challenges (11C 15C)

HP Challenge VA106 - Matrix Reloaded (HP-15C)

HP Challenge VA107 - Matrix Convolutions (HP-15C)

HP Challenge VA108 - Matrix Trilogy (HP-15C)

HP Challenge VA109 - Quiz Evaluating polynomials (HP-15C)

HP Challenge VA110 - HP-15C Arguably Useful Mini-Challenge

HP Challenge VA111 - HP-15C Arguably Useful MC Solutions Comments

HP Challenge VA112 - Really really small HP-15C Mini-Challenge

HP Challenge VA113 - A little HP-15C Quiz for the Weekend

HP Challenge VA118 - A New Small HP-15C Challenge

HP Challenge VA119 - A Very Didactic Little Quiz

HP Challenge VA120 - A Very Didactic Little Quiz Some Comments

HP Challenge VA121 - HP-15C Mini-Challenge RSUM CSUM

HP Challenge VA122 - New HP-15C mini-challenge

HP Challenge VA125 - HP-15C Mini-Challenge Speeding it up

HP Challenge VA126 - HP-15C Mini-Challenge Impossibly Short

Please have a look at the above mini-challenges and see if that's what you want. As I said, you won't find such challenges specifically designed for your HP-15C, with plenty of highly-optimized HP-15C RPN solutions and relevant comments anywhere else, at all.

Regards.
V.

johnb · 12-19-2022, 07:39 PM

I am just thrilled that there are others here who are seeking to increase their knowledge and/or proficiency in mathematics, the same as I am!

It's also funny: it varies WIDELY what different people consider difficult or "advanced mathematics."

Most of my coworkers and friends think I'm some kind of mathematical genius, just because I can apply a solid level of secondary school Algebra I+II / Trig / Simple Statistics to a wide range of problems. (I've had college calculus, linear algebra, and formal logic, but most of that is buried underneath 35 years of C++ language lawyering.)

Then I talk with my friends who are electrical, civil, or process engineers -- LOL. And they're regularly applying stuff like FFTs and Gaussian or Poisson distributions, and then I have to go and read for an entire evening to be even remotely versed on it. (Usually this includes utter failure to work the simplest examples.)

If I had 10 times the normal human lifespan, I think I'd save some money and go on a long sabbatical and go back to school just to do a degree progression in mathematics... just so I'd feel like I actually understand the stuff!

Allen · 12-19-2022, 08:17 PM

(12-19-2022 07:39 PM)johnb Wrote: If I had 10 times the normal human lifespan, I think I'd save some money and go on a long sabbatical and go back to school just to do a degree progression in mathematics... just so I'd feel like I actually understand the stuff!

I agree with this wholeheartedly, sir!
So many people fill their days (and nights) watching TV or similar trivia, that I've found it only takes 20-30 minutes of reading per day (averaged over a 20+ year career) to come out WAY ahead of those pretty much anyone, no matter how good they were in X who stopped learning when they got done with X ( where X = {high school, college, masters, or even PhD degree} .)

I was clearing off my shelf today and found another, perhaps less well known:
Richard Hamming's The Art of Doing Science and Engineering: learning how to learn
it's a bit of a hodgepodge of math, experience, polya-style learning about learning. Not so much about puzzles, though there are a few "lessons learned" in there!

Siegfried · 12-25-2022, 02:54 AM

Thank you for all your detailed suggestions and Merry Christmas and all the best for 2023 to you all!

pier4r · 12-25-2022, 09:30 AM

(12-19-2022 08:17 PM)Allen Wrote: I've found it only takes 20-30 minutes of reading per day (averaged over a 20+ year career) to come out WAY ahead of those pretty much anyone, no matter how good they were in X who stopped learning when they got done with X ( where X = {high school, college, masters, or even PhD degree} .)

I can confirm this because I feel often on the other side of the fence. For example if I try to refresh the topic X for a while, I stop doing the topic Y and I get totally rusty in it and I start to forget it. I also admit that I have periods where, due to various reasons, I do little productive things beside work and I see I start to lose pieces in every topic.

Heck I forget words in my mother tongue after around 10 years of not using it frequently.

The memory (of the majority at least) optimizes and information are forgotten without regular use. So yes keeping oneself active on the long run is incredibly helpful. It is a lesson learned to pass to young people.