A college dropout I know is wanting to get into computer science. They know how to code, but they didn't pay much attention in highschool and dropped out of college. Does anyone know of a good book for this person to read that gives problem solving tools to add to their toolbox? From talking to this person, I feel like I have 20 different tools I can pull out at any time to solve a problem and they have none, but I don't know where I got mine.

For instance, divide and conquer is a tool I use all the time without really thinking about it. I've split a list into sub-lists before, etc.

Please help him as it would help me so thanks in the advance for the post. I’m a college drop out too

https://en.wikipedia.org/wiki/Divide...quer_algorithm

I understand the merge sort algorithm, but can't think when I've ever used it.

What are some of the other 19 tools?

Consider simplified versions of the problem.

Consider extreme versions of the problem.


PairTheBoard

How about checking out the "...for Dummies" book seris?

Are there particular areas for which he wants to learn things?

Generally speaking Id say that I learned problem solving mostly through games and maths, where as the most usefull techniques I gathered from maths were when I considered it a game/was having fun with it.

Sudoku puzzles


PairTheBoard

Learn to code.


PairTheBoard

Get a math textbook at the next level for you and solve all the homework problems in it.


PairTheBoard

How to ask for help on a problem (knowing what to ask?)
Deciding what information is useful and what info can be ignored.
Not falling into tons of traps that are personal to you. I.e. i know i can miss a negative sign very easily, im prone to it, so i make myself be careful with negative numbers.
If somethings too hard, you can skip it.
If somethings too easy, you can get suspicious.
If im taking a test and I cant solve a problem, I skip it. Then when im done with the test, i skim the test looking for any clues that will tip me off as to how to solve the problem.
different ways of brainstorming have also really helped me with problem solving.

here's one. when doing a math problem, you can sometimes give it a once over and estimate the answer. then when you really solve the problem, if your answer is way off from that, you can get suspicious. Its rare that this works, but if, for instance, your finding the mins and maxs of a function, sometimes you can see "oh ****, the max is at about 3, so if i get 24 i know i fk*d up"

sometimes you can carve portions of the number line from the set of possible answers. I do this in my head sometimes. when i see x^2 i can picture the output as an arrow going to the right from 0 on the number line. I can also picture the graph, which is a very different picture.

At first, it looked like you were talking about specific problem-solving techniques for programming. For that, I would suggest a book on algorithms. It gives you a foundation for ways of approaching problems that builds up your toolbox of ways you can try to approach new problems.

But then your second list is sort of more like meta-problem solving techniques. For that, I doubt there's going to be a useful book, but if there were one it's going to be in the self-help section. Maybe it's in a book of proverbs, wise sayings, or fables. Or maybe a book on growth mindset. Or Zen and the Art of Motorcycle Maintenance.

Maybe your friend just doesn't have any experience at all, in which case they need to go out and get some. If the focus really is on programming, try Project Euler. If it's more of a meta thing, I don't have any good advice. Maybe they just need to get a hobby.

there's gotta be books on this very subject.

i'm thinking perhaps naively that you just learn some of this stuff on your own and in life in general. not taught in school... although i was top serious student, so maybe i'm unrealistic.

one thing i always liked when i was faced with tough math questions is evaluate boundary conditions. for probability question, if i was thoroughly confused i would try p=0, p =1, p=1/2 and at least i'd understand something more and have a minimal answer. also, good for checking answer you already have

There is a book on this very subject

How to Solve It (1945) is a small volume by mathematician George Pólya
https://en.wikipedia.org/wiki/How_to_Solve_It

also +1 to Zen and the Art of Motorcycle Maintenance. An extraordinary book that I recommend to everyone.

Sometimes considering an extension of the problem can help you see that your solution must be wrong. For example I’ve seen people make the error of answering 1/3 for the probability of throwing a six if you throw a die twice. They reason that the probability for one throw is 1/6, so for two it’s 1/6 + 1/6 = 1/3. I ask them then what the probability is for throwing a six if you throw the die seven times. The result of 7/6 obtained by the erroneous reasoning shows that reasoning to obviously be in error.

All of these seem to me related to dealing with the pressure of tests or exams. Almost all humans make unforced math errors, e.g. with the negative sign. I'd add that these seem more likely to occur towards the end of an answer, when the mind is bored or complacent.

"collecting terms" is often where a mistake is made..

OP.... google "how to solve any math problem book"

i don't want to mention any book publisher on 2p2's site.. but there is a prominent publisher that's made a business of buying up old classic STEM books and marketing them... i LOVE surfing their catalog.. OP, if you don't know the book company's name, shoot me a PM

Nice video on the 3x+1 problem. At the end he talks about the sponsor, a program called "Brilliant", that sounds like it relates to the thread topic.




PairTheBoard

The answer is you have to have passion for the subject that throws problems your way.

I scraped passes in mathematics (the subject itself) but did extremely well in the other subjects, that of course also contained math. This was for EE so eg. Engineering science, telecommunications, digital electronics etc.


People are suggesting math books and puzzles.
That seems to be an answer to getting good at solving generic problems which may or may not ever be a problem to you.

For example, Using Charlie's example of understanding sorting algorithms but never knowing when to use them is the result of being interested in sorting algorithms per se.
Whearas, i would have came across a problem, realised a sorting algorithm is the answer and then I would naturally become interested. This is how I got good at designing circuits, and writing code.

In short, face the problem first because you put yourself in that position out of sheer self interest.
Explain the problem then on a dedicated forum if needed for guidance.

I know when to use them, but I never have occasion to.

It seems stupidly rare that anyone would ever need to program a sorting algorithm from scratch outside of a classroom environment. But that fact doesn't deny that there's value in the exercise of writing such a program from scratch within that classroom environment.

It's like algebra. Nobody actually cares about the solution of the equation 3x + 4 = 16. But it's helpful for people to understand enough about algebra to do it, as it represents the capacity to work with a system of tools that lets you solve an entire class of equations.

I'm not trying to say otherwise. I only know sorting algorithms because I had to teach them, and I didn't find them the most fun part of the course. In fact, this might be the kind of course book that OP's acquaintance is looking for.

Might have been mentioned.

Do grade 7 math contests (and work your way up). Tons for free online

Russian math contest dominance is based alot on problem. Math knowledge is not enough to do really well

I know this thread is a few months old, and this book recommendation is not about general problem-solving, but "Code Complete" used to be one of the most highly recommended books for software developers. It was a pretty lengthy read, covering various aspects of software development, but it certainly includes problem-solving within that framework.



Table of Contents, from publisher.

Edx

It’s free school from the best schools - including one I went to - they give out certificates too.

It’s a Massive Open Online Course - started by Harvard and MIT.