4 Steps To Solve Any Problem

In this video I talk about a step by step process which you can follow to solve any problem. This problem solving process can be applied to any field of study such as mathematics, physics, computer science, engineering, etc. You could even use this process to help you solve life problems. This process is explained in great detail in the legendary book by George Pólya titled How to Solve It. I think this is a good book for everyone as it is written beautifully and helps clarify your thinking.

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Thank you:)

[nealcarpenter]

Back in '72 I had a chance to talk to Prof. Polya. I told him that I'd read his books (mostly), and it seemed to me that his advice boiled down to 2 things: When faced with a difficult problem 1) do PART of it & try again, or 2) do a SIMILAR problem & try again.
As a really low level grad student, kinda challenging a world famous mathematician and teacher, I was expecting to get brusquely Blown Away. Instead, he smiled & replied, "Young man, I am 85 years old and I'm still learning how to do those 2 things." What a man. I've never forgotten, so I guess I really WAS Blown Away.

[xdlolfam]

1. Understand the problem.
2. Connect what you know with the unknown.
3. Carry out a plan.
4. Examine obtained solutions.

[GretgorPooper]

As a programmer, How to Solve It actually helped me pass quite a few of those technical assessments. It's definitely a good read!

[imrematajz]

Polya is a Hungarian surname and the L is silent. The correct pronunciation is just simply Poya. Thanks for sharing your experience with this wonderful book from this great scientist.

[nna]

I have never read the book of prof. Polya. But when my students asked me to give a talk on how to solve a problem, I tried to deduce a method from my experiences. It turns out that my method is the same as that given by prof. Polya. Each time I face a problem, I divide the problem into sub-problems (a sub-problem can be divided into sub-sub-problems, and so on) and solve them. Each sub-problems must be tested. Eventually, I connect all the sub-problems to solve the problem.

[ANFeuerstahl]

My father [I miss him badly - He was a math teacher and a great admirer of Pólya] once told me that math is basically applied good sense.

[nezzylearns]

YouTube is showing out with their recommendations. My analytical brain really loves this advice. I took from this video that in order to be great at problem solving you have to create better systems of solving them. By following these tips I'm sure my brain will create new neural networks and eventually become a pro at problem solving. Thank you so much. I'm adding this to my Amazon wishlist

[soham]

I failed maths exam by 1 mark and giving an improvement exam and here I'm. I made up my mind to learn problem solving and learning maths from scratch as I will be pursuing CS in first year. Your videos are really helpful. Thanks:)

[jakemoseley]

I read this great book in high school in nowhere Alaska whenI thought I was Mr Cool in math. I got the second highest score in the state on the little Math association high school test, even tho I skipped my Junior year. 800s of course. So off I went to Yale, just full of myself. I bragged to my Friend Richard Mann about my results on the MAA test. He asked my score then howled with laughter, telling me that my score would only have been sixth in his Long Island high school. I bragged to my two years younger classmate Cherlin about reading the Polya book. He said he knew about it and that he had spent time in the summer working with “George.” I got called up to the math Major league but I certainly couldn’t hit major league pitching. This is a really cool book.

[sharonjuniorchess]

The Greeks used mathematics as the source for solving all their problems and this occupied my mind for some time until I realised (discovered) that it was more a way of thinking that resonated with each number. Another person who "discovered" this approach IMO was Edward de Bono who had a classical education and I think this helped him in coming up with his thinking skills courses the component pieces which when all put together can assist in solving any problem in life. Stanford seems to be a place where much of this "type of thinking" was exposed to the world albeit the student has to fathom out the structure it is ubiquitous.

[miguelangeldiaz]

The steps are pretty clear... The issue with problem solving is seeing relationships between things that are seemingly unrelated, and predicting or anticipating the unknown. Unfortunately not all people are capable of doing this

[SeanPat]

I started using this book in 1962 when I was taking geometry and 10th grade and have used it since. Actually the copy I have right now is the fifth one I owned. I loaned out the first four and never got them back so now I just tell people to get it from Amazon. It really does help, but it should be reserved for difficult problems. Essentially, the method enables a person to solve a problem that’s more difficult than they could solve otherwise.

While the book focuses on geometric problems, it can be used to solve almost any problem with a slight generalization of the terms.

[JoeTaxpayer]

I can't say how much I appreciate this reference. I work in a HS as an in-house math tutor, and after reading just a bit in, already am thinking about what I can do better, different, to help my students. Also going to buy your Calculus Udemy courses. I've helped students right through calculus, but never sat and watched a teacher teach the classes. The sample lessons tell me that it's a great step to take.

[Beerbatter]

The is awesome stuff. Very cool book. When I was preparing for my Professional Engineering Exam, I had a University Professor that repeatedly reminded me of the basic steps to take in the exam, no matter what the problem or discipline. This approach served me well during the challenging exam, especially considering there is not much time available for each problem. Thankfully I passed.

1. Carefully read and understand the problem.
2. List and define the knowns and unknowns.
3. Draw a free-body diagram.
4. Write down the fundamental equations and list units to be used.
5. List all assumptions.
6. Simplify the problem by cancelling out unnecessary and irrelevant terms.
7. Rearrange equations as necessary for the unknowns.
8. Plug in the numbers and solve.
9. Justify the solution. Is the answer reasonable from an engineering perspective?

[musicarroll]

I studied under Paul Halmos as a senior and graduate student at UC Santa Barbara from 1976-1979. Amazing teacher!

[jameshansen]

Since the late 80's, pilots have been taught a concept called aeronautical decision-making (ADM) to reduce accidents caused by pilot error. At its core is a decision loop called the DECIDE model, which stands for: Detect the problem, Estimate the need to react, Choose a desirable outcome, Identify solutions, Do the necessary action, and Evaluate the effect of the action. The chapter about ADM used to be the last chapter in the FAA Pilot's Handbook of Aeronautical Knowledge, but they promoted it to chapter 2 in the most recent edition.

[sanjaybhatikar]

I went a step further and reduced it to 2 steps. Step 1, define problem. Step 2, solve problem. Thank you!

[Morning_star]

I realize that this is a book on how to solve arithmetic but I can't help but notice how useful this information is in the real world of practical problem solving

[surfbuf]

‘This is not a text book, you can actually read it and learn from it.” Lol. That was awesome 👏

[andrescientos]

The Auxiliary problem (7:10) is a good technique. It's like how I once read in a book about Zen, digging out a thorn with another thorn.