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.
Now that I'm old I thought I could say nothing of importance to the world but your comment gives me hope. Still I don't think I can get away with any BS ....from Ireland.
@@warriordx5520 It's actually true, that's how generally everyone solves math problems, if we are strictly looking at the steps themselves. I didn't learn anything new in terms of the steps. Putting it into action to get the desired results is an entirely different beast. It basically comes down to practice, practice and practice. However, if someone memorizes these steps it may help them when they are stuck in a problem. Sometimes when we are stuck we just forget the basics very quickly. Although, I don't know about the original book, maybe the example alongside the steps will shed more light than just the step themselves, also, there are obviously a lot more content in the book. I will give this book a go.
@@kkgt6591 there's always Knuth's classic The Art of Computer Programming, and if you like a more formal logical approach, Dijkstra's A Discipline of Programming is pretty cool too.
Consultant/project manager/programmer here and my take away from the video was I need this book to help document/share/and most importantly better sell $$$$ the things I already work on. Not necessarily to help me solve problems, but to better share and explain the plan and what the process is for other people to get on board and support the project. The paragraph he read that pretty much says you already know what to do, but you may not be able to describe it hits home for me. IE. There is always a rabbit hole of solving 10 aux problems to make progress in the real problem. At least if I can explain why its taking so long. From the outside they just see it taking forever.
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.
To achieve a goal, write down all the obstacles between you and your goal. Then knock the obstacles down one by one. When you have knocked down the last one, you have achieved your goal. OBSTACLES ARE THE SIGNPOSTS TO YOUR GOAL.
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.
UA-cam 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
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.
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.
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?
@@touristguy87 I applaud and recognize your commitment to accuracy in public communication, especially in this present age, when so many are eager to embrace ambiguity and its less trustworthy cousin flagrant falsehood as merely alternative methods of distributing information. Often attempts to clarify the exact meaning are dismissed with an annoyed, “You know what I meant!” Perhaps, yet it is not what was said, thus prompting the further inquiries.
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.
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.
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.
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
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:)
@@ehtesham998 Thanks for asking but what and how would you teach? I'm not that poor in maths. Last year I scored 95 in maths but due to ignorance this year I got failed. The reason I want to get into maths to improve my problem solving skills.
Based on observations of book, with its 4 steps, it appears all 4 steps consist of several queries, ultimately indicting additional sub-steps, which may or may not produce more unknows, or "problems." Ones rendition of solving any problem: Step 1: there is no problem, there is no spoon. What one individual sees as a problem, another sees an opportunity, a challenge or puzzle. I was going to complete the viewing of clip, however, the passion of the moment compelled an immediate interjection of doublepence. Thanks for sharinggg
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
I actually have that book, I purchased it as it is recommended in the prologue of the 7th edition Precalculus by James Stewart, Redlin, and Watson. Admittedly I haven't been able to read through it so this video is a well received overview of the book. Too many books, so little time!
Bought this book preparing for a chem undergrad last year. My gap year is coming to a close and I’ve come to notice myself gravitating towards mathematics videos more than any of the other sciences. Copies like “How to Solve It” and UA-camrs like MathSorcerer and 3Blue1Brown have got me considering majoring in mathematics.
I was so dumb when I was young that I did not even know that I could plan things out. I came from a rural environment, I had a learning disability with memory. I never learned algebra, geometry, trig, chemistry, etc. I am technically illiterate in those subjects. I only graduated from high school because I think they just passed me out of kindness. I did know that I wanted to permanently get out of that little town as soon as I turned 18 and I did. I had no plan. I actually did the old “if you don’t know where you want to go then any road will take you there” trick. I did not know how to solve problems using organized steps. But I do now and I am still going to read that book in case their are some techniques I am missing. Thank you for bringing that book to our attention!.
Costs less than a taco and feeds you for a lifetime. Thanks for sharing. Your enthusiasm for this book is great. Makes me wanna dig up another great book about the principles of typography. Not the most exciting topic but there's something about the writers passion for it that makes it special.
This book is a bridge that helps a person gain confidence by asking questions. It ought to be mandatory reading for school leavers on which ever path they find themselves on.
Such a wonderful book. The first time I read it, it seemed to drop straight into my subconscious, and I could barely remember anything in it, but I suddenly got better at solving maths problems. Then I read it again. Unfortunately, I couldn't find a buyable copy and was using my university library's copy. I really should get another copy, and yes, it is applicable to a lot more than just mathematics. BTW, I have a copy of Einstein's "The Meaning of Relativity". A little paperback that you can fit in your back pocket, and I did. The intro by AE is amazing, showing his mind pondering why classical physics is not enough, using simple thought experiments that show that even special relativity is not complete, and then jumping into tensors.
"The first time I read it, it seemed to drop straight into my subconscious, and I could barely remember anything in it, but I suddenly got better at solving maths problems." ...which even you must admit sounds completely vapid. "You suddenly got better at solving math problems". how much better
Went to Amazon India, it said I had bought this book on 30 Aug 2016... :) never even openned it.. I was thinking it is purely mathematics... But I can see that it is way more than that.. almost like a thinking process! My interest is rekindled! Thanks a lot!!!!
Can’t wait to get my hands on this book. I spent 30 years solving complex problems using the 8D problem solving methods. (8 Disciplines). I expect to find that the 8D approach was derived from the methods taught in this book.
Reminds me of an Art Critique : Describe, Analyze, Interpret, and Judge (reflect, assess) ---- I am a HUGE fan of Mr. John Forbes Nash - I'm sure he was quite aware of this book. 😊
This s a great book. I read mine multiple times, and took time to memorize the summary pages. Also you should review his other great books: Mathematics and Plausible Reasoning. There's 2 volumes. It's a book on how to conjecture. Back to How to Solve It. The greatness of this book to me is in the prose and how he times the prompting of your mind to open and grope for dimensions you were not aware of and not so much the content of what he says in particular. I think his book is tailored to technical problems expressed mathematically. But, outside of that, its effectiveness diminishes. I've had more success and much less stress to think about problems like a biologist studies organisms in the lab and in their habitats. I get more mileage reading popular books on ecology, like "Why Big Fierce Animals Are Rare" The best way I've found so far to solve problems, it to solve lots of problems *on your own*, struggle with the problem, solve it on your own. Then go back and see what the solution is or see part of the solution, and solve the problem in another way. Anyways, thanks for the trip down memory lane.
I think because I had a mentally disabled child; I had to teach them how to think, makes me understand the need to know how to learn, think and execute became important. People are so insulted when you tell them what they take for granted. Its not that you cant, there is just a way. Ways can be good and beneficial. Give you a frame work and reference to think further out, your ideas. Now I have to convince people there is still mental retardation. It still shows, its just difficult to see at first because of the steps taken to think things out.
I have found that the TIME and MONEY spent in reading a book is well worth those costs IF i have learned at least one thing from the book. This book looks like one that can teach us many lessons.
Com-Sci 25 years ago.... 1. Identify the problem 2. Understand the problem 3. Identify possible solutions 4. Choose most probable solution 5. Write Code 6. Evaluate/ re-code
Just found a copy on amazon (Princeton version) and I am genuinely looking forward to using this daily. I am going to school to become a programmer and I've been dying to find out why I have been experiencing such hardship and I know it's because I tend to tackle big chunks and then I get frustrated. Thanks for the video!
Thanks for this video. I was fascinated and ordered the book. Just received it, but the modern paperback isn't quite the same as the great layout of the plan on the inside covers in your older, hardback version. Still looking forward to reading it though. Will definitely be looking out for a second hand copy now.
"these days" It might scare you but it was probably worse before because you couldn't see how many people lacked that quality. Now you can not only quantify It but also acquire It with the information accessible on the internet.
I noticed the video and am glad I did because this kind of book is a great book of interest after learning about it because there are people such as myself who read most of everything to learn with math or reading most of the words On a page to begin the thought process with count numbers and the how to think while trying to solve math problems and the many kinds of solutions to the various counting methods Only get me excited to want to purchase this book just from all you presented in it and I just wanted to take a moment to say thank you for presenting a book that seems as if it's great in many ways for good reads and learning purposes that I have now decided from the information in the book It is a must-buy and so excited to have it on my next book order of books that I have ordered on regular books that have excellent meaning to teach the mind for better growth to become better at reading while counting which is not an always easy task for me but some people are natural to doing both at the same time, reading and counting at the same time I mean to that just said and I do believe this book is gonna teach me knew things and how to think better at trying to both reading snd counting at the same time which will provide a bitterness of learning in both areas of studies that I often struggle to do both at the same I am trying to say thank you for making this video and introducing a book that I know I can learn from Again, I am a struggling student in many different subjects, and happy that I have a new book to purchase that I know is going provide me with some how-to methods for learning while trying to count and read at the same time something I struggle to do I just hope it won't be difficult to find or order wish me to look in locating it at book stores, I shall search as many if needed because I want this book Again this great book I must get and it's because you previewed it in this video for an audience to learn about it! Thank you so very much for making this video about a great book and I agree with every word you said about it seems as its a nook to not want to put down and keep reading Just watching it I just want it now and gonna search engine it at the book stores on my next book order Thank you so very much for you noticing such a great book which makes your value of thinking just as great if not greater and not comparing minds just saying it takes a great mind to recognize great words to teach others what great words of how to think to look like, on the page and in the video who presents such a great book of value for me and I know so many other Can't stop thank-you you enough because it's what I need and never knew someone wrote a book that explains it like that and it's my style of thinking to read and figure the numbers with words but which words to ask? And the book has it and the way you showed it was just as grand! Thank you so much again and again I need this book and thanks to you I have a book I can't wait to get my hand on to read cover to cover, and I am so excited about this book I had a great day because of this video, and trying not to be redundant but AGAIN thank you so very much for the book presentation, I need it with my books for learning better... 😊
first, understand the problem, and second, try to divide the problem into simpler parts if possible then repeat the above process till it cannot be subdivided. Solve it in this way. This is from the knowledge of computer programming
The trick is to be on the path of truth, and thus discard the beliefs and dis-beliefs of others. As an example, I am a high school dropout and thus I had no education in the field of physics. But by examining "motion", I soon had fully understood motion 100%, and at the same time had therefore derived the Special Relativity equations all on my own. Others did not "Believe" that I had done so. And so that was why I threw together several videos to show exactly how I did it.
This book sounds awesome and informative. I have to say that you have promoted/recommended this book very well and I can't wait to read it. Thanks for the content.
I actually bought another copy because this one is signed and the dust jacket is fragile lol. I got a newer paperback I can read since I really love the ideas in this book❤️❤️❤️❤️❤️❤️
John von Neumann, pronounced NOY-man. Right. Only the guy responsible for the fundamental architecture of everyday computers. And a whole bunch of other stuff.
A part of me wished schools would teach students some of these methods in tandem with the other things they learned. On the rare occasion when some problem-solving steps are actually taught, they're always an afterthought, since students aren't tested on them, nor are they given the opportunity to apply these steps. Children won't listen to dry lectures - they're boring, but if you teach them problem solving steps when they're asking you how to solve a problem, they will often see the immediate benefits and pay attention right then and there.
Didn't Richard Feymen (spelling?) do a similar thing? Having taken 2 yrs to set up my online business, one of the biggest things I have found is asking the right questions and that only comes after a deep and thorough analysis from which understanding arrives. Courses are great yet give you tidbits of information, the rest one has to figure out by oneself. Eg. I asked the question just earlier this year...can I track emails (who opens them etc)? The answer is yes, and nobody ever teaches you this. Only because I asked the question did I find the answer which then led me down a whole new tunnel to explore and research....and it all takes......time. And by the way, what a difference it makes to marketing, wow. Again, no one teaches or tells you these things
I've had two books by Polya in my collection for years, and I finally read How to Solve It because of your review. I found it to be as interesting and useful as you say--thanks for the review. The other Polya book is Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. Would you consider reviewing Mathematical Discovery?
I took your advice, went for a walk, measured the distance by the maps app, got lost in the park, looked up to the moon, found out which way was south, and maps told me how long it will take me to get back. I remembered that in order to make it back I have to "Imagine my Reality, Then Realize my Imagination". So a 30 minutes walk to run away from solving a problem took me 90 minutes. and the problem wasn't even Math. The problem isn't going to be solved unless there is going to be a recession. That way welders will be available again. Some of us are really praying for a recession.Patience!
Times have moved on. I have not read the book but watched the clip and the 4 points. Ths second step has to be expanded. It is the art formulating and capturing the data. I am sure companies like SpaceX are capturing all what is possible. However most professionals have no clue to do this in their own field and the subject is not taught well at any level.
It is a great book and like some of the greatest achievements it's deceptively humble in appearance. I am so sorry I lost my copy. One day I plan to go to Strand books and buy an old used copy. I agree that the older editions of books are usually the best. One gets the pure unadulterated version without so-called improvements. BTW that book by Von Neumann (NOY - man) and Morgenstern would have been a worthy buy. 😉 In it he outlines a branch of mathematics he invented. His Game Theory got us through the Atomic Age alive and well when applied by Herman Kahn (his IQ = 200! Reading speed = 20K words per minute!) of the Hudson think tank in his magnum opus, Thinking the Unthinkable. Johnny von Neumann dwarfed the greatest minds of his day who all agreed that he was the only true genius among them! Famous von Neumann story. JvN was very patient when explaining things that were complicated to small children. He would make it as simple as possible for them. One of the greatest minds of Europe once said he had the unsettling feeling JvN would also explain his advanced ideas to them as if they were small children so they could understand. However one time he just couldn't explain his theory to a colleague no matter that they spent all day on it. They agreed to disagree and went home for the evening. The other scientist spent all evening thinking over JvN's simplified explanation. Finally he understood it and called him excitedly at 3 in the MORNING! He groggily answered the phone angry over being awakened. The other scientist said, "Johnny!? You were RIGHT!" And started to explain why when JvN testily interrupted him with, "Do me a favor? The next time you decide to wake me at three in the morning do so when I am WRONG about something!" and I guess hung up on the poor but inconsiderate man.
I read this book in my late thirties, and I immediately thought: why didn't I learn this back in high school?? Much of the content is common sense. Some of it I already practiced intuitively, without thinking about. But often I would get stuck, and just think "this is too hard for me", in cases where putting in some effort would be fruitless without being methodical. Until the end of high school, math problems were small enough that intuition was sufficient, but as difficulty and scope grew, I struggled. The simple ideas in this book are powerful, and definitely apply beyond mathematics. The huge benefit of reading Polya's book is that the method isn't implicit like in a typical math course, which usually teaches you the results with some proof, but not the process of searching for a solution. Exercises tend to test your abilities in problem solving, but problem solving itself isn't taught. Smarter people who "get it" see the patterns in the teaching material, and learn to reuse them when applicable. For me, "How to solve it" was the kind of explanation that I really needed. Highly recommended!
Professor , the book by John Von Nuemann that was advertised at the back of the dust jacket is actually revolutionary since it introduces Game Theory which revolutionized economics
!. define the problem. 2. research the problem 3. form a plan a hypothesis. 4. carry it out. 5. is it true or not? These steps are most scientific textbooks.
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.
Beautiful story. Thanks for sharing it with us.
Being humble is one way to identify a quality person.
thanks for sharing
Wow
Now that I'm old I thought I could say nothing of importance to the world but your comment gives me hope. Still I don't think I can get away with any BS ....from Ireland.
1. Understand the problem.
2. Connect what you know with the unknown.
3. Carry out a plan.
4. Examine obtained solutions.
OH MY GOD, i have never ever thought of that! MINDBLOWING!
ffs that's how any average human solves a math problem
Thanks
@@warriordx5520 Your input is not one bit more useful than the initial comment.
@@warriordx5520 Alternatively, just stare at the problem for five minutes, then write down the solution. Fewer steps.
@@warriordx5520 It's actually true, that's how generally everyone solves math problems, if we are strictly looking at the steps themselves. I didn't learn anything new in terms of the steps. Putting it into action to get the desired results is an entirely different beast. It basically comes down to practice, practice and practice. However, if someone memorizes these steps it may help them when they are stuck in a problem. Sometimes when we are stuck we just forget the basics very quickly.
Although, I don't know about the original book, maybe the example alongside the steps will shed more light than just the step themselves, also, there are obviously a lot more content in the book. I will give this book a go.
As a programmer, How to Solve It actually helped me pass quite a few of those technical assessments. It's definitely a good read!
A fellow programmer and would love to hear more recommendations from you.
@@kkgt6591 there's always Knuth's classic The Art of Computer Programming, and if you like a more formal logical approach, Dijkstra's A Discipline of Programming is pretty cool too.
I'm a beginner programmer, i guess I'll add this book to a catalogue of possible resources to help me.
Consultant/project manager/programmer here and my take away from the video was I need this book to help document/share/and most importantly better sell $$$$ the things I already work on.
Not necessarily to help me solve problems, but to better share and explain the plan and what the process is for other people to get on board and support the project. The paragraph he read that pretty much says you already know what to do, but you may not be able to describe it hits home for me.
IE. There is always a rabbit hole of solving 10 aux problems to make progress in the real problem. At least if I can explain why its taking so long. From the outside they just see it taking forever.
...but how much did it help you...
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.
To achieve a goal, write down all the obstacles between you and your goal. Then knock the obstacles down one by one. When you have knocked down the last one, you have achieved your goal. OBSTACLES ARE THE SIGNPOSTS TO YOUR GOAL.
@@shadeburst 👌🏽
Sort of First Principle Thinking
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.
What is good sense?
@@EvilSapphireR Not sh*ting where you sleep
That was my problem math
Non of my math teachers had the faculty of considering us pupils as blanc slates. Anybody recognize this?
@@Vekikev1 True but incomplete
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.
Is he one of the Martians?
Thank you!
Thanks for educating us on the correct pronunciation of "Polya"
UA-cam 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
Amazon ???
Your off !
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.
Very cool
I like this thanks for sharing
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.
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?
"When I was preparing for my Professional Engineering Exam"
for THE PE exam
it's not yours... you took the exam, there's a difference
@@touristguy87 I’ll bet you’re a lot of fun at backyard barbecues!
@@commanderthorkilj.amundsen3426 ...that could actually be true. You're one of many who have told me that, or something much like it.
@@touristguy87 I applaud and recognize your commitment to accuracy in public communication, especially in this present age, when so many are eager to embrace ambiguity and its less trustworthy cousin flagrant falsehood as merely alternative methods of distributing information. Often attempts to clarify the exact meaning are dismissed with an annoyed, “You know what I meant!” Perhaps, yet it is not what was said, thus prompting the further inquiries.
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.
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.
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.
‘This is not a text book, you can actually read it and learn from it.” Lol. That was awesome 👏
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
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:)
Do you want to learn from me???
Did u fail cbse
@@tikkamuchiodkoodoo2661 No.. Our state board.
@@ehtesham998 Thanks for asking but what and how would you teach? I'm not that poor in maths. Last year I scored 95 in maths but due to ignorance this year I got failed. The reason I want to get into maths to improve my problem solving skills.
@@soham8870 Good!!!
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.
As an engineer and an entrepreneur this is a gem of a book!
I discovered "How to Solve IT" In the Whole Earth Catalog" in 1973 or74. It should be a cornerstone in any serious library.
I went a step further and reduced it to 2 steps. Step 1, define problem. Step 2, solve problem. Thank you!
Based on observations of book, with its 4 steps, it appears all 4 steps consist of several queries, ultimately indicting additional sub-steps, which may or may not produce more unknows, or "problems."
Ones rendition of solving any problem:
Step 1: there is no problem, there is no spoon. What one individual sees as a problem, another sees an opportunity, a challenge or puzzle.
I was going to complete the viewing of clip, however, the passion of the moment compelled an immediate interjection of doublepence.
Thanks for sharinggg
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
I studied under Paul Halmos as a senior and graduate student at UC Santa Barbara from 1976-1979. Amazing teacher!
I thoroughly enjoyed the follow up book, Mathematics and Plausible Reasoning. Amazing read!
Oh interesting, thank you for this!
@@TheMathSorcerer self thought is the best
Hi Math Sorcerer! Love the content as always and I've been really enjoy these book reviews lately!
Hey, thanks!
Yes, agreed. Love these book reviews 👌
... A must read book for any math learner. Thx 4 posting it.
I actually have that book, I purchased it as it is recommended in the prologue of the 7th edition Precalculus by James Stewart, Redlin, and Watson. Admittedly I haven't been able to read through it so this video is a well received overview of the book. Too many books, so little time!
So many texts and one life?That's why emphasis will always be on Torah,Talmud and Tosafot. Hebrew Grammar is always a requisite.
Bought this book preparing for a chem undergrad last year. My gap year is coming to a close and I’ve come to notice myself gravitating towards mathematics videos more than any of the other sciences.
Copies like “How to Solve It” and UA-camrs like MathSorcerer and 3Blue1Brown have got me considering majoring in mathematics.
Still available as an ebook! This got me really into Calc and linear algebra. Vellaman's "How to Prove it" is another must have. Wait...signed?! 🤩
I just downloaded both of them for free, thanks for mentioning the second one.
I was so dumb when I was young that I did not even know that I could plan things out. I came from a rural environment, I had a learning disability with memory. I never learned algebra, geometry, trig, chemistry, etc. I am technically illiterate in those subjects. I only graduated from high school because I think they just passed me out of kindness. I did know that I wanted to permanently get out of that little town as soon as I turned 18 and I did. I had no plan. I actually did the old “if you don’t know where you want to go then any road will take you there” trick. I did not know how to solve problems using organized steps. But I do now and I am still going to read that book in case their are some techniques I am missing.
Thank you for bringing that book to our attention!.
Costs less than a taco and feeds you for a lifetime. Thanks for sharing. Your enthusiasm for this book is great. Makes me wanna dig up another great book about the principles of typography. Not the most exciting topic but there's something about the writers passion for it that makes it special.
Love the taco analogy!!
I need to read more math books
I've had this on my reading list for too. This convinced me that now is the time to read it. Thanks!
This book is a bridge that helps a person gain confidence by asking questions. It ought to be mandatory reading for school leavers on which ever path they find themselves on.
👍👍
@@TheMathSorcerer 🖖
Such a wonderful book. The first time I read it, it seemed to drop straight into my subconscious, and I could barely remember anything in it, but I suddenly got better at solving maths problems. Then I read it again. Unfortunately, I couldn't find a buyable copy and was using my university library's copy. I really should get another copy, and yes, it is applicable to a lot more than just mathematics. BTW, I have a copy of Einstein's "The Meaning of Relativity". A little paperback that you can fit in your back pocket, and I did. The intro by AE is amazing, showing his mind pondering why classical physics is not enough, using simple thought experiments that show that even special relativity is not complete, and then jumping into tensors.
"The first time I read it, it seemed to drop straight into my subconscious, and I could barely remember anything in it, but I suddenly got better at solving maths problems."
...which even you must admit sounds completely vapid. "You suddenly got better at solving math problems".
how much better
@@touristguy87 , there's always one.
Went to Amazon India, it said I had bought this book on 30 Aug 2016... :) never even openned it..
I was thinking it is purely mathematics... But I can see that it is way more than that.. almost like a thinking process! My interest is rekindled! Thanks a lot!!!!
Your library just gets better day by day man
Sir, thank you for making us aware of Professor George Polya and his work.
I just started to read it, I will write another review after I finished it. Thank you for the suggestion.
Thank you for the helpful review. ‘How to Solve it’ by George Pólya is also available as an ebook via Perlego, an online, academic, library.
I love when your videos about books pop up early! You can still find them cheap!
God dam I never imagined maths could be so good after watching this video I will now read this book I totally appreciate your work
Today You became one of my math role model.
Can’t wait to get my hands on this book. I spent 30 years solving complex problems using the 8D problem solving methods. (8 Disciplines). I expect to find that the 8D approach was derived from the methods taught in this book.
Amazing! Thank you very much! Old books are really magical!
:)
Reminds me of an Art Critique : Describe, Analyze, Interpret, and Judge (reflect, assess) ---- I am a HUGE fan of Mr. John Forbes Nash - I'm sure he was quite aware of this book. 😊
This s a great book. I read mine multiple times, and took time to memorize the summary pages. Also you should review his other great books: Mathematics and Plausible Reasoning. There's 2 volumes. It's a book on how to conjecture.
Back to How to Solve It. The greatness of this book to me is in the prose and how he times the prompting of your mind to open and grope for dimensions you were not aware of and not so much the content of what he says in particular. I think his book is tailored to technical problems expressed mathematically. But, outside of that, its effectiveness diminishes. I've had more success and much less stress to think about problems like a biologist studies organisms in the lab and in their habitats. I get more mileage reading popular books on ecology, like "Why Big Fierce Animals Are Rare"
The best way I've found so far to solve problems, it to solve lots of problems *on your own*, struggle with the problem, solve it on your own. Then go back and see what the solution is or see part of the solution, and solve the problem in another way.
Anyways, thanks for the trip down memory lane.
i subscribed at the one minute and fifty seven seconds mark. A superb reviewer with an easy to listen to voice!!! Top Marks. :)
Thank you❤️
I think because I had a mentally disabled child; I had to teach them how to think, makes me understand the need to know how to learn, think and execute became important.
People are so insulted when you tell them what they take for granted. Its not that you cant, there is just a way. Ways can be good and beneficial. Give you a frame work and reference to think further out, your ideas.
Now I have to convince people there is still mental retardation. It still shows, its just difficult to see at first because of the steps taken to think things out.
As a result of this video I bought the book and have just begun reading it.
I have found that the TIME and MONEY spent in reading a book is well worth those costs IF i have learned at least one thing from the book. This book looks like one that can teach us many lessons.
its a real beauty this little book, and its back in print as a paperback
I am now reading the book you recommended sir. It's really a very good book.
Com-Sci 25 years ago....
1. Identify the problem
2. Understand the problem
3. Identify possible solutions
4. Choose most probable solution
5. Write Code
6. Evaluate/ re-code
Just found a copy on amazon (Princeton version) and I am genuinely looking forward to using this daily. I am going to school to become a programmer and I've been dying to find out why I have been experiencing such hardship and I know it's because I tend to tackle big chunks and then I get frustrated.
Thanks for the video!
Thanks for this video. I was fascinated and ordered the book. Just received it, but the modern paperback isn't quite the same as the great layout of the plan on the inside covers in your older, hardback version. Still looking forward to reading it though. Will definitely be looking out for a second hand copy now.
As a grad student, that is really helpful, thanks sorcerer!
I have this book...love it! Given the paucity of critical thinking these days....more important than ever👍
And you are the most critical thinker agreeing 100% with everything said...
"these days" It might scare you but it was probably worse before because you couldn't see how many people lacked that quality. Now you can not only quantify It but also acquire It with the information accessible on the internet.
I noticed the video and am glad I did because this kind of book is a great book of interest after learning about it because there are people such as myself who read most of everything to learn with math or reading most of the words On a page to begin the thought process with count numbers and the how to think while trying to solve math problems and the many kinds of solutions to the various counting methods
Only get me excited to want to purchase this book just from all you presented in it and I just wanted to take a moment to say thank you for presenting a book that seems as if it's great in many ways for good reads and learning purposes that I have now decided from the information in the book
It is a must-buy and so excited to have it on my next book order of books that I have ordered on regular books that have excellent meaning to teach the mind for better growth to become better at reading while counting which is not an always easy task for me but some people are natural to doing both at the same time, reading and counting at the same time I mean to that just said and I do believe this book is gonna teach me knew things and how to think better at trying to both reading snd counting at the same time which will provide a bitterness of learning in both areas of studies that I often struggle to do both at the same
I am trying to say thank you for making this video and introducing a book that I know I can learn from
Again, I am a struggling student in many different subjects, and happy that I have a new book to purchase that I know is going provide me with some how-to methods for learning while trying to count and read at the same time something I struggle to do
I just hope it won't be difficult to find or order wish me to look in locating it at book stores, I shall search as many if needed because I want this book
Again this great book I must get and it's because you previewed it in this video for an audience to learn about it!
Thank you so very much for making this video about a great book and I agree with every word you said about it seems as its a nook to not want to put down and keep reading
Just watching it I just want it now and gonna search engine it at the book stores on my next book order
Thank you so very much for you noticing such a great book which makes your value of thinking just as great if not greater and not comparing minds just saying it takes a great mind to recognize great words to teach others what great words of how to think to look like, on the page and in the video who presents such a great book of value for me and I know so many other
Can't stop thank-you you enough because it's what I need and never knew someone wrote a book that explains it like that and it's my style of thinking to read and figure the numbers with words but which words to ask? And the book has it and the way you showed it was just as grand!
Thank you so much again and again I need this book and thanks to you I have a book I can't wait to get my hand on to read cover to cover, and I am so excited about this book
I had a great day because of this video, and trying not to be redundant but AGAIN thank you so very much for the book presentation, I need it with my books for learning better... 😊
You should also check the other two books by George Polya on problem solving
1. Mathematical Discovery
2. Mathematics and Plausible Reasoning
A similar book that I have is The 5 Elements of Effective Thinking. Also written by a mathematician. Highly recommended.
OMG!!! I have two separate editions of George Polya's HOW TO SOLVE IT!!!
oh wow that is awesome!!
Thanks for information
first, understand the problem, and second, try to divide the problem into simpler parts if possible then repeat the above process till it cannot be subdivided. Solve it in this way. This is from the knowledge of computer programming
Thank you for sharing !! I will obtain this book and read it 👍👍👍👍👍👍👍
This is awesome! I found it in PDF. It's going on the short list. Thanks!
Thank you ! I'm so enthousiased by your presentation of this book 🤗 I will get this masterpiece as soon as I can
Wow! This is the kind of book, that makes you think differently.
Yes!
Oh man , so cool you got a original print/version🤘be very kind to it😁
Polya kicks ass🤜!
Thank you for the tip! Just ordered the book from the library, and look forward to read it!
Oh this is awesome, I gotta buy this! Thank you!
Any time!
AYYY YOU FINALLY REVIEWED IT!!!
The trick is to be on the path of truth, and thus discard the beliefs and dis-beliefs of others. As an example, I am a high school dropout and thus I had no education in the field of physics. But by examining "motion", I soon had fully understood motion 100%, and at the same time had therefore derived the Special Relativity equations all on my own. Others did not "Believe" that I had done so. And so that was why I threw together several videos to show exactly how I did it.
This book sounds awesome and informative. I have to say that you have promoted/recommended this book very well and I can't wait to read it. Thanks for the content.
❤️
I actually bought another copy because this one is signed and the dust jacket is fragile lol. I got a newer paperback I can read since I really love the ideas in this book❤️❤️❤️❤️❤️❤️
Each and every video of the Math Sorcerer is so informative and inspiring!!! Thank you 😊
Beautiful edition
Thank you very much for nice book recommendation. Very usefull when programming.
Thanks sir, for your constructive advice.
John von Neumann, pronounced NOY-man.
Right. Only the guy responsible for the fundamental architecture of everyday computers. And a whole bunch of other stuff.
Lovely. I want that book now.
Takk!
thank you!
Thanks for introducing this book. Bought one!
A part of me wished schools would teach students some of these methods in tandem with the other things they learned. On the rare occasion when some problem-solving steps are actually taught, they're always an afterthought, since students aren't tested on them, nor are they given the opportunity to apply these steps. Children won't listen to dry lectures - they're boring, but if you teach them problem solving steps when they're asking you how to solve a problem, they will often see the immediate benefits and pay attention right then and there.
Didn't Richard Feymen (spelling?) do a similar thing? Having taken 2 yrs to set up my online business, one of the biggest things I have found is asking the right questions and that only comes after a deep and thorough analysis from which understanding arrives. Courses are great yet give you tidbits of information, the rest one has to figure out by oneself. Eg. I asked the question just earlier this year...can I track emails (who opens them etc)? The answer is yes, and nobody ever teaches you this. Only because I asked the question did I find the answer which then led me down a whole new tunnel to explore and research....and it all takes......time. And by the way, what a difference it makes to marketing, wow. Again, no one teaches or tells you these things
sure but you can't take 30 sec to google his name
Seems like a good companion book to The Art of Making Sense by Lionel Ruby.
I've had two books by Polya in my collection for years, and I finally read How to Solve It because of your review. I found it to be as interesting and useful as you say--thanks for the review. The other Polya book is Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. Would you consider reviewing Mathematical Discovery?
I HAVE THIS BOOK SIR, LOVE FROM INDIA...
This reading should be mandatory in all high schools.
I took your advice, went for a walk, measured the distance by the maps app, got lost in the park, looked up to the moon, found out which way was south, and maps told me how long it will take me to get back. I remembered that in order to make it back I have to "Imagine my Reality, Then Realize my Imagination". So a 30 minutes walk to run away from solving a problem took me 90 minutes. and the problem wasn't even Math. The problem isn't going to be solved unless there is going to be a recession. That way welders will be available again.
Some of us are really praying for a recession.Patience!
Times have moved on. I have not read the book but watched the clip and the 4 points. Ths second step has to be expanded. It is the art formulating and capturing the data. I am sure companies like SpaceX are capturing all what is possible. However most professionals have no clue to do this in their own field and the subject is not taught well at any level.
It is a great book and like some of the greatest achievements it's deceptively humble in appearance. I am so sorry I lost my copy. One day I plan to go to Strand books and buy an old used copy. I agree that the older editions of books are usually the best. One gets the pure unadulterated version without so-called improvements.
BTW that book by Von Neumann (NOY - man) and Morgenstern would have been a worthy buy. 😉 In it he outlines a branch of mathematics he invented. His Game Theory got us through the Atomic Age alive and well when applied by Herman Kahn (his IQ = 200! Reading speed = 20K words per minute!) of the Hudson think tank in his magnum opus, Thinking the Unthinkable. Johnny von Neumann dwarfed the greatest minds of his day who all agreed that he was the only true genius among them!
Famous von Neumann story. JvN was very patient when explaining things that were complicated to small children. He would make it as simple as possible for them. One of the greatest minds of Europe once said he had the unsettling feeling JvN would also explain his advanced ideas to them as if they were small children so they could understand. However one time he just couldn't explain his theory to a colleague no matter that they spent all day on it. They agreed to disagree and went home for the evening. The other scientist spent all evening thinking over JvN's simplified explanation. Finally he understood it and called him excitedly at 3 in the MORNING! He groggily answered the phone angry over being awakened. The other scientist said, "Johnny!? You were RIGHT!" And started to explain why when JvN testily interrupted him with, "Do me a favor? The next time you decide to wake me at three in the morning do so when I am WRONG about something!" and I guess hung up on the poor but inconsiderate man.
I am getting this book from thr library. Thanks for thr recommendation
Informative. Thank you.🙏
I read this book in my late thirties, and I immediately thought: why didn't I learn this back in high school??
Much of the content is common sense. Some of it I already practiced intuitively, without thinking about. But often I would get stuck, and just think "this is too hard for me", in cases where putting in some effort would be fruitless without being methodical. Until the end of high school, math problems were small enough that intuition was sufficient, but as difficulty and scope grew, I struggled.
The simple ideas in this book are powerful, and definitely apply beyond mathematics. The huge benefit of reading Polya's book is that the method isn't implicit like in a typical math course, which usually teaches you the results with some proof, but not the process of searching for a solution. Exercises tend to test your abilities in problem solving, but problem solving itself isn't taught.
Smarter people who "get it" see the patterns in the teaching material, and learn to reuse them when applicable. For me, "How to solve it" was the kind of explanation that I really needed.
Highly recommended!
Thank you for the random book recommendation
Professor , the book by John Von Nuemann that was advertised at the back of the dust jacket is actually revolutionary since it introduces Game Theory which revolutionized economics
Wow that’s awesome!
!. define the problem.
2. research the problem
3. form a plan a hypothesis.
4. carry it out.
5. is it true or not?
These steps are most scientific textbooks.
Great vid yet again
You re really a bookworm!
Yes, your hope is correct. The video was helpful, a lot, indeed.