Reddit Reddit reviews How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)

We found 27 Reddit comments about How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library). Here are the top ones, ranked by their Reddit score.

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How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
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27 Reddit comments about How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library):

u/[deleted] · 49 pointsr/math

You need to develop an "intuition" for proofs, in a crude sense.

I would suggest these books to do that:

Proof, Logic, and Conjecture: The Mathematician's Toolbox by Robert Wolf. This was the book I used for my own proof class at Stony Brook - (edit: when I was a student.) This book goes down to the logic level. It is superbly well written and was of an immense use to me. It's one of those books I've actually re-read entirely, in a very Wax-on Wax-off Mr. Miyagi type way.

How to Read and Do Proofs by Daniel Slow. I bought this little book for my own self study. Slow wrote a really excellent, really concise, "this is how you do a proof" book. Teaching you when to look to try a certain technique of proof before another. This little book is a quick way to answer your TL:DR.

How to Solve it by G. Polya is a classic text in mathematical thinking. Another one I bought for personal collection.

Mathematics and Plausible Reasoning, Vol 1 and Mathematics and Plausible Reasoning, Vol 2 also by G. Polya, and equally classic, are two other books on my shelf of "proof and mathematical thinking."

u/misplaced_my_pants · 17 pointsr/math

You could read Timothy Gowers' welcome to the math students at Oxford, which is filled with great advice and helpful links at the bottom.

You could read this collection of links on efficient study habits.

You could read this thread about what it takes to succeed at MIT (which really should apply everywhere). Tons of great discussion in the lower comments.

You could read How to Solve It and/or How to Prove It.

If you can work your way through these two books over the summer, you'll be better prepared than 90% of the incoming math majors (conservatively). They'll make your foundation rock solid.

u/yagsuomynona · 6 pointsr/math
u/david55555 · 6 pointsr/math

I think this is the recommended replacement for Polya's "How to Solve It"

http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp/069111966X

Seriously what do you want to be "modernized?"

u/GeneralEbisu · 6 pointsr/math

I'm also planning on doing a Masters in Math or CS. What do you plan to write for your masters?


> Anybody else feels like this?

I think its natural to doubt yourself, sometimes. I dont know what else to say, but just try to be objective and emotionless about it (when you get stuck in a problem).

The following books that helped me improve my math problem solving skills when I was an undergrad:

u/ccondon · 5 pointsr/math

On a more serious note, this book by Polya is wonderful.

u/Darumana · 5 pointsr/selfhelp

I hope I am not too late.

You can post this to /r/suicidewatch.

Here is my half-baked attempt at providing you with some answers.

First of all let's see, what is the problem? Money and women. This sounds rather stereotypical but it became a stereotype because a lot of people had this kind of problems. So if you are bad at money and at women, join the club, everybody sucks at this.

Now, there are a few strategies of coping with this. I can tell you what worked for me and perhaps that will help you too.

I guess if there is only one thing that I would change in your attitude that would improve anything is learning the fact that "there is more where that came from". This is really important in girl problems and in money problems.

When you are speaking with a girl, I noticed that early on, men tend to start being very submissive and immature in a way. They start to offer her all the decision power because they are afraid not to lose her. This is a somehow normal response but it affects the relationship negatively. She sees you as lacking power and confidence and she shall grow cold. So here lies the strange balance between good and bad: you have to be powerful but also warm and magnanimous. You can only do this by experimenting without fearing the results of your actions. Even if the worst comes to happen, and she breaks up with you .... you'll always get a better option. There are 3.5 billion ladies on the planet. The statistics are skewed in your favor.

Now for the money issue. Again, there is more where that came from. The money, are a relatively recent invention. Our society is built upon them but we survived for 3 million years without them. The thing you need to learn is that your survival isn't directly related to money. You can always get food, shelter and a lot of other stuff for free. You won't live the good life, but you won't die. So why the anxiety then?

Question: It seems to me you are talking out of your ass. How do I put into practice this in order to get a girlfriend?

Answer: Talk to people. Male and female. Make the following your goals:
Talk to 1 girl each day for one month.
Meet a few friends each 3 days.
Make a new friend each two weeks.
Post your romantic encounters in /r/seduction.
This activities will add up after some time and you will have enough social skill to attract a female. You will understand what your female friend is thinking. Don't feel too bad if it doesn't work out.

Question: The above doesn't give a lot of practical advice on getting money. I want more of that. How do I get it?

Answer: To give you money people need to care about you. People only care about you when you care about them. This is why you need to do the following:
Start solving hard problems.
Start helping people.
Problems aren't only school problems. They refer to anything: start learning a new difficult subject (for example start learning physics or start playing an instrument or start writing a novel). Take up a really difficult project that is just above the verge of what you think you are able to do. Helping people is something more difficult and personal. You can work for charity, help your family members around the house and other similar.

Question: I don't understand. I have problems and you are asking me to work for charity, donate money? How can giving money solve anything?

Answer: If you don't give, how can you receive? Helping others is instilling a sense of purpose in a very strange way. You become superior to others by helping them in a dispassionate way.

Question: I feel like I am going to cry, you are making fun of me!
Answer: Not entirely untrue. But this is not the problem. The problem is that you are taking yourself too serious. We all are, and I have similar problems. The true mark of a person of genius is to laugh at himself. Cultivate your sense of humor in any manner you can.

Question: What does it matter then if I choose to kill myself?

Answer: There is this really good anecdote about Thales of Miletus (search wiki). He was preaching that there is no difference between life and death. His friends asked him: If there is no difference, why don't you kill yourself. At this, he instantly answered: I don't kill myself because there is no difference.

Question: Even if I would like to change and do the things you want me to do, human nature is faulty. It is certain that I would have relapses. How do I snap out of it?

Answer: There are five habits that you should instill that will keep bad emotions away. Either of this habits has its own benefits and drawbacks:

  1. Mental contemplation. This has various forms, but two are the best well know: prayer and meditation. At the beginning stage they are quite different, but later they begin to be the same. You will become aware that there are things greater than you are. This will take some of the pressure off of your shoulders.
  2. Physical exercise. Build up your physical strength and you will build up your mental strength.
  3. Meet with friends. If you don't have friends, find them.
  4. Work. This wil give you a sense of purpose. Help somebody else. This is what I am doing here. We are all together on this journey. Even though we can't be nice with everyone, we need to at least do our best in this direction.
  5. Entertainment. Read a book. Play a game. Watch a movie. Sometimes our brain needs a break. If not, it will take a break anyway and it will not be a pretty one. Without regular breaks, procrastination will occur.

    Question: Your post seems somewhat interesting but more in an intriguing kind of way. I would like to know more.

    Answer: There are a few good books on these subjects. I don't expect you to read all of them, but consider them at least.

    For general mental change over I recommend this:
    http://www.amazon.com/Learned-Optimism-Change-Your-Mind/dp/1400078393/ref=sr_1_1?ie=UTF8&qid=1324795853&sr=8-1

    http://www.amazon.com/Generous-Man-Helping-Others-Sexiest/dp/1560257288

    For girl issues I recommend the following book. This will open up a whole bag of worms and you will have an entire literature to pick from. This is not going to be easy. Remember though, difficult is good for you.
    http://www.amazon.com/GAME-UNDERCOVER-SOCIETY-PICK-UP-ARTISTS/dp/1841957518/ref=sr_1_1?ie=UTF8&qid=1324795664&sr=8-1 (lately it is popular to dish this book for a number of reasons. Read it and decide for yourself. There is a lot of truth in it)

    Regarding money problem, the first thing is to learn to solve problems. The following is the best in my opinion
    http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X
    The second thing about money is to understand why our culture seems wrong and you don't seem to have enough. This will make you a bit more comfortable when you don't have money.
    http://www.amazon.com/Story-B-Daniel-Quinn/dp/0553379011/ref=sr_1_3?ie=UTF8&qid=1324795746&sr=8-3 (this one has a prequel called Ishmael. which people usually like better. This one is more to my liking.)

    For mental contemplation there are two recommendations:
    http://www.urbandharma.org/udharma4/mpe.html . This one is for meditation purposes.
    http://www.amazon.com/Way-Pilgrim-Continues-His/dp/0060630175 . This one is if you want to learn how to pray. I am an orthodox Christian and this is what worked for me. I cannot recommend things I didn't try.

    For exercising I found bodyweight exercising to be one of the best for me. I will recommend only from this area. Of course, you can take up weights or whatever.
    http://www.amazon.com/Convict-Conditioning-Weakness-Survival-Strength/dp/0938045768/ref=sr_1_1?ie=UTF8&qid=1324795875&sr=8-1 (this is what I use and I am rather happy with it. A lot of people recommend this one instead: http://www.rosstraining.com/nevergymless.html )

    Regarding friends, the following is the best bang for your bucks:
    http://www.amazon.com/How-Win-Friends-Influence-People/dp/1439167346/ref=sr_1_1?ie=UTF8&qid=1324796461&sr=8-1 (again, lots of criticism, but lots of praise too)

    The rest of the points are addressed in the above books. I haven't given any book on financial advices. Once you know how to solve problems and use google and try to help people money will start coming, don't worry.

    I hope this post helps you, even though it is a bit long and cynical.

    Merry Christmas!
u/hodorhodor12 · 2 pointsr/IWantToLearn

I'm a former physicists The way I felt I got smarter over the years as an undergraduate and graduate student was by continuing to solve hard and harder math and physics problems. Throwing yourself at increasingly difficult problems forces you to think systematically (so that you aren't considering the same solution again and again) and creatively (bring in other concepts and apply them to new situations) and perhaps, most importantly, to not give up. I found myself just being able to solve technical problems in other areas faster. My brain naturally got faster just like how someone who continually runs a slightly greater distances or just a little bit faster everyday is going to just naturally develop the muscles to make that possible. Also having a repository of solved problems as reference helps you solve future problems.

​

I found this book useful for problem solving:

https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

u/latam_gringo · 2 pointsr/EngineeringStudents

Check out "How to Solve It" It's a small book but well worth the price. It talks about how to think critically and creatively go about solving problems.

u/farmerje · 2 pointsr/learnprogramming

Two good books:

u/IAmVeryStupid · 2 pointsr/math

My favorite book on problem solving is Problem Solving Through Problems. There's an online copy, too. (I recommend you print it and get it bound at Kinkos if you intend to seriously work through it, though. This type of thing sucks on a screen.)

How To Solve It is another popular recommendation for that topic. Personally, I only read part of it. It's alright.

I can recommend other stuff if you tell me what level of math you're at, what you're interested in learning, etc.

u/foryouandforme · 2 pointsr/programming

how to solve it by g. polya

book wiki

book on amazon

George Pólya wiki

u/EdmundH · 2 pointsr/matheducation

The best advice to get better at solving these problems is to persist. You should have to try, to think, to fail slowly building a picture until you find the solution. Have patience with not knowing exactly what to do.

For more technical general advice Polya's lovely book How to Solve it is excellent.

u/kirakun · 2 pointsr/math

I highly recommend Polya's How to Solve it too.

u/LeashGalactic · 2 pointsr/AskReddit

How to Solve It by Polya is a great book about the use of critical thinking in the process of solving mathematics problems.

http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X

u/doc_samson · 1 pointr/learnmath

Do you understand what unknown variables are and why you are solving for them? Do you know why you are asked to move variables from one side to another?

Regarding problem solving...

If you are dead serious and really want to learn problem solving as a general skill, and are willing to read something that has a few examples a bit over your head but is extremely helpful in general, then may I suggest George Polya's How to Solve It. It is written at probably a high school geometry level but many of his discussions are generic enough that they should give you some insight into the problem solving process.

Essentially Polya wrote a book (maybe the book) on problem solving patterns i.e. when faced with a problem ask this set of questions and try strategy A or B, etc. He has I think 12 core questions to always ask. I found it very helpful myself. The first third or so of the book is a narrative of him showing how an ideal teacher would apply his teaching methods to guide students to discover concepts on their own.

A PDF of his original 1945 edition is available here: https://notendur.hi.is/hei2/teaching/Polya_HowToSolveIt.pdf

But a new edition paperback is on Amazon for $14, I have it and have made tons of pencil notes in the margins.

BTW if you do try to read it, you only need to know a few things to have the first part make sense. A "rectangular parallelipiped" (horrible name) is just a rectangular prism, so imagine it is your classroom's four walls floor and ceiling, etc. If you know how to find the diagonal length of a square or rectangle (the length of a line between two opposite corners) you probably know enough to basically follow along since that is the core of his example. If not, here's the trick, just divide the square (or rectangle) into two triangles and apply the pythagorean theorem. A huge part of his problem solving method revolves around asking yourself if you know of a similar problem with a similar pattern that you can adapt to solve your current problem. It's like being asked to find the area of a half circle, you don't know the formula, but you know the formula for the area of a circle, so you can use that as a base and adapt it to the problem of the half circle.

BTW 2: Math is hard. For everybody. People who are good at math paid for it in blood sweat and tears.

u/jpredmann · 1 pointr/math

This is just my perspective, but . . .

I think there are two separate concerns here: 1) the "process" of mathematics, or mathematical thinking; and 2) specific mathematical systems which are fundamental and help frame much of the world of mathematics.

​

Abstract algebra is one of those specific mathematical systems, and is very important to understand in order to really understand things like analysis (e.g. the real numbers are a field), linear algebra (e.g. vector spaces), topology (e.g. the fundamental group), etc.

​

I'd recommend these books, which are for the most part short and easy to read, on mathematical thinking:

​

How to Solve It, Polya ( https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X ) covers basic strategies for problem solving in mathematics

Mathematics and Plausible Reasoning Vol 1 & 2, Polya ( https://www.amazon.com/Mathematics-Plausible-Reasoning-Induction-Analogy/dp/0691025096 ) does a great job of teaching you how to find/frame good mathematical conjectures that you can then attempt to prove or disprove.

Mathematical Proof, Chartrand ( https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094 ) does a good job of teaching how to prove mathematical conjectures.

​

As for really understanding the foundations of modern mathematics, I would start with Concepts of Modern Mathematics by Ian Steward ( https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247 ) . It will help conceptually relate the major branches of modern mathematics and build the motivation and intuition of the ideas behind these branches.

​

Abstract algebra and analysis are very fundamental to mathematics. There are books on each that I found gave a good conceptual introduction as well as still provided rigor (sometimes at the expense of full coverage of the topics). They are:

​

A Book of Abstract Algebra, Pinter ( https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178 )

​

Understanding Analysis, Abbott ( https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 ).

​

If you read through these books in the order listed here, it might provide you with that level of understanding of mathematics you talked about.

u/Ranalysis · 1 pointr/learnprogramming

I recommend maybe doing more math instead. Or pick up a book called how to solve it . Alot of the things are easily translatable to programming and computer science really is mathematics as well. They're both related.

u/jdigittl · 1 pointr/math

Azcel wrote a good book on Fermat's Last Theorem and Wiles' solution. Amazon

Simon Singh's book on the same subject is also good, but Amazon has it at $10.17 whereas Azcel's is $0.71 better at $10.88.

Either way you get an enjoyable read of one man's dedication to solve a notoriously tricky problem and just enough of the mathematical landscape to get a sense of what was involved.

Another fun & light holiday read is Polya's 'How To Solve it' - read the glowing reviews over at Amazon

u/tophology · 1 pointr/math

You might want a book like How to Solve It which will give you a general toolkit of problem solving techniques. It's not a textbook per se, but if you're struggling with how to even approach math problems then it might be a good first step.

u/BrainFameGame · 1 pointr/learnprogramming

Www.lpthw.org

Www.hackerrank.com

lots of www.google.com

And when he's not in front of a computer he should be reading

http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp/069111966X (don't let the math scare him away if that's not his thing...at its core it's a book about how to solve any type of problem)


u/gtani · 1 pointr/math

Putnam comp http://www.math.rutgers.edu/~saks/PUTNAM/

Also look at "Customers Also Bought" for books by Devlin, Mason etc

http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X/

u/welshfargo · 1 pointr/computerscience

Yes. Read this book, regardless of your major.

u/BeornPlush · 1 pointr/IWantToLearn

Practice, practice, practice, practice. Getting good at maths is 90% equal to the practice you put in. People who seem "naturally" good at maths, most of the time, are just used to trying everything in their head and thus get more practice. Also, they may have done more in the past, and gotten used to using the smaller concepts they need to solve a bigger problem.

2 good books about learning: Waitzkin, The Art of Learning and Polya, How to Solve It.

u/Robin_Banx · 1 pointr/learnmath

Also endorse this book as a primer on mathematical thinking. No background necessary: http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X