What is Problem solving: Definition and 238 Discussions

Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems. Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, medicine and societies in general are related to mental problem-solving techniques studied in psychology and cognitive sciences.

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  1. Owen Ploe

    Need help, to help, a friend with their HW (High School)

    This is the problem set. I am stuck from this point... If anyone could give me a hand I would really appreciate it. I know this is probably really simple, but I don't know any of this and have been trying my best with youtube, and other peoples posts. PS this is for high school
  2. chwala

    Find the smallest value of angle ##α + β ##

    In my approach i have, ##α + β = \tan^{-1} \left[ \dfrac{\dfrac{a}{a+1} + \dfrac{1}{2a+1}}{1-\dfrac{a}{a+1} ⋅\dfrac{1}{2a+1}}\right]## ... ##α + β = \tan^{-1} \left[ \dfrac{2a^2+3a+1}{(a+1)(2a+1)}\right] \div \left[\dfrac{2a^2+2a+1}{(a+1)(2a+1)}\right]## ##α + β = \tan^{-1}...
  3. gimak

    How to study physics? (Question for students and instructors)

    Hello, I've been pondering this question for many years now and I've finally believe I've discovered the answer. The answer is to adopt a set of study strategies that force you to deeply ponder physics as much as possible. I'll explain. When many students first start out studying physics, they...
  4. shivajikobardan

    Studying Programming is coming to me but I forget how I solved the problem...

    I'm surprised that automatically programming is coming to me. It blows my mind. I could not think of any logic in the past months and now I am able to solve puzzles in programming. But the toughest part is I forget how I solved the problem too quickly. For example, the blackjack program. I...
  5. Al-Layth

    Book recommendation for techniques of evaluating Series?

    TL;DR Summary: I am looking for a good thorough book that is devoted to assembling and explaining techniques of evaluating series. evaluating series is a very big problem for me right now. I know nowhere near as much about it as I do integration, and the main reason for this is that its quite...
  6. DioMiner

    Why does this not work? Projectile Motion problem for Dynamics Class

    TL;DR Summary: I want to mainly figure out where in the problem solving I went wrong. I understand the correct answer (since I looked it up), but to me, it does not make any sense. I am honestly stumped at this point. Online solutions say that my equation y = 0.5774x-0.003354x^2 should...
  7. anm_ol

    Relativity Free Books & Lectures on Special Theory of Relativity

    I recently viewed some online free lecture series on Special theory of Relativity. I think I have an understanding of the basics so far, but would like some books for problems on special relativity. (Preferably solutions or at least answer keys included). It would be a great help if they...
  8. S

    Relative velocity and projectile motion problem solving

  9. bigmike94

    Balancing Learning Theory & Problem Solving: A Student's Guide

    From experience how would you balance time on learning theory and problem solving? Maybe learn the theory enough that if you got stuck on a difficult problem you would be able to understand the solution without scratching your head too much? Im using University physics by young and freedman...
  10. P

    Acceleration of Mass m: Problem Solving

    The problem that i am facing has to do with acceleration. The problem states that we have two balls with the same mass m that stands on two different tables. Between these balls are a wire with the length 2l, which i assume means 2 * l, where l is a value i choose. In the middle of the wire (x =...
  11. J

    A Problem solving forces with pressure integration

    Angle theta is different for every place at airfoil surface, so it can't be one theta from leading edge to trailing edge. Can please someone explain pressure integration in depth, step by step?
  12. N

    Compensating for Earth's Rotation With v = ωr

    We know that ##v = \omega r## where ##r = R_{\text{E}} + h##. To compensate for the motion, the plane must fly along the equator at the same speed as the Earth but in the opposite direction, i.e. from east to west, so $$\vec{v} = -\vec{ v}_{\text{E}}$$ $$v_{\text{E}} = \omega_{\text{E}}...
  13. hagopbul

    Exploring YouTube for Exercise Solving Playlists in Math and Physics?

    Hello : i was looking into youtube the other day and watching some lectures , but start to wonder if there is a playlist for exercise solving on youtube for example for undergraduate math and physics ? do anyone knows of such channels or playlists ? Best Regards Hagop
  14. Strange_Baryon

    Calculus Learning Calculus with Stewart: Exercise Sets Explained

    Hello PF, After thinking, googling, and reading many threads here, I decided that I'm going to start learning calculus using Stewart. The problem is that the book puts too many exercises after each section, in addition to those at the end of each chapter. What's the difference between these...
  15. Kappa123

    Geometry Book for improving problem solving skills for these types of questions

    I have a test coming, any good book for understand and getting good at these kinds of questions would be great :) (From the Australian Math Contest)
  16. C

    Using a Problem Solving Technique for a simple word problem

    Summary:: I have a document which was written by previous tutor supervisor/instructor at my undergraduate school. I want to learn how to use this technique for other math/physics subject besides algebra... I will provide an example of how to use this technique. I found an old textbook (College...
  17. Viii

    Troubleshooting Interplanetary Cruise Calculations

    Summary:: You have a spacecraft the size of a cube (2x2x2 m^3, m=3000 kg. It has 24 thrusters (2N each) and one main engine. For preparing your spacecraft for maneuvers, you want to rotate by 180 degrees. For the rotation, you'll use n=4 attitude thrusters per burn. What am I doing wrong...
  18. greg_rack

    Problem solving a parametric indefinite integral

    Since ##h## and ##k## are constants: $$\frac{h}{k}\cdot \int \frac{1}{y(h-y)} \ dy$$ Now, rewriting the integrating function in terms of coefficients ##A## and ##B##: $$\frac{1}{y(h-y)}=\frac{A}{y}+\frac{B}{h-y}\rightarrow B=A=\frac{1}{h} \rightarrow$$ $$\frac{1}{h}\int \frac{1}{y}\ dy +...
  19. rhotonsix

    I Pure mathematics problem solving and relevance to theoretical physics

    I am recreationally self studying physics and math with the ultimate goal of understanding theoretical/mathematical framework of classical mechanics, general relativity, and quantum mechanics (in addition to the actual physics). The question I have is how deep in the realm of pure math does one...
  20. T

    Other Effective Problem Solving: Balancing Necessary Literature with Time Management

    Hello. When i have some problems i want to solve should i read only the needed literature, topics, things to the problem i am trying to answer? Which should be these topics and papers and textbooks i should read to help me answer what i want to answer?Is there any advice on this you could give...
  21. Hamiltonian

    Studying I making math problem solving fun (for me)

    I love physics and I know it's quite hypocritical to say that I don't enjoy math that much. I started studying classical mechanics at the beginning of the previous year, all problems were amazingly fun to solve and could be related to the real world very easily, obviously, I had to get a good...
  22. warhammer

    Classical How to use Kleppner and Kolenkow and how to employ problem solving?

    I am an undergrad in Physics and got acquainted with the aforementioned book. I want to know how the other PF Members have used the book as such, and do they have some advice for me on the same. I am also inclined to know how does one solve the problems of K&K whose concept may be...
  23. sahilmm15

    Books similar to"Art of Problem Solving"

    Can you share some similar books like AOPS . Alternative of each book is preferred. I am finding other ones cause they are not available here. Thanks!
  24. emzy168

    Engineering SOS: Problem Solving Help - Tank Drainage

    Is it just 0? Confused with this question!
  25. greg_rack

    Problem solving an exponential limit

    I know it's probably an easy one, but I'm getting confused on how to treat that exponential numerator in order to escape from the indeterminate form ##\frac{0}{0}##
  26. J

    Is this manipulation "evil" or simply not intuitive due to unfamiliarity?

    The solution is as follows : The substitution is what nags me , which is as follows : This substitution "trick" to me seems impossibly difficult to arrive at "logically" without pretty much reverse engineering the problem. So is this simply a lack of practice/ familiarisation showing ? I feel...
  27. J

    Foundations Are there handbooks compiling math techniques to solve problems?

    Let me explain what I mean. When you try to solve an algebraic equation, or even sometimes a differential equation it is useful to change variables so the new form of the equation is easier to solve, or takes the form of an equation that has already been solved. Another technique is making...
  28. Monsterboy

    Comp Sci Counting Valleys // Complete the countingValleys function below.

    // Complete the countingValleys function below. // The code is in javaScript function countingValleys(n, s) { let currentLevel = [] // an array of numbers that indicate the number of units of altitude above or below sea level regarding each step let altitude = 0 // the...
  29. E

    MHB Problem solving calculating area

    I help students a bit with their math. As a teacher I am over 35 years removed from Math so I am rusty. I had the following questions given to me by some students and I couldn't even remember. The students are required to show their work how to solve this problem.
  30. N

    A Is Wolfram's Answer to the Integral Problem Wrong?

    I had been trying to aplly the sokhotski–plemelj theorem but with no success. Moreover i replaced exponential function with taylor expansion but i still can not solve the integral. thanks
  31. F

    Is a formal, rigorous math education useful in problem solving?

    I'm very curious as to know how a person who pursued a formal, strict and rigorous education in mathematics would fair in comparison with a person who learned applied math by "intuition" (that is without doing any proofs and relying more on the computational part), when confronted with problem...
  32. D

    MHB Automatic Parking Problem Solving

    I have a mathematical problem hope if you can help in solve it. Consider that we have an Automatic Parking Garage contains 900 units , each unit can contains just one car. The Garage open 24 hours per day , 7 days per week (24*7). The working day will divide into three parts 1- (8:00 am - 3:00...
  33. R

    Help critique my problem solving and thinking process (problem included)

    Hello all, thanks for reading my post! I'm posting as I need help with my problem solving and thinking approach. For the most part I can figure out how to set up the problem and what I need to find, but my problem lies in textbook questions that rely more on seeing a more math based approach to...
  34. T

    Relative Density Word Problem

    So I am a bit stuck on this question as my result using the above equations dose not give an numerical value which I assume from the question is needed. So here my method for solving My first thought was that if on the planet the person can throw a rock 10 time further then that it implies in...
  35. B

    When can using a logarithm make solving an equation easier?

    Homework Statement Well, there is a physics problem I was solving and it is really interesting how it is officially solved. We take a small weight and hang it on a steel wire. For how much does the oscillation time change if the temperature of this wire raises for 10K? I looked up solution...
  36. Tyrannosaurus_

    Problem solving: ball drops & ball shot up - they meet where?

    Homework Statement Ball 1 falls from rest from 67 m up. Directly 67 m below, ball 2 has 20 m/s [up]. No air. Where do they meet? Homework Equations non-uniform motion, so key kinematics equations. The Attempt at a Solution d1 + d2 = 67 m <--- is this okay to do? v1i *t + 1/2 a *t2 + V2i...
  37. JorgeM

    Problem solving this volume using Jacobi's Determinant

    Homework Statement Find the value of the solid's volume given by the ecuation 3x+4y+2z=10 as ceiling,and the cilindric surfaces 2x^2=y x^2=3*y 4y^2=x y^2=3x and the xy plane as floor.The Attempt at a Solution I know that we have to give the ecuation this form: ∫∫z(x,y)dxdy= Volume So, in fact...
  38. navneet9431

    Is problem solving an inborn skill?

    I asked this because I find myself in situations which trouble me deeply. I solve a deep interesting problem, I learn a new concept, its good but a single question which I'm not able to do, leaves me depressed, sometimes I can't just understand whether I CAN or CANNOT apply a concept to solve...
  39. Alex Petrosyan

    Studying Are there any good exercise books for Quantum Mechanics?

    hi, I’ve been walking through posts on this forum, and found plenty of book recommendations for QM. My problem is, I haven’t had enough practice in a long while. I could go over Solved Problems in e.g. Galitsky, or Gasiorowitz, but they seem to be a little far from what I want to test...
  40. Y

    MHB Problem Solving: No Idea Where to Start? Hints Here

    No idea where to start. Any hints?
  41. Manny46

    Studying Should examples be looked at before solving problems?

    So, with introductory level Physics, say Mechanics (Halliday's book or Kleppner and Kolenkow), am I making a mistake by looking at examples after reading, and understanding theory before trying to solve exercise problems? How does this change with advanced undergraduate level/beginning graduate...
  42. M

    Classical Improving my problem solving skills....

    Hi everybody! I've just finished my 4th year of physics degree (1st year of the masters degree, to be more exact) and I feel that I've spent most of my time reading theory and studying proofs and very few time on actual problem solving. In order to change that, I decided this summer go through...
  43. T

    MHB Maximizing Multilingualism: Solving Venn Diagram Problems in High School

    There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 29 students who take at least 2 languages at once. If there are 40 Spanish students, 42 French students, and 46 German students, how many students take all three languages...
  44. T

    Other Book recommendations for making guesses, estimates, inferences

    I came across this book 'Street fighting Mathematics, The art of educated guessing and opportunistic problem solving' , by Sanjoy Mahaan, published by MIT press. The book talks about how we can guess some property of the solutions of a number of physics and math problems without actually solving...
  45. M

    MHB Normal Approximation Problem Solving

    I'm unsure on how to start this problem. I tried to make a tree diagram but to no avail did it help out. Question: On average, Mike Weir scores a birdie on about 20.9% of all the holes he plays. Mike is in contention to win a PGA golf tournament but he must birdie at least 4 holes of the last 6...
  46. H

    Difficuilt and/or interesting problems in fluid mechanics

    Homework Statement Can anyone please give me hard and interesting problems regarding fluid mechanics problems such as hydrostatic and air prssure bouyance force and Bernoullis equation(Bernoullis equation problems only for liquids)? I tried looking for them but the ones I found were quite...
  47. fresh_42

    Insights 10 Math Tips to Save Time and Avoid Mistakes - Comments

    Greg Bernhardt submitted a new PF Insights post 10 Math Tips to Save Time and Avoid Mistakes Continue reading the Original PF Insights Post.
  48. P

    Programs Is Double Majoring Worth It for the Love of Learning and Personal Growth?

    For a long time I wanted to get degrees in both mechanical and electrical engineering and I recently heard about double majors. For me it's not as much about jobs I want in the future. I wanted to become an engineer because they are problem solvers. I wanted to invent things and or make them...
  49. jedishrfu

    Exploring the Mind of Feynman: A Talk on Problem Solving and Teaching Style

    A talk (audio only) of Feynman on problem solving: and Bill Gates on Feynman:
  50. CynicusRex

    Schools A college degree for creating the ultimate problem solving mind

    I have frequently read and heard that mastering physics is the ultimate way to mold a problem-solving mind. Therefore, becoming a physics major is supposed to be the best way of doing so. I wonder to what degree that statement holds true. Is it true? Is it biased? Am I misinterpreting...
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