A Method For Solving Math Proofs & Troubleshooting Computers
Things have been light in the math section, but luckily Alex McFerron - math hobbyist extraordinaire - has come to the rescue. This also ties into the subject of troubleshooting methodologies. Thanks, Alex!
G. Polya (1887 - 1985) was a math professor at Stanford. He wrote a book titled “How To Solve It” and just reading a few pages out of this book changed my professional life as a troubleshooter of application software, networks, and as a software debugger. Oh yes, and it changed my life as a math hobbyist, too!
- You have to understand the problem.
- Find the connection between the unknown and the data. Make a plan.
- Carry out the plan.
- Examine the solution obtained.
When I was on the desk, I used to think of each call as a similar thing to a math proof. I had a problem and my first job was to understand it. What were the parameters of the problem (the machines, the IP addresses, time of day, the locations)? What were the unknowns? This took the pressure off in a lot of ways. I didn’t have the answer, but I sure could ask questions about the problem. Once I had enough information, I moved on to steps two, three, and four. This method turned a really scared person, a person who had very little idea of how the software worked, a person who was the first woman on the help desk, into a very knowledgeable troubleshooter of the company’s software. It was all in the method. Also, it made the calls fun.
Today, I am a developer and I use the same method whenever I have a bug. It is all the same process for solving any problem.
So, if someone asks you:
1) How many functions are there from [n] to [n] that are not one-to-one?
or
2) What is the asymptotic order of the worst-case running your algorithm?
or
3) Why is my application crashing?
… then this method can be used and it helps a lot!
First, what are the unknowns? What is the question? Do you understand it? Can you write it down or draw a picture? Can you really explain it to someone else without asking more questions? Are all the questions answered or defined?
Next, what is the data? You might have to run some experiments and make a plan. Follow the plan and do the experiments. In many cases your plan may be attempting to recreate the crash under certain circumstances or getting a result with certain input. If you are solving a math problem, then this stage might be writing a python program to test the function making x in the range of 1 to 100,000 and seeing the results.
Last, you examine the solution obtained. You can repeat the process, too, and do iterations such that you keep narrowing down the problem until you solve it.
Related posts:
- Building A Troubleshooting Methodology
- 5 Ways To Have Fun With Mathematics
- In Case You Missed It: Math On .51
- Circuit Troubleshooting Resources
- Weekend Project: Ubergeeke’s Computer Repair Kit
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