How many arithmetic and basic algebra errors do you make

In summary, self-teaching can lead to a lack of discipline in checking work, resulting in frequent errors in basic algebra and arithmetic. It is also common for those who are self-taught to have misunderstandings of mathematical definitions. It is important to have a feedback mechanism in place, such as setting mini-projects or using computers to track progress and catch mistakes. Successive approximation can also help with organizing calculations.
  • #1
g.lemaitre
267
2
when i do higher maths i make a tone of basic algebra and arithmetic mistakes. i was going a basic AX = B using LU decomposition in linear algebra and I had to go back and check my basic math about 6 times before i got the right answer. is it just me or do a lot of people do this?
 
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  • #2
It's more common than you think.

I had to do a double integral the other day and it took me about four tries to turn an interval (triangle) into the right limits for integration. The interval was a simple triangle and I screwed up the region quite a few times.

It happens.
 
  • #3
maybe my problem is that I'm completely self-taught. the last time i took a math exam was 20 years ago. i taught myself calc and linear algebra without ever having to take a test. i just move on when i feel like i understand and i review when i run into a concept that i don't understand. consequently, I've never had to develop the discipline of checking my work.
 
  • #4
I can tell your problem from your posts. "i". "tone". If you are too careless to write properly, no wonder you are making simple math errors. That's what you will need to work on.
 
  • #5
It does help to have some kind of feedback mechanism in place to have both a reference point for checking things as well as a little pressure to make sure things get done right (in this case to help remove the errors).

The way that programmers do this is to set themselves a mini-project that is modest in its goals, but provides enough of a result so that it can be realized.

What might help you is to have some sort of mathematical project where you could say implement your model and plot it to see if it comes out right. The result of the plot can help you reinforce the results as well as give you feedback on whether you made mistakes in the process.

You'll find that the rewards come from the feedback of your own work, even if it is in little chunks and the great thing is that with computers, you can store all the work, code, simulation results, thoughts and everything else and see it develop over time which is one of the best ways of getting motivated and staying motivated later on.
 
  • #6
g.lemaitre said:
i just move on when i feel like i understand and i review when i run into a concept that i don't understand. consequently, I've never had to develop the discipline of checking my work.

I think the worst ptifall of self-teaching is misunderstanding mathematical definitions. There is always the temptation to recast a definition "using your own words" and get concepts completely scewed up. When it comes to doing calculations, I think there is less danger since you can check your work in various ways. I don't like doing calculations. I usually visualize bits and pieces of a long calculation and try to see how bad things will be. When I get an intuitive idea of that, I try to do things in an organized fashion. I work by "successive approximation".
 

1. How do you determine the number of arithmetic and basic algebra errors in a problem?

The number of arithmetic and basic algebra errors in a problem can be determined by carefully reviewing each step and identifying any mistakes made in the calculations or use of algebraic rules. It is important to double check all work to ensure accuracy.

2. Is it common to make arithmetic and basic algebra errors?

Yes, it is common to make arithmetic and basic algebra errors, especially when solving complex problems or working with large numbers. It is important to be cautious and check your work to minimize the occurrence of errors.

3. What are some common types of arithmetic and basic algebra errors?

Some common types of arithmetic and basic algebra errors include incorrect use of order of operations, mistakes in multiplication and division, errors in simplifying algebraic expressions, and mistakes in solving equations.

4. How can I avoid making arithmetic and basic algebra errors?

To avoid making arithmetic and basic algebra errors, it is important to carefully check your work and use the correct order of operations. Additionally, practicing regularly and seeking help when needed can also improve accuracy in solving problems.

5. What should I do if I realize I have made an arithmetic or basic algebra error?

If you realize you have made an arithmetic or basic algebra error, you should go back and carefully review your work to identify the mistake. Once the error is identified, correct it and rework the problem to ensure the correct solution is obtained.

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