# Mathematical Proof Writing

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Is there a good resource for proof writing? My oldest is on an ARML team, and one of the rounds involves proof writing. It's a team effort, and there are some on her team who have some experience with this, but she would like to contribute more. She is currently taking geometry, but they haven't done much proof writing.

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Have you seen any of the AoPS texts?  Any rigorous Geometry course should have some proofs.  But if you are looking for more sophisticated proofs than the typical two-column proofs in a high school course, then the Art of Problem Solving books are probably the easiest to obtain.

https://artofproblemsolving.com/

Edited by LJPPPKGFGSC
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Art of Problem Solving

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Thanks. Any particular ones? She did use AoPS for Pre-Algebra, Intro to Algebra, Intro to Number Theory, and Intro to Counting & Probability, but she doesn't feel that she really knows how to write proofs well. Maybe she's thinking it's more formal than it is? She is in a school now, so not using AoPS for Geometry. Is that the one to look at?

Edited by MASHomeschooler

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Thanks. Any particular ones? She did use AoPS for Pre-Algebra, Intro to Algebra, Intro to Number Theory, and Intro to Counting & Probability, but she doesn't feel that she really knows how to write proofs well. Maybe she's thinking it's more formal than it is? She is in a school now, so not using AoPS for Geometry. Is that the one to look at?

While they are proving things all the time in algebra, geometry has the most problems that are actually labeled "Prove that...".

She should have a look at the geometry text.

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Great; thanks!

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I used to grade the proof or "power" round at ARML meets. The proofs come from all areas of math. They give you the background info that you need, and then they break the question into multiple parts, some easier than others. Teammates volunteer to prove different pieces of the problem. Points are awarded not only for the correct answers, but also for clear & well-reasoned written arguments.

Any of the AoPS books would be great for getting used to formulating proofs, including geometry. Try number theory and counting & probability if your daughter hasn't been exposed to those areas.

Another idea would be to work through old archived ARML exams. You can find the past two years (look for Proof round) on the main ARML website.

Congratulations to your daughter for making the team! We had lots of fun at the Penn State ARML when dd was in high school. :)

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I used to grade the proof or "power" round at ARML meets. The proofs come from all areas of math. They give you the background info that you need, and then they break the question into multiple parts, some easier than others. Teammates volunteer to prove different pieces of the problem. Points are awarded not only for the correct answers, but also for clear & well-reasoned written arguments.

Any of the AoPS books would be great for getting used to formulating proofs, including geometry. Try number theory and counting & probability if your daughter hasn't been exposed to those areas.

Another idea would be to work through old archived ARML exams. You can find the past two years (look for Proof round) on the main ARML website.

Congratulations to your daughter for making the team! We had lots of fun at the Penn State ARML when dd was in high school. :)

Thank you! That is very helpful!

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I am not familiar with that contest but we are using and liking Mathematical Proofs: A Transition to Advanced Mathematics.

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AoPS has a nice series of articles on writing solutions. https://artofproblemsolving.com/articles/how-to-write-solution

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DS found the AoPS series really helpful.

He had a grader early on who said, "What's your goal? What's your strategy?" Answering those questions, along with setting out givens, has been a very useful default starting point.

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