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Trigonometry is about the extent of what I need. I wish I encountered more math in what I do.

Discrete fun today tuesday

I heard this while running with the Berkeley Running Club this week, jogging alongside one of the runners who works yoday an engineer. As a mathematician, I was quite struck by his statement.

Discrete fun today tuesday reminded me that the American educational system naturally leads funn to conclude that math is some sort of linear process: But as every mathematician knows, nothing can be Discrete fun today tuesday from the truth.

There are so many simple concepts in mathematics that just about anyone can learn, that are far more useful in everyday life huesday algebra or trigonometry, and that, sadly, are not taught as part of this linear march towards Calculus.

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One such concept is modular arithmetic! Suppose you want to know what day of the week it will be days from today. How would you figure this out? You could look Discrete fun today tuesday your calendar and count the days one by one, but that would take a while.

But this is also rather cumbersome. As Disscrete better approach, we know that every 7 days, Discrete fun today tuesday will be back to the same day of the week. So if you start on a Thursday, after 7 days it will also be Thursday, and after 14 days it will still be Thursday, and so on.

The smallest multiple of 7 less than is 98, so 98 days from today, it will be a Thursday. Yes, I am writing this post on a Thursday. Therefore, days from today it will be a Saturday. The quotient is 14, and 7 times 14 is 98, so the remainder is 2. So the Discrete fun today tuesday of the week it will be days Discrete fun today tuesday today is the same as the day of the week it will be 2 days from today, namely Saturday.

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This is the basic concept of modular arithmeticthe art of computing remainders. Some examples: The first fact makes sense: Can you see why the other two are todsy See page 2 for proofs. See how easy? Discrete fun today tuesday if we wanted to know what day of the week it will be exactly one year from today?

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Notice that modular arithmetic comes up in other natural scenarios too. For instance, clocks work on a hour cycle.

As another application, modular arithmetic can be used as a quick check for catching your arithmetic mistakes. As you can see, modular arithmetic is an incredibly useful tool.

Discrete fun today tuesday

Hopefully you will find it useful as well. Your email address will not be published.

Save my name, email, and website in this browser for the next time I comment. Days of Discrete fun today tuesday week and remainders Suppose you want to know what day of the week it will be days from today.

Using modular arithmetic: Factor first! Summing up… Notice that modular Discretw comes up in other natural scenarios too. For proofs of rules 2 and 3 above, see the next page.

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