View source for Madison Math Circle Abstracts 2022-2023

==Spring Schedule==

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! colspan="4" style="background: #e8b2b2;" align="center" | Spring Schedule (see abstracts below)
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! Date !! Location and Room || Program || Speaker
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| Feb 20th || 3255 Helen C White Library || Talks || Uri Andrews
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| Feb 27th || 3255 Helen C White Library || SEP || Math Circle Team
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| Mar 6th || 3255 Helen C White Library || Talks || Yunting Zhang
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| Mar 13th || 3255 Helen C White Library || SPRING BREAK ||
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| Mar 20th || 3255 Helen C White Library || SEP || Math Circle Team
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| Mar 27th || 3255 Helen C White Library || Talks || Amy Tao
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| Apr 3rd || 3255 Helen C White Library || SEP || Math Circle Team
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| Apr 10th || 3255 Helen C White Library || Talks || Chenxi Wu
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| Apr 17th || 3255 Helen C White Library || SEP || Math Circle Team
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| Apr 24th || 3255 Helen C White Library || Talks || Yuxiao Fu
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| May 1st || 3255 Helen C White Library || SEP (Competition) || Math Circle Team

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== Abstract 2/20 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  How to split an apartment'''
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| bgcolor="#BDBDBD"  |   
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.

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== Abstract 3/6 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Yunting Zhang'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  Sequences and Induction'''
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| bgcolor="#BDBDBD"  |   
I will introduce the definitions of set and sequence, and give some special sequences (such as arithmetic sequences, geometric sequences and Fibonacci sequence) and compute the sum of the first n terms of these sequences. I will then introduce the application of the Fibonacci sequence (relation to the Golden Section and "coincidence" in nature). Finally, I'll talk about induction and using induction to prove that the previous summations were correct. 

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== Abstract 3/27 ==
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Amy Tao'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  Guess the number!'''
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| bgcolor="#BDBDBD"  |   
On Monday you will learn a fun number guessing game to psych your friends with. Then we'll talk about why it works and introduce a particular concept. We will then think about a couple of other problems, some of which are related and another of which looks related, but in fact is not. Here's a sampling: does every number have a (non-zero) multiple that is made of just 1's and 0's? How can you get away with fewer birthday candles?

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== Abstract 4/10 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Chenxi Wu'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  Almost periodic sequences'''
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| bgcolor="#BDBDBD"  |   
If an infinite sequence of letters is periodic, then any finite section of this sequence will reappear infinitely many times. However there are sequences with this property which is not periodic. I will show some examples of them and also how they appear in Euclidean geometry and graph theory.

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== Abstract 4/24 ==
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Yuxiao Fu'''
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| bgcolor="#BDBDBD"  align="center" | '''Title:  On Propositional Logic'''
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| bgcolor="#BDBDBD"  |   
Logic is in some sense the art of thinking, for it captures the rules we rely on when we think. In this talk, I plan to provide an introduction to propositional logic, the perhaps most basic form of standard logic, and present some of its rich applications in mathematics and electrical engineering.

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[https://uwmadison.box.com/s/ns14iv68wv8lp4opdht2lxczu5fgi4at Fall 2022 Worksheets]