Posts Tagged ‘Jonathan Kane’

Let’s talk about the sine and cosine functions. One does not need to use very much information about these commonly seen functions in order to understand a large number of curves which can be drawn by graphing sine and cosine in Cartesian and polar coordinates. We will see sine curves, sums of sine curves, Lissajous figures, cycloids, hypocycloids, epicyclodes, and, of course, many rows of roses.

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220px-Straight_Square_Inscribed_in_a_Circle_240pxLearn all about the classic theory of geometric objects with only straight edge and compass. What can you construct, and what is impossible? Which regular polygons can you construct? What if you have help by being given a fixed parabola? Come with your pencils and be ready to draw (compasses provided, or bring your own)!

To perform well on geometry problems on math competitions it is necessary to have a deep understanding.  This understanding can be achieved by retracing the footprints of the very first mathematicians whose only tools were a straight edge and compass.

Dr. Kane is one of our most popular lecturers and is recently retired from his position as a professor at the University of Wisconsin – Whitewater.  Along with Dr. Andreescu he is the co-founder and coordinator of the Purple Comet! Math Meet.  Dr. Kane is also the co-chair of the AIME committee and a faculty member at the AwesomeMath summer camp.

Along with his wife, Jane E. Mertz, Jonathan Kane is the author of several important research papers on the role of culture and gender in mathematical achievement including “Debunking Myths about Gender and Mathematics Performance.”

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Dr. Jonathan Kane will guide students through important theorems from “the results about angles in circles” to the “theory of inversion.”  He will then derive parametric equations for hypocycloids and similar curves.   Finally, the students will tackle many circle related problems which can be solved using these theorems.

Dr. Kane and Dr. Andreescu are the founders of the popular PurpleComet! problem solving contest.   Many people around the world have been talking about the paper authored by Dr. Kane and Dr. Janet Mertz, “Debunking Myths about Gender and Mathematics Performance.”  This follows another very popular paper by Kane, Mertz, Gallian and Andreescu called “Cross-Cultural Analysis of Students with Exceptional Talent in Mathematical Problem Solving.”

In these papers, Dr. Kane and his co-authors challenge the idea of a biological explanation for the difference in mathematical achievement by young men and women.  Instead they describe the many ways that cultural forces create a significant challenge to US students and particularly young women who would otherwise excel at mathematics and problem solving.  Certainly the outstanding performance of Lisa Sauermann at the International Mathematical Olympiad demonstrates this great potential.

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This Saturday we return from our MATHCOUNTS hiatus with a great talk by Dr. Jonathan Kane, co-founder of the Purple Comet Math Meet.

Dr. Kane will discuss combining of fractions \frac{a}{b} and \frac{c}{d} by \frac{(a+c)}{(b+d)} to see what happens.  Sometimes this is what is done when combining groups of results and leads to Simpson’s paradox.  This also leads to very interesting behaviors when a teacher wants to drop the lowest grade from a collection of grades not all worth the same amount.  This talk will also touch on algorithms such as greedy algorithms where Dr. Kane will show cases where it works and cases where it does not work.

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PurpleCometThe 2009 Purple Comet!  Math Meet has completed and the full results are posted here.

Many Metroplex Math Circle attendees participated including the Archimedes’ Successors team which earned an Honorable Mention in the mixed middle school division:

  • First Place(tie): Philippine Team A (Mathematics Trainers Guild Philippines), VASS (Longfellow Middle School), All-Asian Social Turndowns (AAST) with 15 out of 15 correct.
  • Fourth Place(tie): Indigo 2 (PRIVATE INDIVIDUAL), Indigo 4 (PRIVATE INDIVIDUAL), Calculators (BASIC Homeschools), Indigo 3 (PRIVATE INDIVIDUAL) with 14 out of 15 correct.
  • Honorable mentions go to ICAE Gauss was a Boss (ICAE), ICAE Bananas (ICAE), Eagles Rumble (Heritage Christian School), Brookings Home School (Brookings Home School), MyTJPrep (Multiple schools/MyTJPrep), Segimwony (St Mary School), Archimedes’ Successors (Eudaimonia Homeschool Academy), Central Maryland Homeschoolers (Central Maryland Homeschoolers)

Designed by Dr. Titu Andreescu and Dr. Jonathan Kane this contest is very challenging.  The Purple Comet organizers provide coaches with the following counsel:

Coaches: Please encourage your teams that scores below 50% are not uncommon. The problems offered in these meets are of the same calibre as those offered in the top national mathematics exams, and can be quite challenging. We are very pleased to see teams performing as well as they have, and we know they will rise to the challenge and perform even better in the meets to come.

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dr-jonathan-kane-vectors-21This Saturday we are pleased to welcome back Dr. Jonathan Kane.  Dr. Kane’s lecture on vectors promises to be a very good one.  Like many of our best lectures, it appears that Dr. Kane will start with a very basic and intuitive explanation of vectors and will build up to the use of vectors as powerful tools for solving complex problems.

Dr. Kane is a professor at the University of Wisconsin-Whitewater.  He is a member of the AIME Committee and a co-founder of the Purple Comet! Math Meet.

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