Off on a Tangent A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 November 11, 2016 Vol. 15, No. 5 http://www.math.hope.edu/newsletter.html

 Algebra will be explored in next week's colloquium

 Title: What is Algebra? Speaker: Victor Piercey, Ferris State University Time:  Thursday, November 17 at 4 pm Place:  VanderWerf 102

Abstract:
Do we know what algebra is?  Sure, we took it in high school.  But in college, a course on groups and rings called “abstract algebra” appears to have nothing to do with high school algebra.  We also take a course called real analysis which is the study of functions, but functions are part of high school algebra.  So what gives?  Is algebra a collection of topics, or is there something deeper? In this talk, I will share my evolving perspective on what algebra really is and what it means to “do algebra.” I will also discuss how this perspective has impacted my teaching.

 Statistics will be the focus of the Thanksgiving week colloquium

 Title:  The simulation-based, standardized z-statistic: When and Why it works Speaker: Yew Meng Koh, Hope College Time:  Tuesday, November 22 at 4 pm Place:  VanderWerf 102

Abstract:
Simulation techniques provide intuitive paths for statistical inference. A quick and easy measure of the strength of evidence against the null hypothesis of a claimed value for a population proportion would be the simulation-based, standardized z-statistic. A brief introduction to this statistic and also some different modes of convergence in Probability Theory will be given, providing the necessary background for understanding when one could use this z-statistic and why it would be valid to do so.

 Upcoming Colloquia

 The  following additional colloquium is on the schedule for this semester. Thursday, December 1, Hope Research Students

 Students participate in MATH Challenge

 Hope again had a great turnout of students participating in the Michigan Autumn Take-Home Challenge on Saturday, November 5 this year. Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. We look forward to hearing the results in the near future. The following students participated: Emily Joosse, Ben Pederson, Will Henkel, Chris McAuley, Alex Dolehanty, Erik Johnsen, Philip LaPorte, Eric Krzak, Jimmy Cerone, Russell Houpt, Richard Edwards, Michelle Plaver, Ashley Stegenga, Aleah Hahn, Kent Schwartz, and Graham Littlejohn.

 Math Club is going to the movies

 The Math Club will gather on Friday, November 18 for the 7:30 pm showing of  The Man Who Knew Infinity in the Knickerbocker Theatre at 86 E 8th Street. This movie is about one of the world's most creative mathematicians, Srinivasa Ramanujan, who grew up in India and was not formally trained in mathematics.  His meteoric rise from obscurity to the mathematical limelight is one of the greatest success stories in the entire history of mathematics.  Please join us for this critically acclaimed film!  Students get in free with their student ID, while faculty pay \$6.  Please arrive by 7:20 to get a good seat!

 Problem Solvers of the Fortnight

 In our last Problem of the Fortnight we presented the following conversation between Math Man and Vectoria. "Hey, M's.  What'cha doin'?" "Oh, hi, Vectoria."  Math Man hands Vectoria the piece of paper he was looking at and says, " I'm trying to figure out what this is." After a few moments, Vectoria says, "Oh, I get it!  It's a proof!" "Really?  A proof of what?" "It's a trig identity involving an inverse trig function." "Which one?" "Well, it could be any one, I suppose." "No kidding. . . .  I still don't get it.  Which triangles do you use to form the identity? "All three of them." "Hmmm. . . .  This is really hard." "No it's not!  It's as easy as. . . ."  Glancing at her watch, Vectoria stops in mid-sentence as she realizes that she's late.  "Whoa!  Sorry, M's.  I gotta run.  I'm late!" "Wait, wait. . . .  easy as what?  Can't you give me a clue?" As she sprints straight down the hall, Vectoria says, "I think I just did!  Maybe even two!" Vexed, Math Man sighs and stares at the figure again.  "I still don't get it.  I think I'm more confused now than before she came." The Problem of the Fortnight is to help Math Man discover the trig identities lurking in the figure.  You don't have to list every conceivable trig identity that this figure contains, but giving three trig identities ought to help Math Math figure out what this figure is communicating.  Write out three trig identities that use all three triangles contained in this figure and explain your reasoning carefully so that you can give Math Man the best chance of understanding what Vectoria saw in this figure. Congratulations to Philip LaPorte and Daria Solomon for solving the Problem of the Fortnight in the last issue of Off on a Tangent.

 Problem of the Fortnight