The Winter Newsletter! Because winter is too long already.

The forecast this moment is predicting snow…SNOW!…and while it’s not going to be much, it looks like winter won’t end until we post our Winter Newsletter.  This issue is named The Chern Weekly Quarterly Whenever after Shiing-shen Chern (陳省身, Oct. 26, 1911—Dec. 3, 2004), who studied Differential Geometry (including, ummm, Chern classes in algebraic topology), was vice-president of the American Mathematical Society, and who founded the Mathematical Sciences Research Institute at Berkeley and the Nankai Institute for Mathematics.

This issue contains mostly department news and photos, but as always it contains a Sudoku and problems for your mathematical enjoyment!

Problem 5.2.1: Find the ratio of the areas of the circumcircles of a triangle and a square of equal perimeters.

Problem 5.2.2: In the figure at the right, ABCD is a rectangle, BE=BC, and AE is the diameter of the circle. What is relationship between BF and the original rectangle?

Problem 5.2.3: Using the digits 1-9 exactly once each, with only the operations +, —, ×, ÷, and/or exponentiation, write an expression that equals 2011. Now try it with the digits in order.

Problem 5.2.4: A box has three possible perimeters. Suppose box A has perimeters 12, 16, and 20, while box B has perimeters 12, 16, and 24. Which box has the greater volume?

You’re welcome to try your hand at these and post in the comments, for fame (of sorts, although referring to it as “famish” doesn’t make it sound very enticing at all) since we’ll happily acknowledge all who submit solutions in the next issue!  Which isn’t as much of a temptation as just solving for solving’s sake, but still, we do what we can.

Fall Newsletter Is Up!

Actually, it’s been up for almost a month, but I’m just now getting around to telling anyone.  See it here, and as usual, it’s probably more interesting for our current students and alumni than others.  But also as usual, we have a few fun problems to ponder:

Problem 5.1.1: (2000 AIME I) Let be relatively prime positive integers and suppose that the coefficients of  and are equal in the expansion of .  What is ?

Problem 5.1.2: An envelope contains 12 bills: 3 ones, 3 fives, 3 tens, and 3 twenties.  Two bills are drawn at random without replacement.  What is the probability that their sum is at least $20?

Problem 5.1.3: (From a Martin Gardner collection) An absentminded teller switched the dollars and cents when cashing a check for Mr. Brown. After buying a 5-cent newspaper [this is an old problem], Mr. Brown found that he had exactly twice as much as his original check. What was the amount of the check?

It’s a New Newsletter!

We finally published the Winter Spring SUMMER(ish) edition of our department newsletter!  This issue is named the Taniyama Times after Yutaka Taniyama (谷山豊 ) of the Taniyama-Shimura conjecture (proved by Andrew Wiles, and giving Fermat’s Last theorem as a wee little corollary).

This issue will admittedly hold less interest for non-alumni than most of our issues, since it’s primarily about where the Class of 2009 has been spending the past year.  Still, it does contain the following fun problems to work on!

Problem 4.2.1: (2006 AMC10) If x◊y =x³—y, what is h◊(h◊h)?

Problem 4.2.2: Which fits better: a square peg in a round hole or a round peg in a square hole?

Problem 4.2.3: The figure below shows the first three circles in an infinite sequence. What is the total area of the circles? What is the total circumference?

Answers are welcome in the comments, and you might just be acknowledged in the next newsletter!  [If we remember, which is sort of a risk since I’m right now remembering that we forgot to check that when we put together this issue.]

The Latest Newsletter

The Spring issue of our department newsletter is up!  Which is good, because spring ends pretty soon, so we really were working against a deadline.   [Fortunately, Batman and I are the editors so if we do miss a deadline, nothing actually happens.]  Most of the information is local to our college, but there”s some information about summer research programs and conferences, and a bit of advice from folk in the financial world during Career Night.    We change the name of the newsletter each quarter (harkening back to its start three years ago when we couldn’t figure out a name), and this issue is called The Wiley Wiles after, of course, Andrew Wiles.  The best part of naming a newsletter after him is that we could include a picture of our former Chair’s program from the 1996 Joint Mathematics Meetings in Orlando, which Andrew Wiles kindly signed:

Pretty cool, huh?

In case you’d like to do some math this weekend, here are the Problems from the newsletter.  Answers are welcome in the comments!

Problem 3.3.1: What are the next two numbers in the sequence 1, 8, 72, 46,
512, 612, …?

Problem 3.3.2: Choose a positive real number x and compute 100x², x³, and 1.05^x, then arrange the three results from least to greatest. How many orders are possible?

Problem 3.3.3: Express |x| in terms of the maximum function, and express max(x,y) as an absolute value.

Problem 3.3.4: What is the area of the largest semicircle that can be inscribed in a unit square?

The Fall Newsletter: A long name, some money, and some math

The Fall 2008 issue of the Nazareth College Math Department Newsletter has just been posted! Each Newsletter is named after a different mathematician, and this one is called Le Tonnelier de Breteuil Marquise du Châtelet Gazette after Gabrielle Émilie Le Tonnelier de Breteuil Marquise du Châtelet, the 18^th century mathematician who (among other things) translated Newton’s Principia into French. [Question: How much fun did we have coming up with the title?]

The feature article was written by one of our juniors about her study-abroad experience in Germany last fall, and many of the other articles first made their appearance here, but one of the inside stories might have a wider audience — namely, people thinking about college or grad school — and so might shameless plug be worth a special mention shameless plug. There are three scholarship opportunities for math and science folk: two of them (just recently funded by the National Science Foundation! Hooray!) are local to Nazareth College, but the third is available throughout New York State, and might have parallels in other states as well.

• The Robert Noyce Scholarship at Naz is aimed at undergraduate and graduate students seeking teaching certification at the adolescent or childhood/middle childhood levels in science or math (in exchange for service in a “high need” district).
• The Science and Mathematics Scholarship Program at Naz offers scholarships up to $10,000 for “promising, financially needy students” enrolling in biology, chemistry, or mathematics majors.
• Finally, the New York State Math and Science Teaching Incentive Scholarships provide awards to undergraduate or graduate students pursuing careers as secondary math and science teachers, in exchange for five years of full-time employment in the state.

Truth be told, although Batman and I work at Naz (and are the Executive Editors of the Newsletter, in case that wasn’t quite blatant enough), TwoPi actually works at St. John Fisher College just down the road. And they, too, are offering money:

• The Science Scholars Program at SJFC offers $12,000 scholarship for math, computer science, and science majors (entering as freshmen right out of high school).

If scholarships aren’t what you’re looking for, you can still check out the back page of the newsletter for some fun math problems to play around with. My current favorite of the bunch is:

Suppose the number N satisfies log₂(log₃(log₅(log₇ N))) = 4.
How many different prime factors does N have?

The Summer Newsletter is Here!

The Summer Newsletter of the Nazareth College Math Department is up! Okay, so it’s appearing at the end of summer, but that’s the beauty of having no actual deadline: if you’ve decided to spend your summer having a cutie pie baby boy join your family (like Batman) or traveling and seeing how long you can go without mowing the lawn (like TwoPi and myself), August is still technically summer so you’re good.

We normally name each issue after a different mathematician, but this issue is named The Godziller after our good friend Godzilla, who shows up here from time to time. And because we’re nothing if not lazy efficient, several of the articles are “gently used” blog posts from the past couple months. But there’s lots of local news about our students, and the last page has a neat Sudoku Puzzle and some math problems (of varying difficulty) to work on which, if you solve them, will lead to fame and fortune. Or at least a hearty Congratulations and link in the next newsletter.

The Spring Newsletter is here!

We’ve just posted the Spring 2008 issue of Our Newsletter (the seasonal newsletter of the Nazareth College Math Department).   This issue is named The Rudin in honor of Mary Ellen Rudin, according to our tradition of naming each issue after a mathematician (which would have been a great idea to come up with from the start, but in fact only evolved three issues in when we STILL didn’t have any ideas for a Newsletter name).  The lead articles on Extracting Square Roots and Cube Roots come straight from TwoPi’s posts here; other articles are about conferences and competitions our students were in, Alumni News, Toilet Seat Gymnastic (which was in fact our second post ever here, although the article is a little longer than the blog entry), Math Club news, and Problems.  And if any of you submit solutions to problems, we promise to post your name for laud and admiration in the next issue!

The Newsletter and Studying Abroad

Our department‘s Winter Newsletter is here! Which, admittedly, is primarily interesting for people who have been to our department or at least stopped by and asked to borrow a calculator or snag some of the food that often is around, usually right within sight of the sign that says no food is allowed. Today it’s homemade raisin bread left over from a late afternoon Science/Math Division meeting.

The Fall Newsletter is Up!

We’ve just published (electronically) the Fall 2007 Issue of Our Newsletter*. This one is named The Chung after Fan Chung and contains information about our math club, a piece in memory of Professor Pat Moyer, Student Athletics, info from the three of our students who attended Summer REUs, and the regular assortment of Math in the News and Alumni updates.

You can find the issue here (older issues – there are only 5 of them – are available here.)

*of the Nazareth College Department of Mathematics