Date: Thu, 6 Sep 2007 15:51:41 -0500 (CDT) From: Mark Jacobson To: 810-080-02-fall@uni.edu Subject: HW due next Tuesday... Hi Discrete Structures students, HW #2 is due on Tuesday. Be sure to watch the web page, cause if I have any questions by email or in person that indicate any confusions about problems, I will provide hints/directions/clarification/examples via email and on the web page. http://cns2.uni.edu/~jacobson/c080.html Homework #2 (HW #2) in case you lost or did not get the handout... Exercises from section 1.2 (pages 20-23) 1B, 1D, 1F, 1H, 1J, 1L, 1N, 5B, 21B, 21D, 21E, 25, 27C, 27D These problems are due on Tuesday, September 11th in class. Note: The answers to 1A, 1C, 1E, 21A, etc. are in the back of the book. Try to do those problems, and then look at the answer and redo them when stuck or incorrect and you will THEN be able to do the above problems where the answer is not given in the back of the book. Don't just READ the chapter 1.2 pages. DO the practice problems, take notes, do the problems on a sheet of paper that are already solved for you in the book. If you DO section 1.2 like this, that day, or the next day after DOING the problems you see solved in the book, you will discover and might say something like the following: "Oh, now I have an idea and seem to know how to DO the assigned problems! Thanks for suggesting imitating and ACTIVELY following along with the books examples, when I need to and don't seem to understand HOW to do the assigned exercises." http://cns2.uni.edu/~jacobson/c080.html This email note and other notes will be posted at the above URL. Check and use the class web page often. Any email with HINTS or EXAMPLES for HW #2 will be posted there, as well as sent to your @uni.edu email address. Mark --------------------------------------------------------------------------- Regarding the sum 1 + 2 + 3 + ... + 98 + 99 + 100 = ??? from today's class. ... The smart aleck was Carl Friedrich Gauss, who would go on ... --------------------------------------------------------------------------- Gauss's Day of Reckoning --- A famous story about the boy wonder of mathematics has taken on a life of its own by Brian Hayes Let me tell you a story, although it's such a well-worn nugget of mathematical lore that you've probably heard it already: In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in the middle and add them in pairs~W1 + 100, 2 + 99, 3 + 98, and so on~Wall the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2. The paragraph above is my own rendition of this anecdote, written a few months ago for another project. I say it's my own, and yet I make no claim of originality. The same tale has been told in much the same way by hundreds of others before me. I've been hearing about Gauss's schoolboy triumph since I was a schoolboy myself. http://www.americanscientist.org/template/AssetDetail/assetid/50686 See you next Tuesday, if not before. Mark