Math 100 Mathematics Paper 2 - Mathematics 1-2-3

3. (Combinatorics): Define and explain the binomial coefficients, prove Pascal’s Theoremand use it to prove the binomial theorem. Give some applications of the binomialtheorem (i.e. examples where the binomial theorem is used such as proving that thecardinality of the power set of a set with cardinality n is 2 n .2.2 Writing Guidelines1. Follow all the writing guidelines from your textbook and those discussed in class.2. You can include graphics (see Prof. Scheinermann’s sample Mathematics paper athttp://www.ams.jhu.edu/ ers/learn-latex/ for how to do this)3. Your paper will be graded for the correctness of the mathematical arguments thatyou present, the clarity and quality of your exposition and the overall structure of thepaper. Give careful thought to the order in which the parts of your paper appear.4. Try hard to eliminate typos. To that end, do not rely solely on your spell checker; asentence can be spelled correctly yet still be incorrect grammatically or have a differentmeaning than you intend. For instance,“Give careful thought to the order in which the parts of you paper appear.” has a typothat a spell checker won’t catch.2.3 Collaboration: YES Plagiarism: NOYou are allowed (in fact encouraged) to collaborate on this assignment. BUT you need towrite your own paper. And YOU need to write it. Seehttp://www1.ucsc.edu/academics/academic integrity . . .. . . /undergraduate students/resources.htmlfor information about what constitutes cheating/plagiarism. Here is a well-written primeron plagiarism and how to avoid it written by UCSC faculty Gregory S. Gilbert (EnvironmentalStudies) and Ingrid M. Parker (Ecology and Evolutionary Biology):http://scwibles.ucsc.edu/Documents/Avoiding%20Plagiarism.pdf2.4 DeadlineThe deadline to hand in your paper is Friday 2/25/2011, 5pm sharp. You can turn in yourpaper in class, or in BE 373 during office hours on Friday afternoon, or in BE 269 in theappropriate folder.3 Closing RemarksRemember that both Jacqui and I are available in office hours and section for questions. Seethe class web site for office hour details as well as for additional resources for using L A TEXand writing Mathematics papers.2