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

Math 100 Mathematics Paper 2Dr. Frank Bäuerle (Your Name here)Math 100 Winter 2011University of California at Santa CruzFebruary 10, 2011AbstractThis note will contain your second assignment details.1 IntroductionYou should be familiar with L A TEX or your text editor now so that this second assignmentshould go quicker. Jacqui and I are still working on grading your first paper, and we hopeto have this completed by early next week (around the fourteenth of February).2 The Assignment Details for Paper 2In this section we once again describe the problems that you can work on as well as reprintthe general guidelines for writing and submitting your paper.2.1 The ProblemsYou can select one of the following three topics that are from different areas of Mathematics:1. (Calculus): Explain the partial fractions method from Integral Calculus. Give nontrivialexamples to highlight the method and prove the existence and uniqueness ofthe partial fractions for a simple case (e.g. where the denominator has degree 3). Youdo not actually need to integrate, but you need to explain what the partial fractiondecomposition of a rational function will look like and explain how one can find thecoefficients, at least in theory.2. (Logic): Show that any propositional formula is logically equivalent to one in DisjunctiveNormal Form (DNF). You will need to properly define what a propositionalformula is, what it means for a formula to be in DNF, and you need to give someexamples.1

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