LATEX TEST: Read this whole paragraph before clicking on the link: After clicking on the link below, click the link "Sign in" or "Open in Drive" at the top right in order to upload files. Upload your TEX and PDF files here; (Use your first and last name as the file name.)
Day 14, 4/23/15 4/30/15: LaTeX test. Here's a sample test: LatexTest-sample.pdf . The actual test will be very similar.
Day 13, 4/23/15: Survey about comps exam. Practice LaTeX sample test.
Day 12, 4/16/15: LaTeX: Practice2.tex is posted below.
Day 11, 4/9/15: Comps exam, 9:00am-12:00pm, Mosher 1.
Day 10, 4/2/15: Last review day for comps exam. Work with LaTeX if there is time.
Day 9, 3/26/15: We'll work on comps 2009 (and before). And continue with LaTeX.
Day 8, 3/19/15: We'll work on comps 2008 (and before). And review topics (from linear algebra again). If there is time, we'll continue with LaTeX.
Some LaTeX references:
LaTeX Symbols (164 pages, copied from: http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf)
Day 7, 3/5/15: We'll work on comps 2007 & 2008. And review topics (from linear algebra again). And start learning about LaTeX. (Practice1.tex is posted below.)
Day 6, 2/26/15: We'll work on comps 2007. And review topics from linear algebra.
Day 5, 2/19/15: Finish 2005 and 2006 exams. Review convergence of infinite series.
Day 4, 2/12/15. We will continue with Comps Exam 2005 and also start working on Comps Exam 2006.
Day 3, 2/5/15. We will continue with Comps Exam 2004 and also start working on Comps Exam 2005.
Day 2, 1/29/15.
Comps Exam 2004. Write up your solutions before coming to class. I'll ask you to put them on the board in class. Do as many problems as you can; try to do the ones you find difficult, not the easy ones. At the bottom of this page there is a list of topics that are covered on the comps exam. There is also a link to review notes that one of our math majors (Megan Upp) wrote up in 2011 or 2012.
Our first Junior Writing test will be on "Day 2" (1/29/15): Give the definition of each of the following: (i) a ≡ b (mod n); (ii) equivalence relation; (iii) equivalence class. For each definition give an example that illustrates and "sheds light on" the definition. Prove that "congruence mod 2" is an equivalence relation on the set of all integers (make sure your proof is consistent with your definitions). List all equivalence classes for the equivalence relation "congruence mod 2"; explain and justify how you know you've listed all the equivalence classes for this relation. Pretend you're writing a short section of your comps paper of a discrete mathematics book; give a clear and well organized exposition, using precise mathematical language. Do not write in "abbreviated form," like we often do on homework or on the board.
Day 1, 1/22/15: Practice for junior writing test. (We will do this together on the board.)
Give the definitions of "odd", "even", and what it means for two integers to have the "same parity". Give a brief example to illustrate each of your definitions. Then prove that two integers have the same parity iff their sum is even. Pretend you are writing a very short section of your comps paper (or of a book for a Discrete Mathematics course); use clear, precise and formal language. Do not write in "abbreviated form," like we often do on homework or on the board. You may assume every integer is odd or even but not both.
Technically speaking (hints on how to give a presentation)
Lists of topics covered in each of the five sections on the comps exam
Review notes by Megan Upp (I haven't checked these at all)