Math 300 Junior Colloquium

Class Schedule and homework
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Day 14 (4/26/11): Exam on LaTeX. Here's practice test: Practice-Test.pdf ; and its source file: Pratice-Test.tex . For the exam, you will be given a similar test, but only a print out of the pdf version. You will have access to a LaTeX reference manual.

Day 13 (4/19/11 moved to Thursday afternoon, 4/21): Junior writing test #3: Define what it means for two sets to have the same cardinality. Give a simple example --- with proof --- of a set that has the same cardinality as a proper subset of itself. Then briefly give some motivation for the definition above and explain why it "makes sense" even though your example above is counter-intuitive. Define countable and uncountable. Then prove one of the following: (i) the set of integers is countable; or (ii) the set of real numbers is uncountable. In your proofs and examples, if you construct a function and claim that it is a bijection, you do not need to prove that it's one-to-one and onto.

Day 12 (4/12/11): We'll work on LaTeX.  Download and save these three files: Practice2.tex ,  Book-Lamport.pdf ,  figK7family.pdf . To have a specific goal, try to reproduce some of the technical or "especially formatted" things you see in one of the comps exams below.

Day 11 (4/5/11) Comps exam, 8:30-11:0, Fowler 301.
Sign-up list for presenting solutions
List of topics covered on Comps Exam: see bottom of page. Comps exam will be on Tues 4/5/11, 8:30-11:30AM, Fowler 301.
Policies for the comps exam: The exam will be closed book, closed notes, no calculators. A score of 60% is required to pass each section. Only failed sections need to be retaken. A retake will be offered next spring semester (possibly also one in fall). The policies for the retake have not been determined yet and may be different than the current policies.

Day 10 (3/29/11): Comps2008.doc.  Add your names to the sign-up sheet above. Here's a copy of  comps2009.doc

Day 9 (3/22/11): Comps2007.pdf.  Add your names to the sign-up sheet above.

Day 8 (3/15/11): Junior writing requirement test #2. Topic: see Day 6 below.

Day 7 (3/1/11):

  1. Comps2006.pdf.  Add your names to the sign-up sheet above.
  2. Bring questions if you have any for our junior writing requirement test #2 (it will be on Tues Mar 15). Topic: see Day 6 below.
  3. If there's time, we'll continue to work with Latex.

Day 6 (2/22/11):

  1. Continue with Comps2005. (ignore the problems with missing diagrams).  Add your names to the sign-up sheet above.
  2. Hopefully we'll be able to use TeXnic center this time to work on LaTex.
    Instructions: First open the Virtual Machine; then open TeXnic Center (All Programs > Mathematics > TeXnic Center); then Download and  save (do not open) this file: Practice1.tex ; then, from inside TeXnic Center, open the file you just saved.
    Here Some useful links for Latex
  3. Bring questions if you have any for our junior writing requirement test #2 (it will be on Tues Mar 15). Topic: 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 (make sure your proof is consistent with your definitions). List all equivalence classes for the equivalence relation "congruence mod 2"; explain and justify your answer. As with test #1, pretend you're writing a short article or book section; give a clear and well organized exposition.

Day 5 (2/15/11):

  1. Comps2005.pdf (ignore the problems with missing diagrams).  Add your names to the sign-up sheet above.
  2. Work on Latex. (a) Download and open this file: Practice1.tex  (b) Some useful links for Latex

Day 4 (2/8/11): Junior writing test (1st of 3). Topic: see item 3 under Day 2, below. Time

Day 3 (2/1/11):

  1. Continue working on the 2004 exam. Add your names to the sign-up sheet above. Make yourself do problems that you don't know how to do.
  2. We can discuss "linear independence" further, in preparation for the upcoming Jr Writing test on 2/8/11. Bring questions to class.
  3. We'll work on Latex a bit.

Day 2 (1/25/11):

  1. Comps2004.pdf .  We can spend time reviewing for the comps exam by you writing up your solutions ahead of time and then copying them on the board in class. Put your name and the problems you do on the sign-up sheet above. Do as many problems as you wish.
  2. We will see a few simple examples on Latex. (ITS is still working on installing the software we'll need for Latex; once it's installed, we'll get more serious about learning Latex.)
  3. Our first Junior Writing test is listed below. The test will be given on "Day 4" (2/8/11); you have two weeks to prepare for it, and can ask me for help during these two weeks.
    Give the "common" or "standard" definition of "linear independence". Discuss why (prove) it is equivalent to the following (less common) definition: A set of vectors is linearly independent if none of them is a linear combination of the others. In addition to giving precise definitions and proofs, also give examples to illustrate the definitons and the concepts. Pretend you are writing a very short book section or article or lesson for your classmates: give a "clear" (and mathematically accurate) exposition.

Day 1 (1/18/11):

  1. Intro to LaTeX.
  2. Practice test for writing: Prove that two integers have the same parity iff their sum is even. Give clear and precise definitions for all necessary terms: even, odd, same parity. Give examples for your definitions. Pretend you are writing a section of a book. (I will grade but not count this test.)

Topics marked as optional are not covered on the exam --- unless listed as "non-optional" for a different course. For example, some optional Calculus 1 topics are listed as required for Calculus 2.
In Calculus 2, all the required (i.e., non-optional ) topics are covered by the exam, even if they have asterisks.
The exam will be closed book, closed notes, and no calculators will be allowed.

See the bottom of this page.