MATH 220 – Section 903

CATALOG DESCRIPTION: Foundations of mathematics including logic, set theory, combinatorics, and number theory. Prerequisite: MATH172.


Instructor: Dr. Eric Rowell. email: rowell@math.tamu.edu, webpage: www.math.tamu.edu/~rowell. Office Milner 210.

Place and Time: This course meets TR 12:45-2:00pm in  ZACH 119A.

 Office hours:  W 1:30-2:30pm (or by appointment).

Course Objectives: Understand and communicate in the language of higher mathematics. This course is designed to provide a foundation for further study of mathematics beyond calculus. A major part of this foundation is learning to write proofs, and will be the main objective of the course. A secondary objective is to develop a basic appreciation for higher mathematics.As this course has a W-designation a key objective is to learn to communicate mathematics in clear, correct English. 

Text: An Introduction to Abstract Mathematics, Bond & Keane

Material Covered: Most of chapters 1-5. Additional topics may be added.

Grading: Your grade will be based upon 2 Midterms (25pts each), Homework (15pts), a Writing Project (25pts) and quizzes/extended problems (10pts). The grading scale is the usual one: 90-100% A, 80-89 % B, 70-79% C, 60-69 % D, 0-59% F, with one exception: if a student does not pass the writting portion of the course (at least a C) he/she cannot pass the course (i.e. will receive a D or F).   Dates of exams/assignments will be posted below.  Note that the the Writing Project takes the place of a final exam.


Writing Project: The writing project will be a research paper of 5-10 pages on a topic in mathematics.  This will be turned in twice: once as a draft on Tuesday April 8 and a final version in lieu of a final exam on Wednesday May 7.  The draft is worth 10pts and the final version an additional 15pts.  The following is a more detailed description of the writing project.

Quizzes/Extended Problems:  Every Thursday there will be either a short quiz, a midterm exam or a extended problem"--a more involved homework problem with at least 2 weeks' time to ponder.  Extended problems are typically more involved exploratory problems that do not come from the text. The quizzes may be short writing assignments or exam-type problems, and one quiz grade will be dropped.

Homework: Weekly homework sets will be turned in to be graded. Typically homework will be assigned on Thursdays and due the following Thursday.  As writing proofs takes considerable practice, the homework sets will likely be quite time-consuming. Your lowest homework score will be dropped. Late homeworks count as a 0, and may or may not be graded.

Course Policies: Late homework and make-ups for missed exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam is missed. Consistent with University Student Rules, students are required to notify an instructor by the end of the next working day after missing an exam. Otherwise, they forfeit the right to a make-up.

An Aggie does not lie, cheat, or steal or tolerate those who do. Copying work that was done by others is an act of scholastic dishonesty and any instance of it will be prosecuted according to University Student Rules.

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For additional information visit http://disability.tamu.edu.

Copyright Policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One photocopy (or printout from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.


Important Announcements:

Help Sessions: 6-8 pm, Blocker 148, Sunday, Wednesday

    Key Dates (tentative):


Homework Assignments:


      Long Problem Assignments:

      1. (Due Thursday Jan. 30)  Watch the episode "Solve for X" of the CSB show Elementary, either live on CBS Thursday Jan. 16 9pm Central or online afterward at your convenience.  Write a  TYPED essay (1 page or more), addressing all of the following: (a) State the mathematical problem/conjecture that is featured. (You may needd to look it up).  (b) According to the show, what would happen if a solution were found, (i.e. an affirmation of the conjecture)? (c) What do you think would happen if the conjecture were found to be false? (d) What impression of mathematicians does this show leave you with?
      2. (Due Thursday Feb. 13) The ICM is an international mathematics meeting held every 4 years, at which many medals are announced and presented.  It is considered very prestigious to be invited to speak as an invited or plenary speaker, and this year it will be held in Seoul.  In 2010 it was held in Hyderabad, India.  a friend of mine made the statement: "Everyone knows that if you are from ----------- you have a better chance of being invited to speak."  (I have left out the country he mentioned).  By following the embedded links above, can you ascertain what country he was referring too?  You may use relative populations of various countries as a proxy for relative numbers of mathematicians.  You may also want to consider previous ICMs, to see if bias-by-country is more prevalant in some years than others.  A 1 page (hand-written if you prefer) analysis should be sufficient.
      3. (Due Thursday March 20):  Consider the functions on the rationals (Q) with one more symbol ({w}) as follows: s(x)=-1/x if x is not 0 or w, s(0)=w, s(w)=0 and t(x)=x+1 if x is not w, and t(w)=w.  (a) compute (st)^3(x) for all x (that is ststst(x) where st means composition of functions). (b) Define S(0)={0}, S(n)={s(x): x in S(n-1)} union {t(x): x in S(n-1)}. So S(1)=S(2-1)={s(0),t(0)}={w,1}.  Does every rational number appear in S(n) for some n? (c) Consider the "twist'em"=T and "turn'em"=S moves in Conway's rational tangle game (see here, page 11).  Using a sequence of picutres, compute (ST)^3 for an arbitrary tangle, with value, say, k.  So you will start with a picture with a circle with a k inside and 4 lines attach to the circle.  Then try the moves in sequence: first T, then S then T then S then T and finally S again.  What do you notice?  This may take two or more pages with drawings etc.
      4. (Due Thursday April 17): Regarding the game of SET. Devise a version of SET using only numbers.  Do the same for simpler versions of the game in which each card has only 2 or 3 distinguishing characteristics (the standard game has 4). Consider the following questions: (a)   What is the maximum possible number, N, of SET cards such that no 3 of them form a SET? Try this for the 9 and 27 card versions first. (b) Having determined the maximum possible number N of cards such that  no 3 of them form a SET,  determine how many different collections of N cards do not contain a SET.  Feel free to use a computer for these calculations. (c) If you are handed 3,4,5,...,12 cards at random, what is the probability that they contain no SET?  Remark: For the 3^7=2187 card version of the game it is an unsolved problem to determine the maximum possible number of cards with no SET.