MATH 220 – Section 906

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 BLOC 510B

Place and Time: This course meets TR 2:20-3:35pm in  BLOC 161.

 Office hours:  W 1:30-2:30pm (or by appointment).  Note:  Policy on Appointments: if you don't show up to an appointment within the first 10 minutes of the scheduled time, the appointment will be cancelled.  Repeat offenders will have limited appointment availability.

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/Syllabus: 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) for a total of 100 points. 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 November 11 and a final version in lieu of a final exam (via email) on Wednesday Dec 17.  The draft is worth 15pts and the final version an additional 10pts. Here are more detailed instructions on the writing project.

Quizzes/Extended Problems:  Every Thursday there will be either a short quiz, a midterm exam or a "long 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.  This accounts for 10pts of your grade.  The long problems will be posted below.

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. Homework is to be done individually and be your own work.  Homework counts at 15pts, and will be posted below.

Exams: There are two midterm exams, one Thursday Oct. 23 and the other on Thursday Dec. 4.  These are worth 25pts each. Calculators are not allowed (or needed) on the exams.

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:

    Key Dates (tentative):


Homework Assignments/Syllabus (tentative)



Long Problem Assignments:

  1. (due Sept 18): Write 1 page on your project topic.  You should include some basic information (title, a few subject headings) about the topic as well as some reason why the topic is interesting.
  2. (due Oct. 2): Explain why there are exactly 5 Platonic solids (convex, regular polyhedra). Write the definition of Archimedean Solid (look it up!). Can you prove an upper bound on the number of Archimedean Solids? (A more challenging question! Do your best.  Impress me.)
  3. (due Oct. 16): Regarding the game of  SET and the 9 and 27 card variations: Determine the minimum number of cards among which there must be a SET. That is: (a) find the smallest number N so that a collection of N cards must include a SET and (b) exihibit, or prove there exists, a collection of N-1 cards which contains no SET. For a challenge: can you do the case of 3^5 cards?  This can alternatively be viewed as finding the maximum number of cards for which it is possible to have no set.  In this context it is related to something called "caps."
  4. (Due Thursday Nov. 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.