MATH 220 – Sections 903-904

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 Blocker 510B

Place and Time: Section 903 meets TR 12:45-2:00pm  in Blocker 148 and section 904 meets TR 2:20-3:35pm in Blocker 148.

 Office hours:  W 2:30-3:30pm, or by appointment or drop in (if I am not too busy...)

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.


Exams: There are two midterm exams, tentatively scheduled for February 23 and April 27.  There is NO in-class 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 11 and a final version in lieu of a final exam on Tuesday May 9.  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:  Most Thursdays there will be either a short quiz or an extended problem--a more involved homework problem.  Extended problems are more involved exploratory problems that do not come from the text, independent research projects etc. The quizzes may be short writing assignments or exam-type problems, and one quiz/extended-problem 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. One 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, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. 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: MT 6-8pm Blocker 111 and TBA

    Key Dates (tentative):


Homework Assignments:

Long Problem Assignments:

  1. (Due Thursday Feb. 2)  Describe your writing project topic, including a specific reason you are attracted to this topic and what you already know about this project.  This should be 1 page in length.
  2. (Due Thursday Mar. 2) Consider the game of SET (link to wikipedia) in answering the following.
  3. (Due Thursday March 9): Consider the following generalization of the friend/stranger problem discussed in class: At a party, every pair of people are either mutual strangers, have met previously face-to-face or have only met online (not face-to-face).  What is the minimum number N of people at a party necessary to gaurantee that there is at least one group of 3 people with the property that all 3 are strangers, all three have previously met face to face or all three have met (only) online?
  4. (Due Tuesday April 4 and 11): On or before April 4, interchange rough drafts of your research paper with a classmate.  You must read one paper and give written feedback to your partner (and reciprocally).  On April 11 you will give them written feedback (this can be written directly on their draft, or on a separate page).  Evidence of this exchange must be presented to me (i.e. a copy of your feedback or a summary along with your classmate's name).
  5. (Due Thursday April 19): 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.
    • Compute (st)^3(x) for all x (that is, ststst(x) where st means composition of functions).
    •  Define A(0)={0}, A(n)={s(x): x in A(n-1)} union {t(x): x in A(n-1)}. So A(1)=A(2-1)={s(0),t(0)}={w,1}.  Does every rational number appear in A(n) for some n?  Do some experiments to see how fast |A(k)| grows.  Can you predict when some value of Q first appears?
    •  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.