MATH 220 – Section 970

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 970 meets TR 12:45-2:00pm  in Blocker 148.

 Office hoursTuesdays 2:15-3:15 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. 

Some specific goals of the course are to understand:

Text: Mathematical Proofs, 3rd edition by Chartrand, Polimeni, Zhang.

Material Covered: Most of chapters1-9,11. Additional topics may be added.

Grading: Your grade will be based upon 100 points: 2 Midterms (25pts each), Homework (13pts), a Writing Project (25pts) and quizzes/extended problems (12pts). 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 Thursday March 1  and Thursday April 26.  There is NO in-class final exam.

Writing Project: The writing project will be a research paper of 5-10pages on a topic in mathematics: you should choose 1) an area (or areas) of mathematics (i.e. knot theory, graph theory, measure theory, algebraic geometry) 2) a mathematician (or mathematicians) that works/worked in that area (i.e.  Conway,  Fan Chung, Lebesgue, Grothendieck)  and 3)  a major mathematical theorem/technique/object due to that mathematician/those mathematicians (i.e. Conway polynomial, spectral graph theory, Lebesgue integration, scheme theory).

You may include images, figures and indented/block quotes, but these do not count towards the page constrants (so an 11 page paper with lots of images. might be ok, but a 5 page paper with images might not be).  Moreover, the works cited/bibliography does not count towards the page constraints. This will be turned in three times: once as a draft for peer-review on  March 29, again as a draft for Prof. Rowell to grade on April 12, and a final version in lieu of a final exam due on May 8.  In the peer-review you will exchange papers with a classmate (in class on March 29) and return them with comments on April 5 --this counts as a quiz (half for turning in a draft, half for providing comments on your classmate's paper).  The draft due on April 12 is worth 12pts and the final version an additional 13pts.  See below for further information.

Quizzes/Extended Problems:  Most Thursdays there will be either a short, in class quiz or an extended problem due.  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 guaranteed for a university approved excuse in writing, other situtations (interviews etc.) will be considered on a case-by-case basis, but must always be supported with documentation. Wherever possible, students should inform the instructor before an exam or major assignment 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.

Writing Project/Plagiarism: Your Writing Project should be the product of your own research.  This means you should cite references properly (use any standard format you choose).  See this page by Prof. Gregory of Washington and Lee University for a description of plagiarism (which should be avoided, as it is heavily penalized).  Long quotes (4+ standard lines) should usually be indented/blocked, but remember these do not count towards your page constraints.  I reserve 5% of the writing project grades to reward good and interesting writing.  At least 3 sources must be cited, and at least 2 must be static (i.e. unchanging, unlike Wikepedia).  Help is available for general writing questions at The University Writing Center.  Typically, the three main ways students lose points on their papers are: 1. not long enough (discounting images, block quotes, bibliography etc.) 2. Insufficiently credited (inline citations, bibliography) and 3. Poor Grammar/Spelling (This is not twitter. No covfefe, please!).

Grade Grubbing:  Google it, and never do it. It only serves to reduce your self-respect. If you feel there was a grading error on a specific assignment you must submit a regrade request within 2 business days. I do not entertain requests to change course grades without significant justification.  

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:

Long Problem Assignments:

  1. (Due February 1): turn in 1 page typed description of your writing topic.  This can be an outline, but must include: 1) the area of math, 2) the mathematician(s) and 3) the theory/technique/objects you plan to write about.
  2. (Due February 22): consider the following form of the game of set that we played in class: first let us order the colors, shapes, shading and number by 0,1,2 (for example 0=red, 1=green 2=purple, and (0= three 1=one and 2=two). Now each card is represented by a 4-tuple (a,b,c,d), where a,b,c,d are 0,1 or 2 representing the color, shape, shading and number. (in that specific order)  So, for example (1,b,c,0) would be a card with 3 green "c" shaded "b" shapes.  A) suppose that three cards form a set.  What do you notice about the sum of their representing 4-tuples (i.e. (a1+a2+a3,...))?  B) consider a different version of the game where the there are only 3 features (so 27 "cards").  What is the maximum possible number of cards so that no 3 form a SET (and adding one card gaurantees a SET)? C) Consider a 16 card game where there are 2 features with 4 values each (say, number 0,1,2,3 and color red, purple, green, yellow).  Define a SET to be as before: each feature is all the same or all different. Answer the question as in B: what is the maximum possible number of cards so that no 4 cards form a SET (and adding one card gaurantees a SET)? D) Can you repeat exercise B/C for the original game of SET?  (this is pretty hard).
  3. (Due 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. a) compute (st)^3(x) for all x (that is, ststst(x) where st means composition of functions). b) Define A(0)={0}, and recursively A(n)={s(x): x in A(n-1)} union {t(x): x in A(n-1)}. So A(1)={s(0),t(0)}={w,1}.  Does every rational number appear in A(n) for some n? Can you prove your answer? 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.