M192: First-Year Seminar in the Mathematical Sciences
Fall 2000
Instructor: Rick Miranda
W 4:10-5:00pm
EB105
Office: Weber 106; Phone: 491-1303; email: miranda@math.colostate.edu

Text: What is Mathematics?: an elementary approach to ideas and methods, second edition, By Richard Courant and Herbert Robbins, revised by Ian Stewart
Oxford University Press 1996, ISBN: 0-19-510519-2

Course Outline:

Mathematics Seminar Meetings:
a. Number Theory
b. Geometry
c. Modeling
d. Discrete Mathematics
e. Problem-Solving
f. How to Study and Write Mathematics

Math Club Meetings:
a. Concentrations in Mathematics
b. Industrial Mathematics Presentation
c. Enrichment Lecture

Non-Mathematics:
a. Library
b. Career Center
c. Computing at CSU

First Meeting: ENGRG B105 August 23, 2000.

Homework Due 8/30/00:
1. The first edition of this book was written in the 40s.
   Find the incredibly sexist comments in the preface matter.
2. Read Chapter I, pages 1-20.
3. Write and hand in solutions to the ten exercises on pages 17-18.
4. Read about the Fundamental Facts of Prime Numbers,
   Supplement to Chapter 1, section 1.1, pages 21-25.
5. Read Chapter II, Section 1.1 & 1.2 on Rational Numbers: pages 52-63.
6. Read Chapter II, Section 5.1 & 5.2 on Complex Numbers: pages 88-97.

Homework Due 9/6/00:

1. Read Chapter II, Section 4,
   "The Mathematical Analysis of Infinity", 77-88.
2. Prove that the set of odd integers is denumerable.
3. Prove that the set of prime numbers is denumerable.
4. Prove that the set of non-terminating binary strings is not denumerable.
   (A non-terminating binary string is a string of the form "x1x2x3"
   where each digit xi is either 0 or 1.)

Homework Due 9/13/00:

1. Find a self-referential paradox.
2. Give a rigorous proof, justifying every step using an axiom,
   that there is no natural number x such that x+1=x.
   (Hint: use Induction.)
3. Give a rigorous proof, justifying every step using an axiom,
   that 0x=0 for every natural number x.
   (Hint: don't use Induction; use a Property of 0 and the Distributive Law.

Homework Due 9/20/00:

1. Visit these web sites:

http://www.fandm.edu/Departments/Mathematics/writing_in_math/guide.html
This is a A Guide to Writing in Mathematics Classes
by Dr. Annalisa Crannell of Franklin & Marshall College.
There is a nice Checklist for evaluating your mathematical writing here.

http://www.swarthmore.edu/NatSci/smaurer1/WriteGuide/
Here is a nice "Guide to Note-Taking" by Stephen B Maurer
at Swarthmore College that you might find useful.
Also included here is a "Common Errors in Writing Mathematics" that is good.

http://merlin.alleg.edu/employee/r/rholmgre/Writing/writing.html
This offers a A Brief Guide to Writing Homework Solutions
by Richard Holmgren at Allegheny College.
There is another version of Crannell's Checklist too.

http://zaphod.uchicago.edu/~corbin/writing.html
These are a list of 'rules' for writing mathematics
by Christopher C. Hallstrom at the University of Chicago.

2.  Pick out a bad example of some mathematical writing on your part
(e.g., a homework problem from a recent class).
Xerox-copy it and submit it to me, along with a corrected version,
which incorporates the principles outlined in the above documents.