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.