Fall Semester 2005

General Mathematics and Computational Science I


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General Mathematics and Computational Science I and II are the introductory first year courses for students in the two majors. In addition, these courses address anyone with an interest in mathematics and mathematical modeling. Each semester includes a selection of "pure" and "applied" topics which provide a solid foundation for further study, convey the pleasure of doing mathematics, and relate mathematical concepts to real-world applications.

Contact Information:
Instructor:Marcel Oliver
Office hours:  Tu, We 11:15 in Research I, 107

TA/grader:Remus Radu
Office hours:  Wednesdays, 14:15, East Hall 3

Time and Place:
Lectures:  TuTh 9:45-11:00 in East Hall 4

Recommended Textbooks:

In each class, an exercise sheet is given. The following rules apply.
  • Solutions are due during the following class meeting.
  • All questions are worth 5 points.
  • The lowest 20% of scores will be dropped; the rule will be applied per question.
  • Solutions must be collected; abandoned solutions will not count.
  • No exceptions to these rules. The 20% rule will cover short illness, excursions, late adding of the course, and similar situations. For medical excuses longer than a week, special arrangements must be made as soon as reasonably possible.
  • Team discussions are encouraged. However, the written submissions must clearly be individual, distinct work.


Class Schedule (to be updated continuously)

06/09/2005: Part I: Foundations. Introduction; arithmetic progressions, informal introduction to proof by induction
Ivanov, Chapter 1, pp. 1-2.
08/09/2005: Equivalence classes, construction of the integers from the natural numbers
Ivanov, Chapter 1, pp. 3-4.
13/09/2005: Peano's axioms, addition on the natural numbers
Ivanov, Chapter 1, pp. 5-6.
15/09/2005: Multiplication and well-ordering of the natural number.
Ivanov, Chapter 1, pp. 6-7.
20/09/2005: More on induction
Ivanov, Chapter 1, pp. 8-10.
22/09/2005: Rational numbers
27/09/2005: Review for Midterm Exam
29/09/2005: Midterm Exam I
04/10/2005: Part II: Combinatorics and Inequalities. Informal introduction
Ivanov, Chapter 2, pp. 13-15.
06/10/2005: Binomial coefficients, binomial theorem
Ivanov, Chapter 2, pp. 16-18.
11/10/2005: Applications: algebraic identities, Cayley's labeled tree theorem
Ivanov, Chapter 2, pp. 19-20.
13/10/2005: Recurrence relations, generating functions, and formal power series; Fibonacci sequence
Ivanov, Chapter 2, pp. 21-23.
18/10/2005: Elementary Probability
Class Handout.
20/10/2005: Inequalities: Elementary examples
Ivanov, Chapter 4.
25/10/2005: Cauchy inequality and the geometric-arithmetic-mean inequality
Ivanov, Chapter 4.
27/10/2005: Inequalities
Ivanov, Chapter 4.
01/11/2005: Review for Midterm Exam
03/11/2005: Midterm Exam II
08/11/2005: Stirling's formula
Ivanov, Chapter 2, pp. 29-30.
10/11/2005: Part III: Modeling and Optimization. Introduction to Linear Programming
15/11/2005: Linear Programming (continued)
17/11/2005: Linear Programming (continued)
22/11/2005: Linear Programming (continued)
24/11/2005: Microscopic vs. macroscopic dynamics: the Kac ring
29/11/2005: Loschmidt's paradox and Zermelo's paradox
01/12/2005: What is entropy?
06/12/2005: Review for final exam
16/12/2005: Final Exam, 17:00-19:00 in the Research II Lecture Hall

Last modified: 2007/01/31
This page: http://math.iu-bremen.de/oliver/teaching/iub/fall2005/cps101/index.html
Marcel Oliver (m.oliver@iu-bremen.de)