Fall Semester 2006

General Mathematics and Computational Science I

Syllabus

Quick Links:

Summary:
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
Email:m.oliver@iu-bremen.de
Phone:200-3212
Office hours:  Tu, We 11:15 in Research I, 107

TA/grader:Remus Radu
Email:r.radu@iu-bremen.de
Office hours:  TBA

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

Recommended Textbook:

Additional Reading:

Exercises:
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.
  • 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.

Grading:

Class Schedule

05/09/2006: No class
07/09/2006: No class
12/09/2006: Part I: Foundations.
Introduction; arithmetic progressions, informal introduction to proof by induction
Ivanov, Chapter 1, pp. 1-2.
14/09/2006: Equivalence classes, construction of the integers from the natural numbers
Ivanov, Chapter 1, pp. 3-4.
19/09/2006: Peano's axioms, addition on the natural numbers
Ivanov, Chapter 1, pp. 5-6.
21/09/2006: Multiplication and well-ordering of the natural number.
Ivanov, Chapter 1, pp. 6-7.
26/09/2006: More on induction
Ivanov, Chapter 1, pp. 8-10.
Rational numbers
28/09/2006: Review for Midterm Exam
03/10/2006: Public holiday
05/10/2006: Midterm Exam I
04/10/2006: Part II: Combinatorics and Inequalities.
Informal introduction
Ivanov, Chapter 2, pp. 13-15.
10/10/2006: Binomial coefficients, binomial theorem
Ivanov, Chapter 2, pp. 16-18.
12/10/2006: Applications: algebraic identities, Cayley's labeled tree theorem
Ivanov, Chapter 2, pp. 19-20.
17/10/2006: Recurrence relations, generating functions, and formal power series; Fibonacci sequence
Ivanov, Chapter 2, pp. 21-23.
19/10/2006: Elementary Probability
Class Handout.
24/10/2006: Inequalities: Elementary examples
Ivanov, Chapter 4, pp. 46-49.
26/10/2006: Cauchy inequality and the geometric-arithmetic-mean inequality
Ivanov, Chapter 4, pp. 50-51.
31/10/2006: Alternative proofs and applications of the geometric-arithmetic-mean inequality
Ivanov, Chapter 4, pp. 52-53.
02/11/2006: Review for Midterm Exam
07/11/2006: Midterm Exam II
09/11/2006: Laplace's method
Ivanov, Chapter 2, pp. 29-30.
14/11/2006: Stirling's formula
Ivanov, Chapter 2, pp. 29-30.
16/11/2006: Part III: Difference equations.
Introduction; first order linear equations
Class handout.
21/11/2006: The cobweb theorem of economics
23/11/2006: Equilibrium points, stability for first order equations
28/11/2006: Modeling competition in a sparse environment: the logistic difference equation
30/11/2006: Bifurcations
05/12/2006: Second order linear equations, examples
07/12/2006: Review for final exam
20/12/2006: Final Exam, 12:30-14:30, Research II Lecture Hall


Last modified: 2006/11/30
This page: http://math.iu-bremen.de/oliver/teaching/iub/fall2006/cps101/index.html
Marcel Oliver (m.oliver@iu-bremen.de)