Spring Semester 2007

General Mathematics and Computational Science II


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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, Th 11:15 in Research I, 107

TA/grader:Remus Radu
Office hours:  TBA

Time and Place:
Lectures:  TuTh 9:45-11:00 in East Hall 2

Recommended Textbook:

Additional Reading:

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.

Instead of a second midterm exam, there will be a small mini-project, to be presented in form of a poster during the week before spring break.
  • Choose any topic which is closely related to a subject covered in General Mathematics and Computational Science I or II, but goes beyond what was covered in class. Alternatively, you may choose any topic from Ivanov's book not covered in class.
  • Be specific with regard to the topic chosen. The goal is to present a small aspect in detail, not to give a high level overview over a vast area of mathematics.
  • The posters may be worked on individually or in teams of at most two.
  • Poster topic and team members must be announced by email no later than March 1.
  • Posters will be assessed on content and on the oral poster presentation to equal parts. Presentation grades may differ within a team.
  • During the two class sessions where posters are presented, class attendance is mandatory for everybody.


Class Schedule

01/02/2007: Part III: Difference equations (continued).
Reversibility, recurrence, microscopic and macroscopic dynamics, Loschmidt's paradox and Zermelo's paradox
Class handout, Sections 1-2.
06/02/2007: The Kac ring model, ensemble averages
Class handout, Sections 3-4.
08/02/2007: Variance; is averaged behavior typical?
Class handout, Section 5.
13/02/2007: Continuum limit
Class handout, Section 6.
15/02/2007: Introduction to entropy, Computer experiments
Class handout, Section 7.
20/02/2007: Part IV: Euclidean transformations, symmetries, groups.
Ivanov, Chapter 3, pp. 32-34.
22/02/2007: Review of vector algebra; Composition of transformations
Ivanov, Chapter 3, pp. 35-37.
27/02/2007: Introduction to groups, the group of Euclidean motions of the plane
Ivanov, Chapter 3, pp. 38-39.
01/03/2007: Review for Midterm Exam
06/03/2007: Midterm Exam
08/03/2007: Ornaments
Ivanov, Chapter 3, pp. 40-42.
13/03/2007: Part V: Introduction to Graph Theory.
Basic examples; graphs and parity
Ivanov, Chapter 6, pp. 85-89.
15/03/2007: Trees; Euler's formula, Euler characteristic
Ivanov, Chapter 6, pp. 89-94.
20/03/2007: The Jordan curve theorem
Ivanov, Chapter 6, pp. 94-97.
22/03/2007: Pairings
Ivanov, Chapter 6, pp. 94-97.
27/03/2007: Poster presentations
29/03/2007: Poster presentations
10/04/2007: Part VI: Linear Programming.
Introduction, the graphical method
Lial et al., Chapter 3.
12/04/2007: Standard form of an LPP, simplex method
Pedregal, Section 2.2; Class handout.
17/04/2007: Initialization of the simplex method
Pedregal, Section 2.4; Class handout.
19/04/2007: Duality
Pedregal, Section 2.3; Class handout.
24/04/2007: Part VII: Discrete Fourier transform and fast Fourier transform.
Review of Fourier series
26/04/2007: Discrete Fourier transform
Class handout.
03/05/2007: Fast Fourier transform
Class handout.
08/05/2007: Finite abelian groups, characters
L. Babai, The Fourier transform and equations over finite abelian groups, Section 1.
10/05/2007: The Fourier transform on finite abelian groups
L. Babai, The Fourier transform and equations over finite abelian groups, Section 2.
15/05/2007: Review for final exam
26/05/2007: Final Exam, 9:00-11:00, Research II Lecture Hall

Last modified: 2007/07/26
This page: http://math.jacobs-university.de/oliver/teaching/iub/spring2007/cps102/index.html
Marcel Oliver (m.oliver@jacobs-university.de)