Spring Semester 2011

General Mathematics and Computational Science II


Quick Links:

General Mathematics and Computational Science I and II are the introductory first year courses for students in Mathematics and Applied and Computational Mathematics (ACM). 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:  Max Piper

Time and Place:
Lectures:  We 11:15, Fr 8:15 in East Hall 4

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; this rule applies 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.


Tentative Class Schedule

02/02/2011: Part I: Introduction to Graph Theory.
Basic examples; graphs and parity
Ivanov, Chapter 6, pp. 85-89.
04/02/2011: Trees
Ivanov, Chapter 6, pp. 89-91.
09/02/2011: Euler's formula, Euler characteristic
Ivanov, Chapter 6, pp. 91-94.
11/02/2011: The Jordan curve theorem; Pairings I
Ivanov, Chapter 6, pp. 94-97.
16/02/2011: Pairings II
Ivanov, Chapter 6, pp. 94-97.
18/02/2011: Part II: Euclidean transformations, symmetries, groups.
Ivanov, Chapter 3, pp. 32-34.
23/02/2011: Review of vector algebra; Composition of transformations
Ivanov, Chapter 3, pp. 35-37.
25/02/2011: Introduction to groups, the group of Euclidean motions of the plane
Ivanov, Chapter 3, pp. 38-39.
02/03/2011: Symmetry groups
04/03/2011: Ornaments
Ivanov, Chapter 3, pp. 40-42.
09/03/2011: Review for Midterm Exam
11/03/2011: Midterm Exam
16/03/2011: Part III: Boltzmann's dilemma.
Introduction of the model
Gottwald & Oliver, Sections 1-3.
18/03/2011: Ensemble averages
Gottwald & Oliver, Section 4.
23/03/2011: Variance, Scaling limits
Gottwald & Oliver, Section 5-6.
25/03/2011: Entropy, Discussion
Gottwald & Oliver, Section 7, 9.
30/03/2011: Part IV: Linear Programming.
13/04/2011: Poster presentations
15/04/2011: Poster presentations
27/04/2011: Part V: Discrete Fourier transform and fast Fourier transform.
13/05/2011: Review for final exam
TBA Final Exam

Last modified: 2011/02/02
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2011/acm102/index.html
Marcel Oliver (m.oliver@jacobs-university.de)