Spring Semester 2012

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 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:  TBA

Time and Place:
Lectures:  We 11:15, Fr 8:15 in West 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.


Class Schedule

01/02/2012: Part I: Introduction to Graph Theory.
Basic examples; graphs and parity
Ivanov, Chapter 6, pp. 85-89.
03/02/2012: Trees
Ivanov, Chapter 6, pp. 89-91.
08/02/2012: Euler's formula, Euler characteristic
Ivanov, Chapter 6, pp. 91-94.
10/02/2012: The Jordan curve theorem; Pairings I
Ivanov, Chapter 6, pp. 94-97.
16/02/2012: Pairings II
Ivanov, Chapter 6, pp. 94-97.
17/02/2012: Part II: Euclidean transformations, symmetries, groups.
Ivanov, Chapter 3, pp. 32-34.
22/02/2012: Review of vector algebra; Composition of transformations
Ivanov, Chapter 3, pp. 35-37;
Supplementary Notes.
24/02/2012: Introduction to groups, the group of Euclidean motions of the plane
Ivanov, Chapter 3, pp. 38-39.
29/02/2012: Symmetry groups
02/03/2012: Ornaments
Ivanov, Chapter 3, pp. 40-42.
07/03/2012: Part III: Boltzmann's dilemma.
Introduction of the model
Gottwald & Oliver, Sections 1-3.
09/03/2012: Review for Midterm Exam
14/03/2012: Midterm Exam
16/03/2012: No class
21/03/2012: Ensemble average, variance
Gottwald & Oliver, Section 4-5.
23/03/2012: Scaling limits, entropy
Gottwald & Oliver, Section 6-7.
28/03/2012: Kac ring final discussion; midterm exam return.
30/03/2012: No class
11/04/2012: Part IV: Linear Programming.
Introduction: Diet Problem, transport problem; solution of linear programming problems in two variables by the graphical method.
R. Larson, Elementary Linear Algebra, Chapter 9.2
13:30-17:00, Student Poster Presentations, Research I Lobby
13/04/2012: Linear programming problems in higher dimensions: underdetermined linear systems, geometry of feasible region, standard form of an LPP
Practical guide to the simplex method of linear programming, pp. 1-2.
18/04/2012: The simplex method
Practical guide to the simplex method of linear programming, pp. 3-5.
20/04/2012: Initialization, duality
Practical guide to the simplex method of linear programming, Section 2 and 3.
25/04/2012: Duality (continued)
27/04/2012: Part V: Discrete Fourier transform and fast Fourier transform.
Review of Fourier series, definition of discrete Fourier transform, orthogonality relation, inversion The discrete and fast Fourier transforms, Sections 1 and 2
02/05/2012: Sampling and reconstruction of functions
The discrete and fast Fourier transforms, Section 3
04/05/2012: The fast Fourier transform
The discrete and fast Fourier transforms, Section 4
09/05/2012: Fourier transform on abelian groups
L. Babai, The Fourier Transform and Equations over Finite Abelian Groups, Sections 1 and 2
11/05/2012: Review for final exam
25/05/2012 Final Exam, 12:30-14:30 in the Research III Lecture Hall

Last modified: 2012/05/02
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2012/acm102/index.html
Marcel Oliver (m.oliver@jacobs-university.de)