General Mathematics and Computational Science I

Syllabus

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

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

Recommended Textbooks:
• Recommended reading for the different topics will be added throughout the semester. Stay tuned.

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.
• 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.

• The final grade will be computed as a grade point average with the following weights:

 Homework: 20% Midterm I: 20% Midterm II: 20% Final Exam: 40%

• Homework and project grades correspond to percentages of the maximum score as follows:

 Cutoff score: 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% IUB Points: 1.0 1.33 1.67 2.0 2.33 2.67 3.0 3.33 3.67 4.0 4.33 4.67

• Each of the individual scores will be converted to IUB grade points before the overall weighted grade point average is computed.

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