# 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 West Hall 4

Recommended Textbook:
• O.A. Ivanov, Easy as π, Springer-Verlag, 1998.

• U. Daepp, P. Gorkin, Reading, Writing, and Proving, Springer-Verlag, 2003.

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.

• 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

 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