Fall Semester 2007

General Mathematics and Computational Science I

Syllabus

Quick Links:

Class mailing list for announcements and discussion
Homework sheets
Class handouts and exams
Solutions to selected homework and exams

Summary:

General Mathematics and Computational Science I and II are the introductory first year courses for students majoring in Mathematics and in Applied and Computational Mathematics. In addition, these courses address anyone with a general 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@jacobs-university.de
Phone:	200-3212
Office hours:	Tu, We 11:15 in Research I, 107

TA/grader:	Vladimir Molchanov
Email:	v.molchanov@jacobs-university.de
Office hours:	TBA in Research I, 126

Time and Place:

Lectures:

TuTh 9:45-11:00 in the Research I Computer Lab/Lecture Hall

Recommended Textbook:

O.A. Ivanov, Easy as π, Springer-Verlag, 1998.

Additional Reading:

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.

Grading:

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%
Grade 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 grade points before the overall weighted grade point average is computed.

Class Schedule

04/09/2007:	Part I: Foundations. Introduction; arithmetic progressions, informal introduction to proof by induction Ivanov, Chapter 1, pp. 1-2.
06/09/2007:	Equivalence classes, construction of the integers from the natural numbers Ivanov, Chapter 1, pp. 3-4.
11/09/2007:	Peano's axioms, addition on the natural numbers Ivanov, Chapter 1, pp. 5-6.
13/09/2007:	Multiplication and well-ordering of the natural numbers Ivanov, Chapter 1, pp. 6-7.
18/09/2007:	More on induction Ivanov, Chapter 1, pp. 8-10.
20/09/2007:	Rational numbers
25/09/2007:	Part II: Combinatorics and Inequalities. Informal introduction Ivanov, Chapter 2, pp. 13-15.
27/09/2007:	Binomial coefficients, binomial theorem Ivanov, Chapter 2, pp. 16-18.
02/10/2007:	Review for Midterm Exam
04/10/2007:	Midterm Exam I
09/10/2007:	No class
11/10/2007:	Applications: algebraic identities, Cayley's labeled tree theorem Ivanov, Chapter 2, pp. 19-20.
16/10/2007:	Recurrence relations, generating functions, and formal power series; Fibonacci sequence Ivanov, Chapter 2, pp. 21-23.
18/10/2007:	Elementary Probability Class Handout.
23/10/2007:	Inequalities: Elementary examples Ivanov, Chapter 4, pp. 46-49.
25/10/2007:	Cauchy inequality and the geometric-arithmetic-mean inequality Ivanov, Chapter 4, pp. 50-51.
30/10/2007:	Alternative proofs and applications of the geometric-arithmetic-mean inequality Ivanov, Chapter 4, pp. 52-53.
01/11/2007:	Laplace's method Ivanov, Chapter 2, pp. 29-30.
06/11/2007:	Stirling's formula Ivanov, Chapter 2, pp. 29-30.
08/11/2007:	Review for Midterm Exam
13/11/2007:	Midterm Exam II
15/11/2007:	Part III: Difference equations. Introduction; first order linear equations Class handout.
20/11/2007:	The cobweb theorem of economics
22/11/2007:	Equilibrium points, stability for first order equations
27/11/2007:	Modeling competition in a sparse environment: the logistic difference equation
29/11/2007:	Bifurcations
04/12/2007:	Second order linear equations, examples
06/12/2007:	Review for final exam
14/12/2007	Final Exam, 16:00-18:00, Sports Hall

Last modified: 2007/11/17
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2007/acm101/
Marcel Oliver (m.oliver@jacobs-university.de)

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