Fall Semester 2007

General Mathematics and Computational Science I


Quick Links:

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
Office hours:  Tu, We 11:15 in Research I, 107

TA/grader:Vladimir Molchanov
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:

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; 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.


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)