Instructor: Han-Bom Moon
Class meetings: Monday and Thursday 2:30 – 3:45, JMH 406
Office: JMH 418
E-mail: hmoon8@fordham.edu
Course webpage: https://fordham.blackboard.com
Office hours: Monday and Thursday 1:00 – 2:30
Text: Introduction to Mathematical Modeling Using Discrete Dynamical Systems, F. Marotto, ISBN-13: 978-0495014171, ISBN: 0495014176.

Recommended problems

• Sec. 2.1. #1, 3, 5, 7, 9, 10, 11, 13, 17, 21.
• Sec. 2.2. #1, 3, 5, 7, 9, 23, 25, 27.
• Sec. 2.3. #7, 9, 11, 13, 15, 17, 19, 21.
• Sec. 2.4. #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21.
• Sec. 2.5. #1, 3, 5, 11, 15, 17, 19.
• Sec. 2.6. #1, 3, 5, 9, 11, 15, 17, 19, 21.
• Sec. 2.7. #1, 3, 7, 9, 13, 17, 19, 23.
• Sec. 3.1. #1, 3, 7, 11.
• Sec. 3.2. #3, 5, 11, 13, 15, 19, 25, 27.
• Sec. 3.3. #3, 11, 13, 15, 17, 21, 23.
• Sec. 3.5. #7, 11, 17, 19, 23, 25, 29, 33.
• Sec. 3.6. #1, 3, 7, 9, 11, 17, 19, 23, 25, 27.
• Sec. 3.7. #3, 5, 11, 13, 15.
• Sec. 3.8. #1, 3.
• Sec. 4.1. #1, 3, 5, 7, 21.
• Sec. 4.2. #7, 9, 13, 15, 17, 19, 21.
• Sec. 4.3. #1, 7, 9, 11, 15, 21, 25, 29, 33.
• Sec. 4.4. #1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 25.
• Sec. 4.5. #1, 3, 9, 11, 17, 19.
• Sec. 4.6. #1, 3, 5, 7, 9, 11, 13, 15, 21, 23, 25, 29, 31.
• Sec. 4.7. #1, 3, 5, 7, 13, 19, 21, 25, 29.
• Sec. 4.8. #1, 5, 7, 9.

Course objective

This course is an introduction to mathematical methods used to model natural and scientific processes and their dynamics. The main tool is the recursive formula which enables us to make a mathematical model without using differential equations and integration. For such models, we study their dynamical properties such as fixed points, periodic cycles, stability, bifurcation, chaos, and fractals. Concrete examples include various models from finance and biological, social, and physical sciences. In addition, we will study some mathematical gadgets such as basic matrix theory, complex numbers, stochastic modeling. Also we will learn how to use a computer package “SAGE” for mathematical experiments.

Prerequisite

Math 1206 (Calculus I) or its equivalence. This course is designed for mathematics majors and minors.

Grading

I will grade on a curve. Final grades will be computed according to the following breakdown:

Calculator or computer

Only four function or scientific calculators are permitted on homework, midterm tests and the final. Use of graphing calculators, computers, smartphone or any other electronic devices is not allowed.

Homework

There is no way to learn mathematics without solving lots of exercise problems by yourself. Homework will be assigned weekly on the course webpage, and it will be collected on Thursday, before the class starts. Late submissions, e-mail submissions are not accepted. I highly recommend you to work in groups and help each other. But do not copy directly. You must understand how to solve the problems.

Computer projects

Several projects requiring the use of a computer will be assigned occasionally. They should be completed within their deadlines.

Additional materials

I will post solutions of tests and homework. Check the course webpage regularly, at least once in a week. It is always advisable to work as many additional problems from the book as you have time for. In each week I will post on the course webpage a list of recommended problems. You don’t need to submit a solution of recommended problems, but studying them will be very helpful to improve your mathematical writing skill.

Test

There will be two midterm tests and a cumulative final exam. The midterm exam schedule, which will depend on the course progress, will be announced later. The final exam will be on May 12th (Thu) 9:30 – 12:30. The final is cumulative. Make up exams will not be given unless you have a documented reason.

Attendance

Coming to every class during the official academic term is required. Attendance will be taken intermittently. This will be included in the “participation” portion of your grade.

Math Help Room

From the second week of classes, the Math Help Room in JMH 410 welcomes all students to drop by with any math questions. Faculty and upper class math majors will stay and help you.

Academic integrity

As a Fordham University student, you have agreed to abide by the University’s academic integrity policy. All academic work must meet the standards described in http://www.fordham.edu/info/20322/academic_advising/3030/academic_integrity. Lack of knowledge of the academic integrity policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic integrity policy should be directed to the instructor.

Disclaimer

The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary.

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