06191010:
Mathematical Modeling (Autumn-Winter 2005)
Department of Mathematics
Zhejiang University
Announcements General
Course Descriptions and Goals
Topics
Course Objectives
Texts Grading
Syllabus
Assignments
Requirements
Professional Conduct
Miscellaneous
Announcements
- Dec. 28:
Course is over. The website will not update later.
- Dec.20:
期末答疑时间：2006年1月14日下午2:00-5:00，地点：西1－2楼教师休息室
- Dec. 04:
由于网络问题，前两天FTP不能连接。今天已修复。Homework#3的deadline推迟一天，即12月5日周一晚。
- Nov. 15: Announce
Homework#3, deadline is Sunday,
Dec. 04
- Sep. 27: 课件改为PPT格式供下载
- Sep. 27: Announce
Homework#2, deadline is Monday,
Oct. 17
- Sep. 27: Add
数学建模优秀论文选 for references
- Sep. 25: 机房机器已安装Matlab,
Mathematica等数学软件
- Sep. 25:
上机时间仍为每周二下午，但时间提前到从下午第三节课开始（以前是从下午第四节课开始）
- Sep. 21: Announce
ID number of the students
- Sep. 14: Deadline of Homework#1 is
postponed to Tuesday, Sep. 27
- Sep. 13: FTP for homework uploading (ZJU internal):
ftp://10.13.61.167:21
username/password: MM05
- Sep. 13: Announce
Homework#1, deadline is Sunday,
Sep. 18
General
Course Descriptions and Goals
Mathematical
models describe a variety of real-world situations, providing unique information
and insight. Systems that can benefit from modeling range from daily occurrences
(e.g. optimizing campus parking) to highly complex interactions (e.g. predicting
weather) to currently theoretical scenarios (e.g. computing the best vaccination
or treatment strategy in case of bioterrorist attack).
Mathematical modeling is a mathematical tool for solving real
world problems. In this course, students study a problem-solving process. They
learn how to identify a problem, construct or select appropriate models, figure
out what data needs to be collected, test the validity of a model, calculate
solutions and implement the model. Emphasis lies on model construction in order
to promote student creativity and demonstrate the link between theoretical
mathematics and real world applications.
Throughout this semester, we study a variety of modeling
types. Topics include proportionality models, fitting models to data, creating
simulations, dimensional analysis, probabilistic modeling, optimization, and
both discrete and continuous models. For day-to-day details, see the calendar
pages of our class website.
Additionally, students work in small groups on a
semester-long modeling project. Early-semester activities include discussions of
possible project ideas, a workshop on technical writing, project proposals, and
brief presentations in class. Later activities include individual group
meetings, peer-reviewed rough drafts, and longer final presentations to the
class.
Topics
Some of the major
topics to be covered include (not necessarily in the order given) :
-
Types of Mathematical
Models: Numerical, Analytical, Graphical.
-
Algebraic Models:
Linear, Quadratic, Exponential.
-
Models of Ratio &
Proportion: Graphs, Critical Path, Weighted Averages.
-
Models of Weighted
Averages.
-
Practical Applications
of Models.
-
Regression - Finding
Curves of Best Fit.
Course Objectives
Mathematical Modeling
is an area of applied mathematics that uses mathematical tools for exploring and
studying "real world" problems. The overall objective of this course is to
provide an introduction to the process of mathematical modeling while giving
students an opportunity to
- develop and construct appropriate
models for various problem situations,
- analyze given models to uncover
underlying assumptions, and
- investigate particular problems to
find out what has already been done toward developing solutions.
Through work on assigned projects,
students increase their fluency in technical reading and writing, and develop
skills in mathematical problem solving. Students learn to
- use the modeling process to
translate problem situations to mathematical expressions,
- use a variety of mathematical
resources and tools to study problem situations, and
- use appropriate technology to
assist in the problem-solving process.
Beyond the content of individual
courses, the major in mathematics is designed to prepare students for the 21st
century by helping students to become problem solvers, effective communicators,
users of appropriate technology, and team players. In this course, students will
be engaged in a variety of activities which will help them to move toward
achieving these goals.
As problems solvers, students will
be learning to:
- identify key points in a problem
situation,
- generate alternative strategies,
critically analyze these strategies, and make decisions regarding
appropriate strategies to use in the situation,
- implement a variety of
problem-solving strategies,
- evaluate and transform
mathematical expressions,
- integrate information from a
variety of sources (e.g., teachers, textbook, library, peers, technology,
other courses, your own exerimentation and observations, and life
experience), and
- solve problems using the tools of
mathematical analysis,
- demonstrate being a problem solver
by working with some problems that are relatively large.
As effective communicators,
students will be learning to:
- communicate effectively to
different audiences (e.g., your peers, small group conversation, large group
discussion),
- read and interpret mathematics and
technical information,
- express ideas in mathematical
language using written notation,
- demonstrate active listening
skills,
- listen to others in the group,
- use oral and written English in an
appropriate and effective manner, and
- paraphrase, explain results, and
support your ideas.
As users of appropriate technology,
students will be learning to:
- make appropriate decisions about
when and how to use technology in problem-solving situations, and
- use the computer as a tool to
study problem situations.
As team players, students will be
learning to:
- work effectively as a member of a
team,
- identify her/his own strengths and
weaknesses as part of a team,
- work cooperatively in a small
group to explore and learn important ideas and concepts of calculus, and
- acknowledge alternative points of
view and problem-solving strategies.
In this course, projects give
students an opportunity to apply the principles of mathematical modeling
creatively in various problem scenarios. While each project is related to the
mathematical strategies that covered in class activities and lecture, students
are expected to do some reading beyond the textbook and some library research to
gain a solid background understanding of the problem scenario. Students are be
expected to use appropriate technology as they study the problem, and to include
the results of their investigations in a written report.
Each year in early February, there is
an international Mathematical Modeling Contest. A secondary objective
of this course is to assist students in developing skills to participate in this
contest. The skills needed to participate in the math modeling contest --
working cooperatively in a group, developing and carrying out a problem-solving
plan, using whatever resources are available, collecting appropriate data -- are
essential in today's competitive job market.
Texts
Required textbook:
数学建模. 杨启帆，方道元编著. 浙江大学出版社.
Optional textbook:
A First
Course in Mathematical Modeling, Second Edition, by Frank Giordano, Maurice
Weir, William Fox, 1997.
Readings:
Various
journal, conference, or WWW materials as appropriate.
Grading
Credit toward the semester grade will
be allocated to each of the components as indicated in the following table.
| Assignments |
30% |
| Projects (3 or 4) |
40% |
| Final Exam |
30% |
Note: Final examination will be
in-class, closed-book. More information will be provided prior to it.
Syllabus
Note: Here you can view or
download the notes that we use in class. DO NOT depend solely on these notes as
many details are missing. You should read the textbook and take notes in class.
Assignments
Homework
Projects
Note: Please zip your submission stuffs
of the assignment into one single file either using WinZip or WinRAR. Name the
file name as "ID_Name_Homework_#1.zip" or "ID_Name_Project _#1.zip" where ID is
your unique ID number in the class. For
Example, my submission file name might be "99_刘利刚_Homework_01.zip".
Requirements
Calculators and Computers
Calculators and
computers are legitimate tools for doing mathematics. One of the goals of the
Department of Mathematics & Computer Science is that our students develop a
facility with various forms of technology and learn to use these effectively to
explore and solve problems. Throughout the semester, students will be given
opportunities to use electronic communication tools (such as email and a
graphical web browser). Students will be encouraged to use a spreadsheet,
statistical software, an electronic scratchpad, graphing tools, and other
software when it is appropriate for the problems which are being studied.
Students who have access to a graphing calculator will find it helpful
throughout the semester.
Each student will need to have access to computers and/or to work in the
computer lab on some of the homework assignments and projects. Computer lab
schedules are posted on the doors of the computer lab. Although other classes
also meet regularly or occasionally in the labs, there is one lab which is
always reserved for student use. You will need to plan to hold some of your
outside-of-class group meetings in the computer labs.
Requirements
Assignment Submission
- All students are expected to
complete their homework assignments by their due dates.
All assignments are due prior to
11:59:59 PM Wednesday night every week.
- Submission stuffs
Your ID number, your name, the
assignment number or name, source codes, related document
- Submission approach
Please submit your assignment stuffs via my FTP not via email.
- Late Work
No late work will be accepted. If you know you will miss a test due to an
excused absence, you must contact me ahead of time to schedule a make-up
session.
- Late programming assignments
follow the following rules:
25% deduction for 1-day late
50% deduction for 2-day late
Not accepted after being 2-day late
Regarding your marks, contact the grading TA within two weeks after the
assignment is handed back. After this two-week period, your assignment stays
as it is graded.
Professional Conduct
As a
student in our class, you are expected to conduct yourself in a professional
manner.
Limited Collaboration Policy.
Unless otherwise indicated, any homework assignment or programming exercise
given in this class will be an individual assignment. The work you submit is to
reflect the knowledge, understanding, and skill that you have attained as an
individual. However, the instructor does want to encourage the development of a
community of scholars who are actively engaged in discussion of the ideas
related to this course. With this in mind, you are allowed to discuss solutions
of the homework and programming problems with other students if done so
according to the following guidelines:
- You
may discuss ideas for homework and programming assignments with your
classmates. However, you cannot collaborate on writing the solution or the
program code. That is, you can talk about the problems and ideas for solving
them, but you cannot write things down with anyone else. You are, of course,
prohibited from copying or seeing another student's written solution, and
you are not allowed to show your work to anyone else.
- You
should accept help with care. If you work too closely with another student,
you might mislead yourself into believing that you understand the concepts
and techniques better than you actually do. Don't forget that the instructor
has office hours and can probably give you hints or suggestions to get you
started.
- You
should give help with care. Do not help anyone too much. When you have
solved a problem, it is tempting to just tell other students how you solved
it. Instead, try to allow them to come to the solution on their own. Maybe
give them a hint to help them get "over a hump." Remember that helping
someone too much will hurt them in the long term if they can't work through
problems on the exams by themselves. So avoid the temptation to do so. If
you can't help other students without giving away the whole solution, direct
them to see the instructor (who may or may not have a way to "edge" them
toward the solution).
- You
are not obligated to help anyone. If you feel uncomfortable helping another
student for any reason, please direct them to see the instructor.
Miscellaneous
Resources of Mathematical Modeling
Mathematical Tools
- Mathematica
- Mathlab
- Maple
Documentations
Professionals
Send any comments or
suggestions to Dr. Ligang Liu,
ligangliu@zju.edu.cn
Copyright © 2005, Ligang Liu
Last modified: Wed. Dec. 28, 2005