MAT 4830Mathematical Modeling

Winter 2013

http://myhome.spu.edu/lauw

Dr. Wai W. Lau

Dr. Lau

Wai

Dr. Wai W. Lau

Dr. Lau

Wai =

Dr. Wai W. Lau

Dr. Lau

Wai =

=

Course Web Page

http://myhome.spu.edu/lauw

Link to this document and other course information

Office Hours

See course web page By Appointment

Prerequisites

MAT 2401, 3237 and 3360

This course

Focuses on construction and analysis of mathematical models of problems in the real world.

This course

Focuses on construction and analysis of mathematical models of problems in the real world.

Challenging, Demanding, Exciting, and Rewarding• Individual works (Traditional lecture /HW)

• Team works (Case Studies and Modeling Contests)

Technology

Appropriate technology (Maple) will be utilized to provide a more convenient way to solve real world problems.

Technology

Appropriate technology (Maple) will be utilized to provide a more convenient way to solve real world problems.

Students will learn and master basic Maple programming techniques.

Technology

If you have not use Maple before, you probably need to spend sometime to learn the basic today.

If you have already programmed Maple before, it is a good time to review.

Technology

If you have not use Maple before, you probably need to spend sometime to learn the basic today.

If you have already programmed Maple before, it is a good time to review.

Student version can be purchased at discounted price ($??, code ???)

Case Studies

Students will study problems as a group. Each group will prepare presentations

and reports. Students will practice work sharing, time

management, and possibly interdisciplinary cooperation.

Case Studies

Students will study problems as a group. Each group will prepare presentations

and reports. Students will practice work sharing, time

management, and possibly interdisciplinary cooperation.

Case Studies

Students will study problems as a group. Each group will prepare presentations

and reports. Students will practice work sharing, time

management, and possibly interdisciplinary cooperation.

Case Studies

Specific case studies may include (but not limit to):• Airline Overbooking

• Tollbooths Modeling

• Sprinkler Systems for Irrigation

• Probability Models for Finger Prints

• The Airport Security problem

• The Exhaustible Resource Problem

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

Fri./Sat./Sun.

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

Mon./Tue.

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

Tue./Wed.

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

Electronic copies of reports and PPT due 4

p.m. The day before prepsentation

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

One member will present.

Case Studies – Typical TimelineRead the material

Group Discussion

Report Production

PPT Production

Presentation

Hard copies of reports and PPT due at the beginning

of your presentation.

Case Studies

All reports must be typed. All presentations must use PowerPoint

Slides. Electronic copies of reports and PPT due

4 p.m. on the day before presentation. Hard copies of reports and PPT due at

the beginning of your presentation.

Case Studies

Each report is around 2 pages (not counting the cover sheet). It should consist of:• A short summary

• Analysis and Critique You may use the diagrams from the files. Retype all formula. Do not copy-and

paste from the files.

Case Studies

Each presentation is about 15 min. Other groups need to pay attention and

ask questions. Part of your grade is assigned according to your participation.

Being nice or ignorant or lack of interest will result in lower grades.

Attentive and actively involve in discussion will get you bonus points.

Case Studies

Members should commit to share the workload.

Members of the same group will get grades according to their involvements.

Modeling Contests

Each group will enter into one of the following modeling contests (2/5-2/9):

• MCM: The Mathematical Contest in Modeling

• ICM: The Interdisciplinary Contest in Modeling

Modeling Contests

Case Studies are selected from past contest problems

Registration Fee: $100 per team Part of the mid-term exam

Modeling Contests

A “N” grade will be given at the end of the quarter.

Grades for the MCM will be assigned as follows

Models and Topics

Various continuous and discrete models will be discussed in this class. 

Substantial weight will be placed on applications to biological modeling. 

However, the modeling techniques learned will be applicable to other areas of application.

Models and Topics

Specific concepts, models and techniques students learn in this course include:• Discrete and Continuous Probability Models

• Monte Carlo Simulation

• Mean Time Between Failures

• Simple Queuing Theory

• Modeling Molecular Evolution

• Matrix Models of Base Substitution

Models and Topics

• Phylogenetic Distances

• Phylogenetic Trees

• Tree Construction: Distance Methods

• Maximum Parsimony

• Probability Distributions in Genetics

• Linkage

• Gene Frequency in Populations

• Other interesting topics if time permits.

Texts

1. Allman and Rhodes, Mathematical Models in Biology

2. Zeng, Scientific Computing with Maple Programming (Manuscript, Chapter 1)

3. Other supplemental Materials

Expectations

Able to provide written explanations of the ideas behind key concepts.

Able to clearly present and explain solutions to problems in both written and verbal form.

Read and write proofs appropriate at this level.

Expectations

Able to work as a team to solve problems.

Able to use Maple to write short programs.

Expectations - Handouts

You are expected to print and bring your handout to class.

Fail to have your HO repeatedly will negatively impact your grade.

Homework

Homework problem sets will be assigned.

All work must be typed. The ONLY references you can use are

the textbooks and the lecture note.  You cannot use any other resources such as other books, software, and the internet.  

Homework

Group HW Individual HW

Group Homework

You are required to work together in a group of 2 or 3.

Individual Homework

No discussion with any other person, except may be the instructor. 

Discussing or copying homework is considered as an act of academic dishonesty

Homework

Your homework must be neat and easy to read.   Otherwise, no points will be given. The instructor may make you redo your homework sets (again and again) until the presentations are acceptable.

Homework must be written with proper logical format.

Homework

Staple your Homework.  Points will be taken off if you fail to do so.

Homework is due at the beginning of the class.  Absolutely no late homework.

Homework

Homework must be written with proper logical format.

Pay attention to the notations and format used in the lecture. You need to follow the notations and format of the class notes in the case that they are different from the textbook and supplemental materials.

Class  Participation:

1. There are reading assignments.  I will ask questions during the class period to check your reading progress

2. There are classwork in some class sessions.

At the end of the quarter, your grades on class participation will be determined by the above activities and other observations by the instructor.

Exams

1 mid-term exam and a final

Points Distribution

Exam 1 120 points

Final 120 points

Homework 80 points

Class Participation 20 points

Case Studies 60 points

Final Class Grade

90% A Range

80% B Range

70% C Range

60% D Range

Below 60% E

Help!!

Talk to me. I am available during office hours and other times.

If Maple is new to you…..

Finish tonight the

Maple Essential Tutorials 1-3

Maple Tutorials

1. Log into your account

2. Download the Maple Essential Tutorials from the course webpage

3. Run the Tutorials to learn the basic commands

Homework

Read Zeng 1.1, 1.2 (Some commands may not work

properly!)

Consultant Groups…

Each group should have 3 members. Commit to work with each other. A mixed “talents” is a good idea. Create a name for you “consulting

company”.