MAT 4830 Mathematical Modeling

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MAT 4830Mathematical Modeling

• Winter 2013

http//myhome.spu.edu/lauw
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Dr. Wai W. Lau

• Dr. Lau
• Wai

3
Dr. Wai W. Lau

• Dr. Lau
• Wai

Y
4
Dr. Wai W. Lau

• Dr. Lau
• Wai

Y
Why?
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Course Web Page

• http//myhome.spu.edu/lauw
• Link to this document and other course
  information

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Office Hours

• See course web page
• By Appointment

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Prerequisites

• MAT 2401, 3237 and 3360

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This course

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

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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)

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Technology

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

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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.

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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.

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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 ???)

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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.

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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.

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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.

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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

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Case Studies Typical Timeline
Fri./Sat./Sun.
Read the material
Group Discussion
PPT Production
Report Production
Presentation
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Case Studies Typical Timeline
Read the material
Mon./Tue.
Group Discussion
PPT Production
Report Production
Presentation
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Case Studies Typical Timeline
Read the material
Group Discussion
Tue./Wed.
PPT Production
Report Production
Presentation
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Case Studies Typical Timeline
Read the material
Group Discussion
Electronic copies of reports and PPT due 4 p.m.
The day before prepsentation
PPT Production
Report Production
Presentation
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Case Studies Typical Timeline
Read the material
Group Discussion
PPT Production
Report Production
One member will present.
Presentation
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Case Studies Typical Timeline
Read the material
Group Discussion
PPT Production
Report Production
Hard copies of reports and PPT due at the
beginning of your presentation.
Presentation
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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.

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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.

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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.

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Case Studies

• Members should commit to share the workload.
• Members of the same group will get grades
  according to their involvements.

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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

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Modeling Contests

• Case Studies are selected from past contest
  problems
• Registration Fee 100 per team
• Part of the mid-term exam

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Modeling Contests

• A N grade will be given at the end of the
  quarter.
• Grades for the MCM will be assigned as follows

Results Points (/60)
Unsuccessful 0
Successful
Honorable Mention

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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.

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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

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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.

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Texts

• 1. Allman and Rhodes, Mathematical Models in
  Biology
• 2. Zeng, Scientific Computing with Maple
  Programming (Manuscript, Chapter 1)
• 3. Other supplemental Materials

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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.

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Expectations

• Able to work as a team to solve problems.
• Able to use Maple to write short programs.

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Expectations - Handouts

• You are expected to print and bring your handout
  to class.
• Fail to have your HO repeatedly will negatively
  impact your grade.

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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.  

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Homework

• Group HW
• Individual HW

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Group Homework

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

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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

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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.

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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.

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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.

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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.

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Exams

• 1 mid-term exam and a final

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Points Distribution
Exam 1 120 points
Final 120 points
Homework 80 points
Class Participation 20 points
Case Studies 60 points
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Final Class Grade
90 A Range
80 B Range
70 C Range
60 D Range
Below 60 E
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Help!!

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

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If Maple is new to you..

• Finish tonight the
• Maple Essential Tutorials 1-3

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Maple Tutorials

• Log into your account
• Download the Maple Essential Tutorials from the
  course webpage
• Run the Tutorials to learn the basic commands

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Homework

• Read Zeng 1.1, 1.2
• (Some commands may not work properly!)

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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.