MAT 4830 Mathematical Modeling Winter

Dr. Wai W. Lau Dr. Lau Wai

Dr. Wai W. Lau Dr. Lau Wai =

Dr. Wai W. Lau Dr. Lau Wai = =

Course Web Page 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 Timeline Read the material Group Discussion Report Production PPT Production Presentation Fri./Sat./Sun.

Case Studies – Typical Timeline Read the material Group Discussion Report Production PPT Production Presentation Mon./Tue.

Case Studies – Typical Timeline Read the material Group Discussion Report Production PPT Production Presentation Tue./Wed.

Case Studies – Typical Timeline Read 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 Timeline Read the material Group Discussion Report Production PPT Production Presentation One member will present.

Case Studies – Typical Timeline Read 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 ResultsPoints (/60) Unsuccessful0 Successful Honorable Mention

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 1120 points Final120 points Homework80 points Class Participation20 points Case Studies60 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”.