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MAT 4830 Mathematical Modeling

MAT 4830 Mathematical Modeling. Winter 2019. http://myhome.spu.edu/lauw. Dr. Wai W. Lau. Dr. Lau Wai. Dr. Wai W. Lau. Dr. Lau Wai =. Y. Dr. Wai W. Lau. Dr. Lau Wai = =. Y. Why?. Course Web Page. http://myhome.spu.edu/lauw

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MAT 4830 Mathematical Modeling

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  1. MAT 4830Mathematical Modeling Winter 2019 http://myhome.spu.edu/lauw

  2. 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?

  5. Course Web Page http://myhome.spu.edu/lauw Link to this document and other course information

  6. Office Hours • See course web page • By Appointment

  7. Prerequisites • MAT 2401, 3237 and 3360 • You are assumed to know the basics of Maple. Maple proficiencies is implied in the pre-req. as we use Maple in all our calculus classes.

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

  9. 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)

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

  11. 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.

  12. Technology • If you have not use Maple before, you probably need to spend sometime to learn the basic (before our first programming lecture). • If you have already programmed Maple before, it is a good time to review.

  13. Technology • If you have not use Maple before, you probably need to spend sometime to learn the basic (before our first programming lecture). • If you have already programmed Maple before, it is a good time to review. • Student version can be purchased at discounted price ($??, code ???)

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. Case Studies • If you look at the past schedule, we used to have 4.5 weeks for prep of 3 case studies and a mock MCM. • This year, we only have two weeks. • So the schedule will be extremely busy for the first 3 weeks. • You will have a day or two off to recoup after that.

  19. Case Studies – Atypical Timeline Read the material Group Discussion PPT Production Report Production Presentation

  20. Case Studies – Atypical Timeline Read the material Group Discussion Electronic copies of reports and PPT due 9 p.m. The day before presentation PPT Production Report Production Presentation

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

  22. Case Studies – Atypical Timeline Read the material Group Discussion PPT Production Report Production Hard copies of reports and PPT due at the beginning of your presentation. Presentation

  23. Case Studies • All reports must be typed(Show Sample) • All presentations must use PowerPoint Slides(Show Sample) • Electronic copies of reports and PPT due 9 p.m. on the day before presentation. • Hard copies of reports and PPT due at the beginning of your presentation.

  24. 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.

  25. 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.

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

  27. Case Studies – Grading Guide • Do you meet all the deadlines? • Do you meet all the requirements? • Are you able to understand the paper? • Are you able to “discover” the good (and bad) things about the paper? • Can you present the ideas, written and oral?

  28. Case Studies – Grading Guide • Some of these principles are used to rank your actual paper.

  29. Case Studies – Grading Guide • Letter grades will be given by the end of day it is presented. • At least one team member should come to talk to me about possible improvement on the next case study. • (I prefer to talk to the whole team, but I know the scheduling is difficult.)

  30. Modeling Contests Each group will enter into one of the following modeling contests (1/24-1/28): • MCM: The Mathematical Contest in Modeling • Problem A (continuous) • Problem B (discrete) • Problem C (data science) • ICM: The Interdisciplinary Contest in Modeling • Problem D (operations research/network science) • Problem E (environmental science) • Problem F (policy)

  31. Modeling Contests • Case Studies are selected from past contest problems

  32. Modeling Contests • Registration Fee: $100 per team • I need $100 cash, no coins, from each team bynext Monday. • Also email me the official names of your team members that you would like to appear in the certificates.

  33. Modeling Contests • A “N” grade will be given at the end of the quarter. • 120 points of your class grade • 100 points for the ranking • 10 points for the class presentation • 10 points for the poster presentation at the Erickson conference (see sample in OMH 202)

  34. Modeling Contests • A “N” grade will be given at the end of the quarter. • Grades for the MCM ranking will be assigned as follows

  35. SPU Records

  36. SPU Records

  37. Comparison to Local Universities (WA, 2018)

  38. Random Comparison to Major US Universities (2018)

  39. Random Comparison to Major US Universities (2013)

  40. Random Comparison to Major US Universities (2014)

  41. Random Comparison to Major US Universities (2015)

  42. Models and Topics • Various continuous and discrete models will be discussed in this class.  • Substantial weight will be placed on applications to biological modeling and time series modeling/forecasting..  • However, the modeling techniques learned will be applicable to other areas of application.

  43. 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 • AR(p) Models • MA(q) Models • ARIMA(p,d,q) Models

  44. Models and Topics • Modeling Molecular Evolution • Matrix Models of Base Substitution • 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.

  45. Actuary VEE (??) • The time series topics are in line with SOA Validation by Educational Experience, Applied Statistical Methods Part II Time series/forecasting • You are responsible for course approval application (One of you just need to complete the application once.)

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

  47. 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.

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

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

  50. 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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