MATH-4400A (CRN 1759) Fall 2017 Course Syllabus

When, where, and who

My job is to help you to succeed in this class. I will be happy to discuss issues related to this course (or anything mathematical) in person or via email. In addition to the normal office hours listed above, alternative meeting time may be arranged (please give me at least 48hr advanced notice).

What we will learn

Use of mathematical models and computer simulations for solving real world problems.

Prerequisite

  • MATH-2660 (Linear algebra)

Textbook

No textbook is required. However, the following books will be used as references:

  • A first course in mathematical modeling (4th edition) by F. Giordano, W. Fox, S. Horton, and M. Weir ISBN: 978-0-495-01159-0
  • An introduction to mathematical modeling by E. Bender ISBN: 978-0-486-41180-4

Attendance and participation

Participation in in-class discussions and activities is an important part of the learning process. Therefore class attendance is expected and will be recorded.

Code of conduct

Please be respectful of other people in the classroom and use common sense. In particular, please…

  • DO NOT use cell phones
  • DO NOT use social media
  • DO NOT take photos without permission
  • DO NOT sleep

Students who violate these rules will be asked to leave the classroom and will not be allowed to return until they have spoken privately with me.

Software programs

Computer programs are indispensable in mathematical modeling and simulation as many basic tasks will be nearly impossible to do by hand. Therefore you are expected to be able to use some software programs. The following programs are recommended:

  • Matlab / Octave (these two are nearly equivalent programs for numerical computations, but Octave is completely free)
  • Mathematica / Maple / Sage / SymPy (these are the standard programs for symbolic computations, and among them Sage and SymPy are free)

You will be expected to be able to carry out basic calculations in at least one of the above software programs.

Programming languages

Programming languages are the means by which you can ask computers to do things. The ability to program is an essential skill in the modern job market. In the context of computer simulation, basic programming skills can be very useful. Familiarity with the following programming languages are not required but strongly recommended:

  • Matlab / Octave
  • C / C++
  • Python / Ruby
  • Javascript

Projects

This course is largely based on projects. You are expected to spent much of your time in (team) projects.

Discussions

Participation in in-class and online discussions will an important component of the learning process as well as your scores.

Final exam

The mandatory final exam is scheduled at 11:00am – 12:00pm Dec. 5.

Grade composition

Your final course grade is determined according to your overall performance in (team) projects, in-class and online discussions, and the final exam. It is calculated according to the following weights.

Component Points
Projects 800
Discussions 150
Final Exam 50

Grading scale

  • A: 90% - 100%
  • B: 80% - 89.9%
  • C: 70% - 79.9%
  • D: 60% - 69.9%
  • F: below 60%

Other policies

Academic dishonesty: Cheating of any kind will not be tolerated. In particular, you cannot copy (totally or partially) someone else’s solutions or allow someone else to copy your solutions on quizzes or exams. You will receive an “F” in the course if you are caught. Please consult Student Handbook for additional guidelines.

Disability accommodations: Students who need accommodations are asked to arrange a meeting during office hours to discuss your accommodations. If you have a conflict with my office hours, an alternate time can be arranged. To set up this meeting, please contact me by e-mail. If you have not registered for accommodation services through the Center for Disability Services (CDS), but need accommodations, make an appointment with CDS, 147 Taylor Center, or call 334-244-3631 or e-mail CDS at cds@aum.edu

Free academic support: All students have the opportunity to receive free academic support at AUM. Visit the Learning Center (LC) in the WASC on second floor Library or the Instructional Support Lab (ISL) in 203 Goodwyn Hall. The LC and ISL offers writing consulting as well as tutoring in almost every class through graduate school. The LC may be reached at 244-3470 (call or walk-in for a session), and the ISL may be reached at 244-3265. ISL tutoring is first-come-first served. Current operating hours can be found at http://www.aum.edu/learningcenter.

Student Privacy Policy: The Family Education Rights and Privacy Act of 1974, as amended, (FERPA) requires institutions receiving federal monies to protect the privacy of students’ educational records. For details go to the AUM’s FERPA website: http://www.aum.edu/academics/Registrars-office

Schedule

  • Day 0 : Overview and motivations
  • Day 1 : Basic languages of mathematics
    • The language of calculus
      • limits, derivatives, integrals
      • critical points
      • Taylor series
      • differential equations
    • The language of linear algebra
      • vectors and matrices
      • products of vectors and matrices
  • Day 2 : Case study: electrons on a sphere
  • Day 3 : Case study: the diet problem
  • Day 4 : Discussion: What is mathematical modeling?
  • Day 5 : Project milestone I: Problem statements
    • What problem do you want to solve?
    • What are the assumptions?
    • What are the constraints?
    • How can you know if your solution is correct?
  • Day 6 : Case study: bunnies and foxes
  • Day 7 : Mathematical tools: system of linear equations
    • What is a linear system?
    • What kind of solution sets could we have?
    • How to solve them?
  • Day 8 : Mathematical tools: linear programming
    • What is a linear programming problem?
    • What kind of solutions could we have?
    • How to solve them?
  • Day 9 : Project milestone II: mathematical description
    • How to translate your problem statement into a mathematical question?
    • What kind of assumptions do you have to make?
    • What are the variables involved?
    • What kind of mathematical problem are you trying to solve?
  • Day 10 : Mathematical tools: Nonlinear equations
    • What is a nonlinear equation in one variable?
    • How to solve such an equation?
    • What kind of solutions could we have?
  • Day 11 : Mathematical tools: Systems of nonlinear equations
    • What is a nonlinear system?
    • How to solve such a system?
    • What kind of solution set could we have?
  • Day 12 : Project milestone III: initial approach
    • How do you plan to solve your problem?
    • What are the method you have tried?
    • Did those work?
    • What are the difficulties and how do you plan to overcome them?
  • Day 13 : Mathematical tools: differential equations
    • What is a differential equation?
    • How many types of differential equations are there?
    • How to solve a differential equation?
  • Day 14 : Differential equation again
  • Day 15 : Discussion: mathematical tools
  • Day 16 : Project milestone IV: progress presentation
  • Day 17 : Discussion: computer simulation
    • What does simulation mean ?
    • How are they used?
  • Day 18 : Project milestone I: ideas
    • What phenomenon do you want to simulate?
    • Any plans?
  • Day 19 : Mathematical tools: continuation method
  • Day 20 : Case study: head, shoulders, knees, and toes
  • Day 21 : Mathematical tools: Monte Carlo methods
  • Day 22 : Mathematical tools: genetic algorithms
  • Day 23 : Mathematical tools: neural networks
  • Day 24 : Project milestone II: initial approaches
  • Day 25 : (optional) Case study: swarm behavior
  • Day 26 : Case study: simultaneous synchronization
  • Day 27 : Project milestone III: progress report