Intro. Mathematical Modeling (Syllabus)

MTH4028-41   Intro. Math Modeling                                            Prof.  Sang-Gu Lee

031-290-7025 Room : 32304 sglee@skku.edu

 

Class Hour

Monday and Wed. 13:30-14:45

Lecture Room

Science Campus

31351A

 

 

 

 

 

Textbook and References

Textbook

Mathematical Modeling

Neuwirth and Arganbright

2004

Thompson Brooks / Cole

Reference

Contemporary Linear Algebra with Sage

Sang-Gu LEE

2012

Kyungmoon Books

Textbook

Matrix Analysis

Roger A. Horn, Charles R. Johnson

2012

Cambridge Univ. Press

 

 

 

 

 

 

 

 

 

 

 

Contents

Mathematical modeling with Sage and Excel (PBL course!!)

 

 

 

Goal

Mathematical modeling with Sage and Excel (PBL course!) Mathematical modeling usually begins with a situation in the real world, sometimes in the relatively controlled conditions of a laboratory and sometimes in the much less completely understood environment of meadows and forests, offices and factories, and everyday life. We will start from basic knowledge in Matrix Theory and history of matrices and modern mathematics. Then, we will start to practice some Mathematical Models in our working area. We will cover the most of the traditional and recent Linear Models. Your participation will be expected.

 

 

 

 

 

 

Tentative Schedule

1 week

Orientation and Introduction of the class. We will start from basic knowledge in Matrix Theory and a discussion on PBL plan!! Mathematics is studied because it is a rich and interesting discipline and because it provides a set of ideas and tools that are effective in solving problems which arise in other fields. We will cover the Fibonacci model. http://youtu.be/cZVoJkBIGpo ,

2 week

Generalized Fibonacci model and Gershgorin Theorem http://youtu.be/EwEU8Ai4PPM, http://youtu.be/SIXAhIqRPw8 , http://youtu.be/_0vLZmkXCnQ

3 week

Growth Model : exponential growth model, logistic growth model, http://youtu.be/9a7HumXe9To

4 week

Component Analysis: population model, http://youtu.be/eN16DEwlLTo

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 week

Epidemic Models: SIR, SIS, SEIR, http://youtu.be/5L0WF_1dTYw

6 week

 Predator-Prey model: Lotka-Volterra model,

7 week

 Equilibrium: Supply-Demand Model, Harvest Model, http://youtu.be/0UdIGOJhk2g

8 week

Physical Models: Projectile Motion, Planet Orbit, http://youtu.be/5UMW-tq7Tbk

 

 

 

 

 

 

 

 

 

9 week

Math and Art with Sage, http://youtu.be/RIhOBsxMvxE

10 week

Math Modeling of Blackour Game

 

 

 

 

 

 

 

 

11 week

Google Matrix and its modeling: Information retrieval models

12 week

Encryption

 

 

 

 

 

13 week

Real Example of Math modeling(´ëÇÐÀԽðúÁ¤): Analytic Hierarchy Process

14 week

Math Modeling with Sage and Geogebra

 

 

 

 

 

15week

Student PBLPresentation, Sage-Geogebra http://youtu.be/OiBih9aXkHw  

16week

FinalExam   http://youtu.be/jp3512p-GAs, http://youtu.be/B5T8dizDVc4, http://youtu.be/3aTOm07sclo

 

 

 

 

 

HW

QnA, PBL report, It will be posted after each class.

You will create one Mathematical Model in your working area.

 

 

 

 

 

Eval

attendance

HW

PBL

Exam

Participation

presentation

ETC

Total

10%

10%

30%

30%

5%

100%

10%

5%

ETC

Midterm Exam will be based on thefollowing topics:

Linear Equations

Linear Systems and Matrices

Leontief Input/Output Analysis

Markov Processes

Data Fitting- Polynomial Interpolation, Least Squares

Difference Equations

http://www.youtube.com/watch?v=adWzUKKmO2k

MathModeling-Exponential(8)

MathModeling-OurWorldl(9) http://matrix.skku.ac.kr/2011-Album/MathModeling-9/MathModeling-9.html

MathModeling-Geometry(10)

MathModeling-Arts(11)

MathModeling-Politics(12)

MathModeling-Business(13)