Intro. Mathematical Modeling (Syllabus)
MTH4028-41 Intro. Math Modeling Prof. Sang-Gu Lee
031-290-7025 Room : 32304 sglee@skku.edu
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Class Hour |
Monday and Wed. 13:30-14:45 |
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Lecture Room |
Science Campus |
31351A |
Textbook and References |
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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 |
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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
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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 |
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10% |
10% |
30% |
30% |
5% |
100% |
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10% |
5% |
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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 |
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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) |