SySc 512 - Quantitative Methods of Systems Science

Instructor: Patrick Roberts
Office hours: Monday 1:00 - 2:00 PM, & Wednesday, 6:00 - 7:00 PM, Harder House -Room 03.

Time and Location:
   PSU, Harder House - Room 104
   04/02/07 - 06/15/07, Monday & Wednesday, 4:00 - 5:50 PM

Text: There will be 3 texts, one for each section of the course:
Dynamical Systems with Applications using MATLAB (2004) Stephen Lynch, Birkhauser Boston.
(Supplementary MATLAB files from Lynch)
Probability Theory: A Concise Course (1977) Y.A. Rozanov, Dover.
Optimization Theory with Applications (1987) Donald A. Pierre, Dover.
Software: The numerical exercises can be solved using your favorite software, but the supported package will be Matlab (Tutorial by Mark Goldman).
Octave is a free alternative to Matlab with similar syntax.

Class Syllabus

Class notes, slides, and code:

Section A: Dynamics
Apr 2
Introduction to course
2-Dimensional flow geometries

Homework 1

Readings: Strogatz88
Matlab code: plot_1dDEq.m, plot_2dDEq.m, vectorfield.m

Apr 4
Discrete linear dynamics & Mappings

Readings: Lynch, Chapter 2
Matlab code: henon_map.m; Java applet: Logistic Cobweb

Apr 9
Diagonalization & eigenvalues

Homework 2
Readings: Lynch, Chapter 8, 10

Matlab code: eigenvalues.m, IODE

Apr 11
Homework 1 review

Matlab code: hw1_1.m, hw1_2.m, hw1_3.m

Apr 16
Higher dimensional dynamics & linearization
Readings: Lynch, Chapter 12, 13
Matlab code: plot_3dDEq.m; Java applet: Hopf Bifurcation

Apr 18
Stability & Gradient systems

Homework 2 due, Homework 3
Readings: Lynch, Chapter 11
Section B: Optimization
Apr 23
No class
Apr 25
Unconstrained optimization

Slides(pdf) , Class Notes
Homework 3 due
Readings: Pierre, Chapters 1, 2.1-2.4

Apr 30
Dynamics of Optimization
Practice Midterm
Class Notes, Practice Midterm Solutions
Pierre, Chapters 6.1-6.2, 6.6
May 2

May 7
Review midterm

Homework 3 solutions (hw3_1.m, hw3_2.m)
Homework 4
May 9
Constrained optimization

Class Notes,
Pierre, Chapters

May 14
Dynamic programming

Class Notes,
Pierre, Chapters
Homework 4 due
Homework 5, (gradientDescent.m, grad.m)

Section C: Uncertainty
May 16
Probability & Bayes rule
Class Notes (coinFlip.m, DeMere.m)
Reading: Rozanov, Chapters 1-3
May 21
Random Variables & Distributions

Class Notes,
Reading: Rozanov, Chapters 4-6
Homework 5 due
Homework 6

May 23
Uncertain Dynamics
Class Notes,
Reading: Rozanov, Chapters 7-8
May 28
No class
Memorial Day
May 30
Statistics: Hypothesis testing, likelihood, Monte Carlo
Homework 6 due
Class Notes, NetLogo Demo (Central Limit Theorem), hypothTest.m (stixbox)
Jun 4
Estimation & information
Class Notes, Dayan & Abbott, Chapter 3
  Reading: Rozanov, Appendix 1
Jun 6
Review & course evaluation
Review Slides(pdf) 
Practice Exam, Practice Exam Solutions
Jun 11 Final exam. Mon, June 11, 15:30-17:20


Due Assignment
Apr 9

Homework 1: Mathematical graphics and linear algebra.

Apr 16

Homework 2: Dynamical Systems.

Apr 25

Homework 3: Linear Algebra Review.

May 2 Homework 4: Optimization.
May 16 Homework 5: Discrete optimization.
May 28 Homework 6: Uncertainty.
Jun 4 Homework 7:


Due Exam
May 2 Midterm Exam: Dynamics & Optimization
Jun 11 Final Exam

Grading Policy

Homework 1/3, Midterm 1/3, Final 1/3

Exercises will be due every two weeks. Homework assignments will be graded pass/fail. Students are expected to complete all homework assignments successfully. Late assignments will be accepted only with prior approval.

The grade in the course will be based on successful completion of the homework, and the result of both exams (midterm and final). Each exam will be graded based on its completeness, clarity, and demonstrated depth of understanding.

Course Description

An introduction to the quantitative representation and investigation of systems with an emphasis on mathematical tools and their applications to systems. Topics include linear dynamics, optimization, and uncertainty. The level of presentation assumes familiarity and fluency with calculus. Notions from linear algebra unify the topics and will be presented. Required course work includes both calculations to be done on a computer (we will mostly use MATLAB) and calculations to be done by hand.

Prerequisites: Calculus, familiarity with probability or statistics, computer literacy, exposure to matrix calculations, and graduate standing.