COURSE SYLLABUS

Course Number: MATH 6690
Course Title:  Introduction to Chaotic and Random Phenomena
Credit Hours:  3
Prerequisites: MATH 1620
Corequisite:   

Course Content/Objectives:

* Statistics and modeling of random phenomena in connection to 
   computational complexity, data analysis, processes of chance, 
   and chaotic nonlinear systems. 

* Computer simulation and experimenting  within Mathematica, 
   supported by Internet resources.

week
 1.  Introduction to Mathematica                                   
 2.  Data types (categorical, numerical, multidimensional, fractal)
 3.  Order statistics, quantiles, means, scatter, moments          
 5.  Graphic representations                                       
 6.  Correlation and regression                                   
 7.  Fractals, entropy, Hausdorff dimension                        
 8.  Repeated experiments and the law of large numbers             
 9.  Distribution functions. Monte Carlo methods                   
10.  0-1 random variables. Poisson and Gaussian approximation      
11.  Basic estimation and testing                                  
12.  When is random - random?                                      
13.  Computational complexity  of random strings                   
14.  Dynamical systems, orbits, ergodicity                         
15.  Chaos in dynamical systems, attractors, fractals              

Possible Textbook: M. Denker and W.A. Woyczynski, 
Introductory Statistics and Random Phenomena, Birkhauser, Boston 1998

Mathematica help: S. Wolfram, The Mathematica Book, Wolfram Media, 
Champaign, IL, 1966; plus other listed on page 52 of the textbook.

Mathematica packages can be downloaded from publisher's UVW Web Site
http://www.birkhauser.com/book/isbn/0-8176-4031-2.


Grading and Evaluation Procedures:
	
	Series of projects, augmented by quizzes. The number, the weight 
	of projects (e.g., more elaborate midterm and final projects), 
	and detail criteria are to be specified by the 
	instructor at the beginning of the semester.
	
Statement related to policies on unannounced quizzes and class attendance:
	
	Particular policies on unannounced quizzes, class participation, homework depend upon an instructor and are announced at the beginning 
	of the semester.

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