Welcome to the Math 725 (Fractal Geometry) home page. Please click on any of the following to see:
Math 725 Section S1 syllabus 

Assignment 1 Due Thursday, September 10, 2015 at the beginning of class  (in pdf format)   
Note:  To view or print out pdf files, you may need the Adobe Acrobat reader, which you may download for free if you don't have it yet by clicking  here.

Assignment 2 Due Thursday, September 17, 2015 at the beginning of class   

Assignment 3 Due Thursday, September 24, 2015 at the beginning of class


Assignment 4 Due Thursday, October 1, 2015 at the beginning of class

Assignment 5 Due Thursday, October 22, 2015 at the beginning of class

Assignment 6 Due Thursday, October 29, 2015 at the beginning of class;    Solutions  (in pdf format)
Note:  To view or print out pdf files, you may need the Adobe Acrobat reader, which you may download for free if you don't have it yet by clicking  here.

Assignment 7 Due Thursday, November 12, 2015 at the beginning of class 

Assignment 8 Due Thursday, November 19, 2015 at the beginning of class 

Assignment 9 Due Thursday, December 3, 2015 at the beginning of class  
New!

Notes on how to solve linear recurrence relations with constant coeffficients   
Follow the links to Step 1 (finding the homogeneous solution to the homogeneous equation);
  Step 2 (finding a particular solution, if the recurrence relation is inhomogeneous);
  Step 3  (combining the homogeneous and particular solutions);
  Step 4  (use initial conditions to eliminate the undetermined constants from Step 1).

Files that will let you compile basic programs (in zip format) (to use, you might need to (1) save qbasic.zip to your hard disk, by right clicking and using "Save target as" with Internet Explorer or using "Save link target as" with Netscape and then (2) unzip or extract qbasic.zip to c:\, using the create directory option, and (3) double click on "Microsoft Quick Basic" in the qbasic directory that should be created.  After the first time, only step (3) will need to be done.)    However,  this version of Microsoft Quick Basic won't work on a 64 bit version of Windows 7 Home Premium.  I don't know yet if  it will work on a 32 bit version of Windows 7.  If you find Quick Basic doesn't work on your computer, you may also download Octave (which is similar to MATLAB) using the links below:

Octave installation instructions

Octave tutorials: How to get started  (in pdf format); this consists of extracts from Introduction to Octave (in pdf format)
Note:  To view or print out pdf files, you may need the Adobe Acrobat reader, which you may download for free if you don't have it yet by clicking  here.

Program fractal.bas  (a modified version of the program FRACTAL on p. 142 of the text)   and  fractal_9_143.m  (run fractal_9_143.m with Octave or Matlab)

Program orbitlogistic.m  to generate the orbit diagram for the logistic function  f (x) = cx( 1
x )  ( This enables Exercise 2.7 on page 28 to be answered).

Program orbit02.bas (a modified version of the program ORBITDGM on p. 70 of the text)   and  orbit2.m  (run orbit02.bas with qbasic; orbit2.m with Octave or Matlab)

Program  julia4a.bas  (a modified version of the program JULIA1 on p. 88 of the text)  and julia4a.m  (To download this file, right click on the link and select "Save target as..."; run julia4a.bas with qbasic; julia4a.m with Octave or Matlab).

A video demonstrating how to use Qbasic, Matlab or Octave to generate an orbit diagram or plot a Julia set  

Program julia5b.bas to find the julia set for T(z)=z^3+c as in Exercise 7, p. 96 using the backward orbit method  as in chapter 7  and julia5b.m

Program Mandelbrot1.bas (a modified version of the program on p. 117 of the text)  and  mandelbrot2.m  (To download this file, right click on the link and select "Save target as..."; run mandelbrot1.bas with qbasic; mandelbrot2.m with Octave or Matlab).

Program  julia7p3.bas (to find the Julia set of  ce^z, where c is a complex number; c=c1+ic2, where c1 and c2 are real)

A graphing calculator emulator (Microsoft Mathematics 4.0)

**Current and future Master's level Math courses offered at Salem State University

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My favorite Web sites   (including a map of Salem State University and a link to MBTA schedules for routes serving Salem)

Home page for  Mathematics at Salem State University    or    Salem State University   or   ***Graduate Math programs at Salem State University    or  Graduate programs in general at Salem State University

Specific Information on Master of Science (MS) in Mathematics or Master of Arts in Teaching (MAT) Mathematics programs at Salem State University

To send me e-mail, click on arosenthal@salemstate.edu