Psychology Undergraduate StudentsMAT 1932, Spring 2005, Dr. Larry S. Liebovitch
The Mathematics and Science of Fractals 15094 M.W.F
11:00 - 11:50 AM (GCS 109 Boca Raton)
This course uses different teaching and learning styles for students who have been previously intimidated by mathematics.It can be used as one of the mathematics courses (besides Statistics) needed to fulfill the mathematics requirement for undergraduate Psychology majors. |
Larry S. Liebovitch, Ph.D.
Florida Atlantic University
Center for
Complex Systems and Brain Sciences
777 Glades Road, Boca Raton, FL 33431
telephone:
561.297.2239, fax: 561.297.2223
http://www.ccs.fau.edu/~liebovitch/larry.html
If you want to speak with me please telephone, DO NOT SEND E-MAIL (I am overwhelmed with e-mail which I do not have time to read.)
Overview
Course Policies
Homework | 60% |
Journal | 15% |
Exams | 25% |
Textbook
The textbook will be the CD-ROM which will be distributed to the class.
Materials on the CD-ROM
Lecture Contents
# | Title |
1 | Introduction: Course Objectives |
2 | Pre-Assessment: Students' Knowledge of Mathematics |
3 | What is Mathematics? |
4 | A New Way to Count: The LOGARITHMIC Scale |
5 | More From Paper Folding: Logarithms |
6 | Using Symbols to Represent Paper Folds: L's and R's |
7 | Paper Folding Iterations: Real Folds in Real Paper and the Symbols L and R |
8 | Symmetry and Invariants: A More General Form of Self-Similarity |
9 | Invariants: Examples from Science |
10 | The Koch Curve: Introduction to the Snowflake |
11 | The Koch Curve: Area and Limits |
12 | The Koch Curve: Zeno's Animals and The Area of the Koch Curve |
13 | The Koch Curve: Length and Dimension |
14 | The Middle Third Cantor Set: Making a Fractal by Removing Pieces |
15 | The Sierpinski Triangle: Many Different Ways |
16 | Paradigms: How The Eye Works |
17 | Fractals in the Eye: Statistical Self-Similarity |
18 | What Graphs Tell Us: Discovering the Straight Lines |
19 | What Graphs Tell Us: What the Straight Lines Mean |
20 | What Professors Really Do |
21 | Dimension: Exponents and Graphs |
22 | Dimension: Slopes and Logarithms |
23 | Many Different Dimensions: Fractal, Topological, Embedding |
24 | Figuring Out the Fractal Dimension: Box Counting |
25 | Figuring Out the Fractal Dimension: The Scaling Relationship |
26 | More Scaling Relationships: How Nerves Work |
27 | Even More Scaling Relationships: The Mass and Density of Fractals |
28 | Newspaper Crumpling: Dimension, Density, and Scaling Relationships |
29 | Finding Fractals: Outside the Classroom |
30 | Making Fractals: Inside the Classroom |
31 | Statistics: When the Mean is Meaningless |
32 | Statistics: Bell Curve and Fractal PDFs |
33 | Fractal Statistics: How the Ear Works and More |
34 | Fractal Statistics: How the Heart Works and More |
35 | Chaos: Simple Things That Look Complicated |
36 | Chaos: An Exquisite Sensitivity |
37 | Concept Maps: The Big Picture |
38 | Post-Assessment: Students' Knowledge of Mathematics |