Extrinsic Useful Material:

General Course Material:

Specific Course Material

Index:

1. Algorithms and Ancient Machines
2. Algorithms and Modern Machines
3. Processing Numbers
4. Processing Text
5. Processing Images
6. Computational Geometry
7. Searching Data Bases
8. Computers as Models of Brains and Intelligence
9. Computers in Statistics and Exploratory Data Analysis
10. Computer Vision
11. Network Security
12. Computer Graphics and Visualization
13. Philosophical, Ethical and Social Implications of Computers

1. Algorithms and Ancient Machines:

(1) Pebbles, Knotted Strings, the Abacus, and other Computing Devices

1. Computers: From the Past to the Present
2. Modular Arithmetic with Ashtrays and Pebbles
1. Modular Arithmetic Calculator
2. Modular Arithmetic Practice Session
3. Gravity as a Computer
1. Computing the Centroid of a Polygon with a Plumbline
4. The Knotted String Computer
5. Pythagoras' Theorem:
1. Pythagoras' Theorem (An award winning proof and interactive demo)
2. Animated Proof of the Pythagoream Theorem by M. D. Meyerson
3. A Hinged Dissection Proof of the Pythagorean Theorem
4. Other Dissection Proofs (with interactive Java applets)
5. The Chinese Square Proof of the Pythagorean Theorem
6. Two dozen other proofs of the Pythagorean theorem
7. The Converse of Pythagoras' Theorem
6. The Abacus
1. The Abacus in various number systems
7. Napier's Bones in Various Bases
8. The Virtual Museum of Computing
9. Links to History of Computing

(2) The Straight Edge and Compass

10. Euclid's Elements
11. Euclid of Alexandria
12. More Euclid on the Web
13. Relative computing power of machines
1. The Collapsing Compass
2. The Compass without straight edge (Mohr-Mascheroni)
14. Heron's Shortest Path via a Line (with interactive Java applet)
1. More on Heron's problem and other constrained shortest path problems (with interactive Java applets)
2. More about Heron of Alexandria
15. The Lunes of Hippocrates
1. More about Hippocrates of Chios

2. Algorithms and Modern Machines:

1. The Turing machine
• A Turing Machine Java applet simulator
• More about Alan Turing
2. Computability theory
• What computers can't do
3. Binary Numbers
• Decimal-to-Binary Converter
• Converting using stacks
• Binary to decimal converter
• Practice session
4. Error correcting codes
• Hamming distance (with Java applet)
• Coding theory: the first 50 years
• Hadamard matrices
5. Logic gates
6. How logic gates add 2 + 3
7. Boolean logic
8. Boolean logic gates
9. Boolean gates and adders
10. Boolean Algebra
11. More Boolean Algebra
12. Logic and Boolean algebra
• Truth Table Practice Session
13. Searching the Web with Boolean logic
14. More about George Boole
15. Computational Complexity
• Big "O" Notation
• Polynomial complexity
• Exponential complexity and the Towers-of-Hanoi puzzle

3. Processing Numbers:

3.1 Creating Numbers

1. What is a Number?
• More on irrational numbers
• Two proofs of the irrationality of the diagonal of the unit cube
2. Elementary number theory
3. Numbers: Real, rational, integer and binary numbers (bits and bytes)
4. Floating Point Numbers
5. Newton's Method:
1. Introduction to Newton's method
2. Computing approximate square roots with Newton's Method
6. The Euclidean factorization algorithm
7. Prime Numbers:
1. Prime numbers (FAQ's)
2. Historical introduction to primes
3. The Prime Number Home Page
4. Euclid's Proof of the Infinitude of Primes
5. Prime Number Generator

3.2 Creating Order

1. Sorting Numbers:
1. Selection sort tutorial
2. Bubble sort tutorial
3. Heap sort tutorial
4. Merge sort tutorial (Divide and Conquer)
2. Sorting Algorithm Animations (Applets also sort your own set of numbers!)
3. More Sorting Algorithm Animations
4. Sorting Code

3.3 Creating Disorder (Randomness)

5. Probability and Random Number Generation
1. Visualizing randomness
2. More on generating random numbers
6. Monte Carlo Simulation:
1. Buffon's Needle
2. Rolling Dice
7. Randomness and the Netscape browser

4. Processing Text:

1. Data compression
1. Introduction to Data Compression
2. Fundamental Concepts
3. Shannon-Fano Coding
1. More about Claude Shannon
2. The Significance of Claude Shannon's Work
3. Pictures of Shannon
4. More about Robert Fano
4. Huffman coding
5. More About David Huffman
2. Morse Code
1. Morse Code basics
2. The International Morse Code
3. More about Samuel Morse
3. Introduction to probability and information theory
4. Entropy
5. Markov models of natural language (monkeys and typewriters)
• The Shannonizer
6. Spelling correction programs.
• Spell checkers are wonderful but .....
7. Determining unknown authorship of manuscripts.

5. Processing Images:

1. Tiles, pixels and grids.
2. Obtaining grey-level images with a digital camera.
3. Obtaining binary images from grey-level images (thresholding).
4. Finding connected components in binary images (contour tracing with cellular automata).
5. Smoothing:
1. smoothing images (noise removal)
2. smoothing polygons
6. Sharpening images (spatial differentiation).
7. The Medial Axis of a shape (with interactive Java applet)
8. Cellular Automata
• Conway's game of Life
• Interact with a Java Applet of Life
• Another nice applet for Life
• More about John Conway

6. Computational Geometry:

1. Polygons: crossing, simple and convex.
2. Polygonizing Sets of Points
3. The area of a polygon.
4. Determining if a point is inside a polygon.
5. Smoothing polygons and polygonal waveforms.
6. Application to point facility location (minimal spanning circle of a set of points in the plane).
7. Convex Hulls:
• The Gift-Wrapping Algorithm (Jarvis' March)
• The Quick-Hull Algorithm (stretching an elastic band)
• The 3-Coins Algorithm (Graham scan)
8. Linear programming and optimization problems (with Java applet)

7. Searching Data Bases:

1. Data Structures.
• Arrays.
• Linked lists.
• Stacks.
• Queues.
• Trees.
• Binary trees.
• More information on binary trees.
• Logarithms
2. Binary search.
• Creating Binary Search Trees (Java applet)
• Searching in a Binary Search Tree (Java applet demo)
• The Number-Guessing Game

8. Computers as Models of Brains & Intelligence:

1. Real and Artificial Neurons
2. Threshold logic units.
3. Dr. Gurney's course on neural networks.
4. Perceptrons & neural networks (learning machines).
5. Playing Games
• Play Checkers with Chinook (The World Champion)
• Play Othello with Keyano and other programs
• Play Chess with The Turk
• Game trees
• Other Games, Toys and Puzzles
• Clever games for clever people
• Tetris
6. Artificial Life
7. Decision theory.
8. Recognizing patterns (how can a robot tell an orange from a banana).
9. The Poetry Generator
10. Artificial intelligence on-line demos
11. Expert Systems
• The I-Ching

9. Computers in Statistics and Exploratory Data-Analysis:

1. Graphs and networks.
2. The minimal spanning tree and its application to cluster analysis.
3. Unsupervised learning.
4. Robust estimation of location (onion peeling).

10. Computer Vision:

1. The Hough transform.
2. Detecting lines in a digital image with the Hough transform.
3. Image segmentation in document analysis.
4. Text-line orientation inference in document analysis (another application of the minimal spanning tree).

11. Computer Network Security:

1. Electronic mail.
2. Coding theory.
3. Basics of classic ciphers
4. More about private-key cryptography.
• Transposition ciphers.
• Substitution ciphers.
5. Cryptanalysis (breaking secret codes).
6. Creative Cryptography
7. Francis Bacon and Cryptography
8. Are there cyphers in Shakespeare? (by PennLeary)
9. Public-key encryption
10. Basics of public-key cryptography.
• The Knapsack problem.
• The Unbounded Knapsack Problem (with Java applet)
• The Hellman-Merkle-Diffie cryptosystem.
• Security on the Internet (Netscape).

12. Computer Graphics and Visualization:

1. Turtle geometry.
2. Fractals:
• A Tutorial on Fractals.
• Introduction to Fractals.
• Fractals with Newton's method
3. Hidden surface removal.
4. The painter's algorithm.
• Tutorial
• 3D interactive Java demo of the algorithm at work.
5. Virtual reality.

13. Philosophical, Ethical and Social Implications of Computers:

1. Bibliography on the Philosophy of Artificial Intelligence
2. Can a computer think?
1. Turing's test.
2. Searle's Chinese Room Argument.
3. The Robot Reply.
4. How to pass the Turing Test by cheating
3. Conversing with Computer Programs - The Loebner Prize.
1. About the program DEBRA (the Canadian winner of the 1994 Loebner Prize).
2. Obtain sex advice from DEBRA
3. About the program JULIA
4. Talk to JULIA about Cats and Dogs.
5. About the program ELIZA
6. Obtain free psychotherapy from ELIZA.
4. Computer Art
1. MONDRIMAT: competition with Mondrian?
5. Privacy.
6. Computers and Law.
7. Computers and Medicine.
1. Medical Robotics and Computer-Assisted Surgery
8. Men and Women in Computing Science:
1. Women and Computer Science
2. Past Notable Women in Computing and Mathematics