Some Teaching Materials

Perpetually Under Construction

Page Description

Course Home Pages

Look at these pages to find, for example, course outlines, sylabi, homework assignments, review sheets, notes, and the like that I provided for my students in a particular term. Many of the items that are more universally applicable have links below categorized by content rather than by course and term. Generally, only the most recent instantiation of each course is listed, but often the home page for that course includes links to other terms when I have taught it.

Courses at Calvin College

• Math W50: How do they know my opinion? (Interim 2000).
  A three week intensive course introducing statistics to a general college audience.
• Math 100: Elemenst of Modern Mathematics (Spring 01)
• Math 143: Introductory Statistics (Spring 00)
• Math 156: Discrete Math for Computer Science (Fall 01)
• Math 161: Calculus I (Fall 01)
• Math 162: Calculus II (Spring 01)
• Math 190: First-Year Seminar (Fall 99)
• Math 221: The Real Number System and Methods for Elementary Education (Fall 99)
• Math 381:Advanced Logic (Spring 01)
• Math 391:Mathematics Colloquium (Fall 2000)

A course at Boston University

• CS 113 Accelerated introduction to programming using C. (1997)
  

Web Overheads

• Overview & Statistical Literacy
  • What is statistics?
  • Seven Critical Components that determine the soundness of statistical studies. (J. Utts)
  • How to Evaluate a Study
    • Common Pitfalls
  • Checklist for Statistical Pictures
  • Probability Basics
  • Two Basic Inference Procedures
  • Reports of Hypothesis Tests

• Experiments with surveys

  To demonstrate both the methodology of experiments and the importance of good question design in surveys, I have made two versions of each of these surveys:

  • Survey 2 ( results from Spring 2000)
  • Survey 3 ( results from Spring 2000)

• Other interesting stuff
  • Did the Holocoust really happen? (example of poor wording of a question)
  • Researcher to use death camp data: version 1, version 2 (two versions of the same report)
  • Biased Questions designed by my class
  • Price and income increases (Consumer Price Index, minimum wage, gas prices, college tuition, etc.)

My Demos (webforms, applets, etc.)

• Histogram Bin Sizes. See the effect bin size has on the picture a histogram gives. Try it on your own data! [JAVA]
• Golf Balls in the Yard. Intro to hypothesis testing, Chi-squared.
• Sampling Distributions. Intro to Central Limit Theorem. [JAVA]
• Generate random integers in a specified range or random digits. Useful for sampling

Other Demos

• Old Faithful Eruption Times. Investigate histogram bin sizes. (Webster West - S. Carolina)
• Normal Distribution Applets from Seeing Statistics. My favorite of these can be used to find the percentage of a normal distribution (with user specified mean and standard deviation) that lies between any two values by dragging the edges of the shaded portion of a normal probability curve.
• Sampling Distributions, Confidence Intervals, etc.
• Sampling Reese's Pieces
• Sampling Distributions Demo displays results of sampling (modest sizes) from normal, skewed, uniform or user-defined distributions. Can display results of several other sample statistics in addition to sample means.
• Confidence Intervals Simulator (CUWU) for proportions. Shows error bars for repeated samples from same population.
• Confidence Interval Simulator for Means
• Correlation Coefficient and Regression Lines.
  • Correlation Coefficient Guessing Game. Match correlation coefficients to scatter plots. This is one of several games available from the CUWU Statistics Program
  • MSTE Best Fit Applet. Add data points and then try to fit the regression line by hand. Display shows measure of error, equation of hand-drawn line, and will reveal the regression line. Incorrectly refers to equations of lines as "slope", but otherwise very nicely done.
  • Workshop Statistics Regression Applet Add and move points and see the effects on the regression line and correlation coefficient.
  • Outliers and Regression. See the effects of adding an outlier (Webster West - S. Carolina).
• Monty Hall Problem. This problem was made famous by a serious of articles run in the Ask Marilyn column. Here are some demos of the problem:
  • This is one of several games available from the CUWU Statistics Program.
  • The Let's Make a Deal version done by Webster West includes an explanation.
  • The MSTE Monty's Dilemma page adds an extra twist: you may keep you original choice, switch, or flip a coin to decide. This applet also allows you to select one of the three strategies and run it repeatedly and tabulate the results.
  For more information about Ask Marilyn, check out the Marilyn is Wrong! website which seeks to document any of her errors but also has interesting information about her and her column.

More JAVA Demos

• Rice Virtual Lab in Statistics developed by David lane and others ar Rice University. This site has quite a large index organized by topic.
• The CUWU Statistics Program by John Marden at Champaign-Urbana Web University.
This site has a modest number of applets of generally high quality.
• Workshop Statistics Applet Collection (in progress): As of January 2000, this contained four applets: simlulation confidence intervals, histogram bin widths, regression lines, and Reese's pieces, all listed above. Nothing else is there yet, but what is there is good. Maybe a site to watch in the future.
• Probability (and Statistics) Demos at Cut The Knot, a site with demos from many areas of mathematics.
• MSTE JAVA has several applets, some of which are related to statistics, others to other areas of mathematics.
• Globally Accessible Statistical Procedures (GASP) collected at the Univ. of South Carolina.
• Interesting JAVA Applets compiled at Duke University.
• Virtual Laboratories in Probability and Statistics by Kyle Siegrist at Alabama--Hunstville.
• JAVA Applets by Balasubramanian Narasimhan at Stanford University.
• SurfStat JAVA Applet Hotlist - part of the on-line textbook at University of Newcastle.

Statistics Packages available as JAVA applications

• WebStat by Webster West looks a lot like Minitab.
• Statlets - a multi-featured JAVA-based statistics package, with free WWW access for small datasets (10 variables x 100 cases). Produced by NWP Associates, Inc.
• Statiscope. A one page univariate stat pakage done by Mikael Bonnier - Lund, Sweden.

Stuff for Off-line Stats Packages

• Fathom is not available as a JAVA applet, but a demo version is available for download. I have heard great things about Fathom as software for teaching statistics.
• Wolfram provides information (and a free pallette) for doing Statistics with Mathematica

Non-JAVA demonstrations

Some Experimental WWW Pages being developed by Juha Puranen at the Univ. Of Helsknki includes a look at how a scatterplot varies as correlation changes.

I've Got a Little List

• Statistics and Statistical Graphics Resources maintained by Michael Friendly. Among other things, this site contains a large list of other lists, links for particular software packages, and a large number of links to sources for data.
• Robin Lock's list of WWW resources for statistics. Many things on my list come from his, but there are many other things there as well.
• Statistical Literacy Related Links Page (put together in conjunction with Jessica Utts' book Seeing Through Statistics

Data, Data, Data

• DASL The Dataset and Story Library. A collection of datasets and related documentation (stories). May be searched by data subjects or by statistical techniques.
• Journal of Statistics Education Data Archive. Datasets contributed by statistics teachers. Raw data are in a .dat file with explanations a .doc file. Many of these datasets are tied to longer JSE articles discussing their use in statistics classes.
• Statlib Dataset Archive
• ICPSR has some links to various data sets, mostly from social science research projects.
• Robin Lock's list includes a section on where to find data.
• a few odd things I have used:
  • C.A.N.D.L.E.S. Holocost Museum with links to information about Dr. Mengele and his experiments on twins at Auschwitz.
  • Consumer Price Index Data
  • Michigan gasoline prices (Courtesy of the American Automobile Association)

Textbooks

• Workshop Statistics by Alan Rossman and Beth Chance (Key Curriculum Press / Springer)
• Seeing Through Statistics by Jessica Utts (Duxbury)
• Seeing Statistics by Gary H. McClelland uses over 100 JAVA apples to make statistics visual. Four demo applets for normal probabilities are available on the web page.
• CyberStats by Jessica Utts (with others) is an online text. Unfortunately, you can't see anything without registering.

Information, Please

• Survey 101: A white paper about designing a good survey.
• "Do You Believe the Polls?" -- a chat with J.A. Paulos
• Places to find articles
  • Chance News. Chance News is an electronic newsletter that collects articles about statistics. Often these include interesting questions for discussion in class. It is possible to search past issues as well as to read current issues. Also at this location: links to lectures with audio, video and overheads on a variety of statistics topics.
  • New York Times

Videos

• Against All Odds (time outline)
• For All Practical Purposes statistics segments (time outline)
• Are We Scaring Ourselves to Death? an ABC News special with John Stossel (time outline, discussion questions)
• Life by the Numbers (time outline)

Elementary Education

Links Elswhere

• BBC education section (example items below)
  • NumberWork
  • Methods of subtraction article
  • The Mathematical Education of Teachers: the current draft of this CBMS document is available online. Input and comments are welcome.

Discrete Mathematics

Logic

Textbooks and related sites

• LMCS: Logic for Mathematics and Computer Science by Stanley N. Burris (U. Waterloo)
• LPL: Langauge, Proof, and Logic by J. Barwise and J. Etchemendy
  • Hints and Solutions for exercises.
  • Rykman's Logic Works supposedly has a number of things on it that are intended to be coordinated with the Barwise/Etchemendy text. Not much is actually there yet, but perhaps in the future this will be an interesting site.
  • Obituary for Jon Barwise, who died in March, 2000.

Course Home Pages

• Philosophy 7405: Mathematical Logic, Richard Thomason at U. Michigan [LPL+]
• Philosophy 202: Symbolic Logic, M. O'Rourke at U. Idaho [LPL]

Theorem Provers

• Automated Reasoning at Argonne has info on various theorem provers.
  • You can try out two of these (Otter and MACE) online using Son of BirdBrain.

Machine Simulators

• Eileen Head has written some sophisticated Java simulators for several kinds of machines including Turing Machines, Finite State Machines, and Push-Down Automata. [Style appears to be ala Hopcroft and Ulman]
• A nice Turing Machine applet by Suzanne Britton/Skinner. [Source available!]
  This was extended to a multiple tape version by some students.
• A graphically fancy Turing Machine applet From the Winner's Circle at sunsite.utk.edu. This applet has nifty graphics (a cute little machine, a tape that rolls onto spools on either end rather than just disappearing off the screen, etc.) but on my screen the rules list is too small to read and you only have a choice of 4 programs to run, at least as it is set up on this page.
• http://stud1.tuwien.ac.at/~e9108323/
• Virtual Turing Machine. This is done as a form-based perl program. (Doesn't require JAVA)
• Finite State Machine Explorer. A DFA/NFA type simulator programmed by Matt Chapman as undergraduate project.
• A description of how to simulate a Turing Machine in Conway's Game of Life.

Busy Beaver Problem

• Go here to find out what the Busy Beaver Problem is and to find some interesting links about it.
• Heiner Marxen's Page lists some known facts and record-holders.

Courses, Tutorials, Demos, etc.

• Collection of Lecture Notes, Surveys and Papers housed at the University of Paderborn.
• Eric Schecther's Math 250 Home Page includes a number of links to other sources and well as some discussion of his approach to logic.
• Gateway to Logic by Christian Gottschall

Notes

• Mike Stob's Logic Notes: Postscript notes by Mike Stob for an advanced undergraduate logic course. Traditional syllabus aiming for Goedel's Theorem.
• Randall Pruim's Logic notes. These only cover a few selected topics from an undergraduate Advanced Logic course. Most notably, there is material on cardinality, countability, and diagonalizationan, and there is a section giving a brief introduction to set theory. (dvi, postscript)

Prolog

• Pruim's Prolog Page: These materials were used in conjunction with the predicate logic part of a discrete math course. Includes a prolog interpreter that can be run over the WWW, an example from Monty Python, examples, exercises, ...

Miscellaneous Teaching Resources

• Project Interactivate has many interactive activities designed to meet goals of the NCTM Standards for mathematics education. Here are a couple examples:
  • Sierpinski's Carpet
    • Here is a still shot of Sierpinski's carpet after five steps.
    • And here is another Java applet for generating it
  • Sierpinski's Triangle

Technology for Teaching

• A list of Java Applets
• Mathwright

This page maintained by:

Randall Pruim
Department of Mathematics and Statistics
Calvin College
rpruim@calvin.edu