Understanding Mathematics: A study guide
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http://www.math.utah.edu/~alfeld/math.html  


Peter Alfeld, University of Utah  
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that being lost in mathematics is the natural state of things? etc.), and a definition of "understanding mathematics" (with examples), lists of frequently asked questions (What kind of numbers are there? Why can't we divide by zero? What is 0 to the power 0? What on earth is a logarithm? In a nutshell, what are the trigonometric functions?) and mathematical gems (Why is the square root of 2 irrational? How do we know that there are infinitely many prime numbers? The Four Color Map Problem. Fermat's Last Theorem. Transfinite Numbers, Set Theory. The Mandelbrot Set, and some modifications. The Platonic Solids), some simple but unsolved mathematical problems, and suggestions on acquiring mathematical understanding, and reading the fine print.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Lesson Plans and Activities, Problems/Puzzles, Articles, Frequently Asked Questions (FAQs) 
Math Topics:  Graph Theory, Fractals, Polyhedra, Set Theory, Number Theory 
Math Ed Topics:  Psychological/Affective Issues 
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