This is from the father of a 10 year old girl learning calculus through Calculus&Mathematica:
Bill Davis expressed interest in my daughter Sarah's study and progress in Calculus & Mathematica. I'm delighted to share her success!
We have educated her exclusively at home, using the Internet to search for likely candidate courses. Sarah, 10, who is in her fourth year of education, is classified as an eighth grader (rather arbitrarily) at The Clonlara School (Ann Arbor MI), where she is officially enrolled. Before the Calculus course, she blitzed elementary arithmetic in three years using John Saxon's SAXON MATH series through "Algebra 1/2", the pre-algebra course. We calculate she has done over 30,000 problems, working every exercise in each of the eight books. She scored a 100% average on all exercises and tests.
We planned that she would proceed naturally to Saxon Algebra 1 but Sarah developed other plans, unknown to us. She played with the Internet over the summer and found Wolfram Research, where your course is referenced and described on-line at the Ohio State U. website. One thing led to another and she began to play with the sample MEI downloads . Next thing we know she asked if she could take the C&M course.
Thinking traditionally, I questioned whether she could do the work without the usual Algebra 1 & 2, Geometry and Trig pre-requisites. But I knew already she had demonstrated the necessary mathematical maturity, and extraordinary abilitites with functions. I realized that I could help her fill any knowledge gaps along the way. So we agreed, acquired Mathematica and the MEI courses, and Sarah set sail in C&M. She hasn't missed a beat since.
She finished Parts I and II, Growth and Measurement, and is proceeding next to Part III, Taylor's Formula and Power Series. Sarah hasn't missed a problem on any of the exercises or tests, and has her usual 100% average. We expect that she'll finish the course sometime before May. She plans to work on through the summer, undertaking the Vector Calculus next; then follows Differential Equations; and finally the Matrices, Geometry and Mathematica course.
Surprising as it may seem, Sarah's preparation has proven more than adequate. Your course's extraordinarily clear presentation and rich detail, when coupled with Mathematica, give Sarah an intellectual bulldozer. She has enough experience with C&M that I can confidently predict that she will progress rapidly through each of the other MEI courses.
There is another, subtle key to Sarah's success, which your course turns especially well. That is, it encourages an uncompromising standard of excellence. Mathematica, as a programming tool, requires exact instruction: else, as any program, it simply won't work. Sarah has mastered Mathematica's syntax and the exacting skill of expressing problems in it. Usually her expresions parse precisely and work the first time. The degree of excellence she expects is well-illustrated by an anecdote from her ballet class.
A tall girl for her age, Sarah towers over girls even two and three years older than she. So she takes ballet mostly with 13- and 14-year-old girls. One day she overheard several of them complaining of math test results in the low 90s, and wishing their teacher would "lighten up". Sarah, who mastered the same math a year ago, listened quietly but, discretely, said nothing. When she came home, she told me what happened and then commented, "They don't seem to get it. Either it's right or it's not right in Math...there's no middle ground; either Mathematica expressions work or they don't -- the only acceptable Mathematica result is 100%...period." I can't think of a single course I had, even in college and grad school, that led me to the same conclusion. Now, at age 10, Sarah has developed rare maturity and discipline...largely due to your course's uncommon superiority.
On Sarah's behalf, Jayne and I give you our heartfelt gratitude and salute you! Thank you for doing the impossible.
With our highest esteem and kindest regards, [Father] Carmel-by-the-Sea CA -- ------------------------------------------------------------------ Jerry Uhl email@example.com Professor of Mathematics, Professor of Education University of Illinois at Urbana-Champaign
"If the activity of a science can be supplied by a machine, that science cannot amount to much. . . It is precisely... the mathematician who invented the machine for his own relief, and who for his intelligent" ends, designates the tasks which it shall perform." -----Felix Klein
"Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house." -----Henri Poincare