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Notebook[{
Cell["\<\

My Favorite Quotations
\
\>", "PrefaceTitle",
  CellMargins->{{Inherited, Inherited}, {Inherited, 0}}],

Cell["Jerry's Top Ten", "Subsection"],

Cell["\<\
#1  Peter Lax, Past President of the American Mathematical \
Society\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Calculus as currently taught is, alas, full of inert material . . . \
The real crisis is that at present [calculus] is badly taught; the syllabus \
has remained stationary, and modern points of view, especially those having \
to do with the roles of applications and computing are poorly represented. . \
.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["#2 Gian - Carlo Rota", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
  The student needs to develop an understanding, however partial \
and  imperfect, by descriptions rather than definitions, by typical examples \
rather than grandiose theorems.... Understanding mathematics means being able \
to forget the medicine and enjoy the food.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["#3 Richard Feynman", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\

Many of the math books . . . are full of  . . . nonsense - of carefully and \
precisely defined words that are used by pure mathematicians in their most \
subtle and and difficult analyses, and are used by nobody else . . ..  The \
real problem in speech is not precise leanguage.  The problem is clear \
language.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["#4 Ralph Boas", "Subsection"],

Cell["\<\
Mathematical skills are like any other kind.... If you are learning \
to play the piano, you usually start by practicing under supervision; you \
don't begin with theoretical lectures on acoustical vibrations and the \
internal structure of the instrument. Similarly for mathematical \
skills.\
\>", "Text"],

Cell["#5 Ralph Boas", "Subsection"],

Cell["\<\
Authors of textbooks need to remember that they are supposed to be \
addressing students, not the teachers...
Contemporary prose style is simpler and more direct than the style of the \
19th century- except in textbooks of mathematics. ....I blame the authors of \
textbooks for not realizing that contemporary students speak a different \
language.\
\>", "Text"],

Cell["#6 Bill Thurston", "Subsection"],

Cell["\<\
Mathematicians have developed habits of communication that are \
often dysfunctional. We go through the motions of saying for the record what \
the students \[OpenCurlyQuote]ought\[CloseCurlyQuote] to learn while students \
grapple with the more fundamental issues of learning our language and \
guessing at our mental models.  Books compensate by giving samples of how to \
solve every type of homework problem. Professors compensate by giving \
homework and tests that are much easier than the material \
\[OpenCurlyQuote]covered\[CloseCurlyQuote] in the course, and then grading \
the homework and tests on a scale that requires little understanding.  We \
assume the problem is with students rather than communication: that the \
students either don't have what it takes, or else just don't care.  Outsiders \
are amazed at this phenomenon, but within the mathematical community, we \
dismiss it with shrugs.\
\>", "Text"],

Cell["#7 Jacob T. Schwartz", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Many conventional academic skills amount to the ability to select \
and apply. . . procedures rapidly and correctly....[Computer] courseware can \
concentrate on one skill at a time, in a manner impossible for a textbook and \
hardly available to the classroom teacher, namely by asking the student to \
handle only that part of a procedure on which pedagogical stress is to be \
laid, while other aspects of the same procedure are handled automatically by \
the computer. . . . This scheme, which combines student interaction with \
computer assistance, has the merit of focusing attention on the key strategic \
and conceptual decisions needed to handle a problem. . . This should be of \
significance to both the strong student . . . and the weak student.\
\>", \
"Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["#8 Alfred North Whitehead", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Civilization advances by extending the number of operations we can \
do without thinking about them.  Operations of thought are like cavalry \
charges in a battle - they are strictly limited in number, they require fresh \
horses and must be made only at decisive moments.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
 #9 Lynn Arthur Steen, Past President of the Mathematical \
Association of America\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Mathematics-speaking machines are about to sweep the \
campuses....The ready availability of powerful computers will enable students \
to set new ground rules for college mathematics... Teachers will be forced to \
change their approach and their assignments.  They will no longer be able to \
teach as they were taught in the pencil and paper era... 

Undergraduate mathematics will become more like real mathematics . . . By \
using machines to expedite calculations, students can experience mathematics \
as it really is - as a tentative, exploratory discipline in which risks and \
failures yield clues to success. Computers change our perceptions of what is \
possible and what is valuable. . .

Weakness in algebra skills will no longer prevent students students from \
pursuing studies that require college mathematics .  . .

\
\>", "Text",
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  AspectRatioFixed->True],

Cell["#10 Henri Lebesgue", "Subsection",
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Cell["\<\
Our teaching does not make full use of that historic event, which \
is probably the most important event in the history of science, namely, the \
invention of the decimal system of numeration.

Measure and Integral HoldenDay 1966 K. 0. May Ed.



\
\>", "Text",
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Cell["Jerry's favorites from the modern era", "Title"],

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Cell[" Gian - Carlo Rota", "Subsection",
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Cell["\<\
The student needs to develop an understanding, however partial and  \
imperfect, by descriptions rather than definitions, by typical examples \
rather than grandiose theorems....

The facts of mathematics are verified and presented by the axiomatic method. \
One must guard, however, against confusing the presentation of mathematics \
with the content of mathematics. An axiomatic  presenation of a mathematical \
fact differs from the fact that is being presented as medicine differs from \
food. It is true that this particular medicine is necessary to keep \
mathematicians from self-delusions of the mind.  Nonetheless, understanding \
mathematics means being able to forget the medicine and enjoy the food.

The best introduction to mathematics is not achieved by rigorous \
presentation. What one wishes for is a feeling for a piece of mathematics. \
Let the student work with unrigorous concepts that lead as quickly as \
possible to a half-baked understanding of the main results and their \
applications. Rigorous presentation can occur later....to be given only to \
those who develop a genuine interest in mathematics. . .  The axiomatic \
method of presentation has reached a pinnacle of fanaticism in  our time.

The pretense of identifying mathematics with a style of exposition is having \
a corrosive effect on the way mathematics is viewed by scientists in other \
disciplines.

 . . . The mistaken identification of mathematics with the axiomatic method \
has led to a widespread prejudice among scientists that mathematics is \
nothing but a pedantic grammar, suitable only for belaboring the obvious and \
for producing marginal counterexamples to useful facts that are by and large \
true.


Most mathematicians who teach mathematics fail.  They bask in the illusion \
that the majority of their students should become mathematicians or their \
teaching is wasted...

Nowhere in the sciences does one find a wide a gap as that between the \
written version of a mathematical result and the discourse that is required \
to understand the same result. 

It has been an acknowledged fact, since Poincare pointed an accusing finger \
at the Twentieth Century, that much of the mathematics of our time has had \
negative overtones. 


If mathematics were formally true but in no way enlightening, then \
mathematics would be a curious game played by weird people. ,,, \
Mathematicians seldom explicitly acknowledge the phenomenon of \
enlightenment.....

Anyone who is about to teach the undergraduate curriculum should come down to \
earth by looking through the Schaum's outline series before burdening \
students with those well-printed, many colored, highly advertised hardcover \
volumes that are pathetically passed off as text books.

Most elementary probability texts books are carbon copies of each other.
\
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Cell["\<\
Ralph Boas, Past President of the Mathematical Association of \
America\
\>", "Subsection"],

Cell[TextData[{
  StyleBox["\n",
    FontColor->RGBColor[0, 0, 1]],
  "Why do we speak and write about mathematics in ways that interfer so \
dramatically with what we ostensibly want to accomplish?\n\n",
  StyleBox["When you want a young child to learn about cats, do you explain \
that a cat is a relatively small,primarily carnivorous mammal with rectile \
claws and distintive sonic output. Or do you arrange for the child to play \
with lots of kitties and let them form their own first impressions? \n\nWhen \
you want a student to learn about math, do you give a great lecture, \
introducing new ideas, new terminology, new notation Or do you arrange for \
the student to play with lots of math kitties and let them form their own \
first impressions?",
    FontColor->GrayLevel[0]],
  "\n\nAuthors of textbooks need to remember that they are supposed to be \
addressing students, not the teachers...\nContemporary prose style is simpler \
and more direct than the style of the 19th century- except in textbooks of \
mathematics. ....I blame the authors of textbooks for not realizing that \
contemporary students speak a different language.\n\nMathematical skills are \
like any other kind.... If you are learning to play the piano, you usually \
start by practicing under supervision; you don't begin with theoretical \
lectures on acoustical vibrations and the internal structure of the \
instrument. Similarly for mathematical skills.\n\nThe point that a definition \
is satisfactory only if the students understand it was already made by \
Poincare in 1909, but teachers of mathematics seem not to have paid much \
attention to it.\n\n\nAs a means of instruction, lectures ought to have \
become obsolete when the printing press was invented. We had a second chance \
when the Xerox machine was invented, but we muffed it.\n\nOnly professional \
mathematicians learn anything from proofs. Other people learn from \
explanations. A great deal can be accomplished with arguments that fall short \
of formal proofs.\n\n A sweater is what a child puts on when its parent feels \
cold, but a proof is what students have to listen to when the teacher feels \
shaky about a theorem.\n\nExperienced parents know that when a child says \
Why? it doesn't necessarily mean that it wants a reason; it just wants more \
conversation.\n\nIf you are going to explain to an average class how to find \
the distance from a point to a plane, you should  first find the distane  \
from {2,-3,1} to the plane x - 2y - 4 z = 7. After that, the general \
procedure will seem almost obvious. Textbooks used to be written this way.\n\n\
At the beginning, a lot of the students' effort has to go into memorizing \
words, when it could go more advantageously into learning mathematics. Paying \
more attention to vocabulary than content obscures the content.\n\n"
}], "Text"],

Cell["\<\
 Robert White, Past President of the National Academy of \
Engineering\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
If a field ever needed to be brought out of mystery to reality, it \
is calculus. . . Calculus is really exciting stuff, yet [the traditional \
course is] not presenting it as an exciting subject. . . Calculus must become \
a pump instead of a filter in the pipeline.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
 Peter Lax, Past President of the American Mathematical \
Society\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Calculus as currently taught is, alas, full of inert material . . . \
The real crisis is that at present [calculus] is badly taught; the syllabus \
has remained stationary, and modern points of view, especially those having \
to do with the roles of applications and computing are poorly represented. . \
.

There is too much preoccupation with what might be called the magic in \
[traditional] calculus.  For instance, too much time is spent in pulling \
exact integrals out of a hat, and, what is worse, in drilling students how to \
perform this parlor trick.  Summing infinite series is another topic that has \
the aura of a magic trick, and is overemphasized at the expense of the \
concept of approximation.. . . I feel that rigor at this level is misplaced; \
it appears as an arid game to those who understand it, and mumbo jumbo to \
those who don't.. . . Many students have difficulty in grasping the idea that \
the integral of a function over an interval is a number.  The reason is that \
this number is difficult to produce by traditional methods, i.e. by \
antidifferentiation, and so the central idea is lost.  Numerical methods have \
the great virtue that they apply universally.  When special methods are \
introduced to deal with each one of the pitifully small class of \
[differntial] equations that can be handled analytically, students are apt to \
lose sight of the general idea that every differential equation has a \
solution and that this solution is uniquely determined by initial data. . . \
That today we can use computers to explore the solutions of [differential] \
equations is truly revolutionary; we are only beginning to glimpse the \
consequences.
\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
 Lynn Arthur Steen, Past President of the Mathematical Association \
of America\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
[The tradional calculus course deals with] precisely the ability  \
to do [by hand] the kinds of things that calculators and computers are now \
doing. . .  There is a great deal of concern about making sure that freshman \
courses . . . make a significant conribution to broaden the aims of \
undergraduate education - that they help students learn to think clearly, to \
communicate, . . . etc.   There is very, very little in the [traditional] \
calculus course of today that does any of these things. . . .
Mathematics-speaking machines are about to sweep the campuses....The ready \
availability of powerful computers will enable students to set new ground \
rules for college mathematics... Teachers will be forced to change their \
approach and their assignments.  They will no longer be able to teach as they \
were taught in the pencil and paper era... 

Undergraduate mathematics will become more like real mathematics . . . By \
using machines to expedite calculations, students can experience mathematics \
as it really is - as a tentative, exploratory discipline in which risks and \
failures yield clues to success. Computers change our perceptions of what is \
possible and what is valuable. . .

Weakness in algebra skills will no longer prevent students students from \
pursuing studies that require college mathematics .  . .

Mathematics learning will become more active and hence more effective.  By \
carrying most of the calculational burden of mathematics homework, computers \
will enable students to explore a wider variety of examples, to study graphs \
of a quantity and variety unavailable with pencil-and-paper methods, to \
witness the dynamic nature of mathematical processes, and to encourage \
realistic applications using typical-not oversimplified-data.

Students will be able to explore mathematics on their own without, constant \
advice from their instructors.  Although computers will not compel students \
to think for themselves, these machines can provide an environment in which \
student-generated mathematical ideas can survive.

Study of mathematics will build long-lasting knowledge, not just short-lived \
strategies for calculation.  Most students take only one or two terms of \
college mathematics, and quickly forget what little they learned of memorized \
methods for calculation.  Innovative instruction using a new symbiosis of \
machine calculation and human thinking can shift the balance of mathematical \
learning to understanding, insight, and mathematical intuition. \
\>", "Text",\

  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Bill Thurston", "Subsection"],

Cell["\<\
Mathematicians have developed habits of communication that are \
often dysfunctional. We go through the motions of saying for the record what \
the students \[OpenCurlyQuote]ought\[CloseCurlyQuote] to learn while students \
grapple with the more fundamental issues of learning our language and \
guessing at our mental models.  Books compensate by giving samples of how to \
solve every type of homework problem. Professors compensate by giving \
homework and tests that are much easier than the material \
\[OpenCurlyQuote]covered\[CloseCurlyQuote] in the course, and then grading \
the homework and tests on a scale that requires little understanding.  We \
assume the problem is with students rather than communication: that the \
students either don't have what it takes, or else just don't care.  Outsiders \
are amazed at this phenomenon, but within the mathematical community, we \
dismiss it with shrugs.

However, I think the real question for communicating mathematics is how \
language is used; there are many styles of writing, and I think much of \
modern mathematical writing overuses symbols in a way that significantly \
interferes (at least for me) with geometric thinking.  Any language can be \
used to evoke geometry.  We don't need to spell out the equation for a \
`spiral staircase' to get the geometric image, since spiral staircases are \
part of a common assumed culture. Cultural assumptions can be mistaken, but \
for any given audience, there are enough geometric ideas that can be evoked \
by reference, so that
if used with imagination they can go pretty far in describing mathematical \
phenomena geometrically.
\
\>", "Text"],

Cell["Lee Shulman", "Subsection"],

Cell["\<\
[Pedagogical Content Knowledge is the] particular form of content \
knowledge that embodies the aspects of content most germaine to its \
teachability.... the ways of representing and formulating the subject that \
make it comprehensible to others. \
\>", "Text"],

Cell["Paul Halmos", "Subsection"],

Cell["\<\
The job of the teacher is to translate the textbook into the \
vernacular.\
\>", "Text"],

Cell["Saunders MacLane", "Subsection"],

Cell["\<\
                     Intuition - trial - error - speculation - \
conjecture - proof 
is a sequence for understanding of mathematics. 
\
\>", "Text"],

Cell["Reuben Hersh ", "Subsection"],

Cell["\<\
There's another unrecognized cause of the failure [of mathematics \
education]: misconception of the nature of mathematics.

A philosophy of mathematics that obscures the teachability of mathematics is \
unacceptable.
\
\>", "Text"],

Cell["\<\
Ronald Douglas,  Committee on the Mathematical Sciences in the year \
2000\
\>", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
We no longer ask students to understand.  Now  it is [algbebraic] \
manipulation pure and simple. . . .What we're teaching is not only the wrong \
thing- in that it is not what students will use [outside the calculus \
classroom]- it is obsolete [because of computers and calculators]. It is like \
spending all your time in elementary school adding and subtracting and never \
being told what addition and subtraction are for.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[". Jacob T. Schwartz", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Many conventional academic skills amount to the ability to select \
and apply. . . procedures rapidly and correctly....[Computer] courseware can \
concentrate on one skill at a time, in a manner impossible for a textbook and \
hardly available to the classroom teacher, namely by asking the student to \
handle only that part of a procedure on which pedagogical stress is to be \
laid, while other aspects of the same procedure are handled automatically by \
the computer. . . . This scheme, which combines student interaction with \
computer assistance, has the merit of focusing attention on the key stategic \
and conceptual decisions needed to handle a problem. . . This should be of \
significance to both the strong student . . . and the weak student.\
\>", 
  "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Stephen Wolfram", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\

When I started off doing mathematics, I wasn't very good at it.  I never \
learned my multiplication tables and it was certainly the conclusion of my \
teachers at that time that there was no way I would ever go on and do \
anything . . . mathematically oriented.  As it turned out, I found out about \
computers and found out that you could make computers do these kinds of \
things. \
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Ralph Abraham", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Mathematical concepts may be communicated easily in a format which \
combines visual, verbal, and symbolic representations in tight coordination. \
\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Scott Kim", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Before Gutenburg, illustration and type were one in the same; they \
were inseparable.  But afterward, the two disciplines became separate and \
diverged.  Now that we've got  the [graphic computer], I can see a medium \
where they come back together again.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Thomas West", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Perhaps, . . . one should consider teaching mathematics backwards, \
that is, teaching the images and patterns first and teaching the conventional \
symbol system, rules and rigorous processes later.  This kind of fundamental \
change . . . may be worth the trouble, especially if it can be shown that \
some of those who could not do well with elementary mathematics may still do \
superbly well with the more advanced forms. It may require entirely different \
ways of teaching, but it may, in the end be more appropriate for a new era in \
mathematics and work, when all the easy things will be done by machine and \
the hard things will be the only things of value left for humans to do.\
\>", \
"Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[TextData[StyleBox[" Richard Benson",
  Evaluatable->False,
  AspectRatioFixed->True]], "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
There's a terrible problem that I run into in teaching, which is \
that when you tell people something, you keep them from knowing it.  If they \
find it on their own, they'll know it in a way they never will if you tell \
them.  What I try to more and more is to bring students to my studio and get \
them really working.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Samuel Florman", "Subsection"],

Cell[TextData[{
  StyleBox["Recently I met with an engineering administrator at a fine \
university - a liberal, progressive institution where one would expect the \
best sorts of things to be happening.  To my surprise, he complained bitterly \
about the mathematics department. The math professors refused to say even a \
few words to engineering students about ",
    Evaluatable->False,
    AspectRatioFixed->True],
  StyleBox["applicability",
    Evaluatable->False,
    AspectRatioFixed->True,
    FontSlant->"Italic"],
  StyleBox["  of mathematics to engineering, refused to include in their \
classes a few examples of how engineers ",
    Evaluatable->False,
    AspectRatioFixed->True],
  StyleBox["actually",
    Evaluatable->False,
    AspectRatioFixed->True,
    FontSlant->"Italic"],
  StyleBox["  use math. He wanted them to help his students see that \
mathematics was not a mere obstacle to be overcome, but a vital element of \
the profession to which they were committed.  But apparently the mathematics \
professors were determined to teach their subject straight pure on its own \
terms, as if each student were destined to become a Ph. D. in that field. It \
was a matter of pride in their speciality and honor for their department.  \
The engineering administrator was utterly disheartened. And if at a liberal \
institution the math department resists co-operation with the engineering \
school, I can only imagine how frustrating things are in other places and in \
other circumstances. It is difficult enough for engineering deans to achieve \
change within the realm they nominally control. When they go ouside their \
domain - as they must do to revamp the curriculum in a meaningful way - the \
problems seem overwhelming....\n",
    Evaluatable->False,
    AspectRatioFixed->True],
  "At the core of the problem is a combination of both disciplinary hubris \
and academic territoriality, both militating against cooperative ventures \
across disciplinary and administrative boundaries.",
  StyleBox["\n\n\nInstead of trying to interest the students in engineering, \
to nuture enthusiasm for the profession to be their life's calling, the \
[engineering] program was designed to be an obstacle course. The first two \
years were dedicated almost exclusively to mathematics and basic sciences, \
with no effort made to show how these often brutally difficult studies would \
help the future engineer to do constructive work. . . . The Spartan legacy \
dies hard - ' If I had to do it, you can do it.' . . .   If the course of \
study that once produced intrepid engineers is now perceived as suitable for \
nerds, then none but nerds will pursue it.\n\n\nWith a recrafted curriculum, \
introducing real engineering at an early stage and showing it to best \
advantage, the situation can be improved. Instead of a medicinal dose of math \
and science, let freshmen get a taste of engineering design and how \
engineering fits into society at large. Math and science will then take on \
added  meaning and appeal.\n\n",
    Evaluatable->False,
    AspectRatioFixed->True]
}], "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Stephen Jay Gould", "Subsection"],

Cell["\<\
If textbook cloning represented the discovery of a true educational \
optimum . . ., I would not object...Good teaching requires fresh thought and \
genuine excitement... Rote copying can only indicate boredom...A carlessly \
cloned work will not excite students however pretty the pictures.  We will \
not have great texts if authors cannot shape content but must serve a \
commercial master as one cog in an ultimately powerless consortium with other \
packagers.\
\>", "Text"],

Cell["Jeff Knisley", "Subsection"],

Cell["\<\
Mathematics courses are so locked in that even the suggestion of \
change precipitates a crisis.\t\t\
\>", "Text"],

Cell["Andre Weil", "Subsection"],

Cell["\<\
[If] logic is the hygiene of the mathematician, it is not his \
source of food.
\
\>", "Text"],

Cell["\<\
Andrew Gleason,Past President of the American Mathematical \
Society\
\>", "Subsection"],

Cell["\<\
There are two kinds of rigor: Intellectual rigor and mathematical \
rigor.  They are not always the same.
\
\>", "Text"],

Cell["Philip Davis", "Subsection"],

Cell["\<\
Classical proof must must move over and share the educational stage \
with other means of arriving at mathematical evidence. Mathematical textbooks \
must modify the often deadening rigity of the  Euclidean model of exposition.

The capabilities of all mathematicians are elevated by their association with \
computation.  ... mathematics develops in such a way that the role of the \
mathematician is always manifest. . . 

In connection with computer visualization, I have argued for the recognition \
of visual theorems where what the eye sees need not be verbalized let alone \
formalized in traditional formal mathematical language.
\
\>", "Text"],

Cell["William Boyce 1995", "Subsection"],

Cell["\<\
The traditional course on differential equations that I took many \
years ago and taught up until the past couple of years dealt almost entirely \
with derivation of formulas for solutions of various kinds of differential \
equations,... Most of the algebraic manipulations featured in the traditional \
course can now easliy be relegated to a computer. ... A good deal of this \
traditional material can be dispensed with and replaced by experiences more \
valuable for the student... A decrease of time spent on symobol manipulation \
by hand should provide an opportunity for more emphasis on conceptual \
understanding,...Details of mathematical procedures and algorithms are \
rapidly forgotten unless they are used frequently, but underlying concepts \
and ideas become part of an individual's mindset.
\
\>", "Text"],

Cell["Stephen Boyd", "Subsection"],

Cell[TextData[{
  "I can't say too strongly how unimportant symbolic manipulation is in \
engineering. We see the effects of MSM (mindless symbolic manipulation) every \
day: Students who can integrate",
  Cell[BoxData[
      \(\(\(\ \ \)\(t^3\ \ Cos[t]\)\)\)]],
  " but have no idea what they are doing and why.... Not only is the material \
of an MSM course useless and outdated, but the message it sends to students \
is bad. It basically suggests that learning math is mastering a certain list \
of stimulus-response behaviors.....No wonder we in EE and CS and other \
engineering fields rely less and less on people in math to deliver the basic \
training needed in our fields."
}], "Text"],

Cell["David Olson", "Subsection"],

Cell["\<\
Visual mathematics: no magic bullets, but such tantalizing \
potential!
\
\>", "Text"],

Cell["Tony Siegman, Stanford Electrical Engineer", "Subsection"],

Cell[TextData[{
  "So far as differential equations are concerned, from looking back at what \
I did 4o years ago, compared to what I practice now, it seems to me that I'd \
eliminate a large amount of DE solving and categorizing tricks I learned in \
those days. My current view is: If ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " knows how to solve it analytically, then I don't need to know. If ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " doesn't know how to solve it analytically, hell, I'll just solve it \
numerically."
}], "Text"],

Cell["V. I. Arnold", "Subsection"],

Cell["\<\
The axiomization and algebraization of mathematics, after more than \
50 years, has led to the illegibility so such a large number of mathematical \
texts that the threat of complete loss of contact with physics and the \
natural sciences has been realized.\
\>", "Text"],

Cell["Matthias Kawski", "Subsection"],

Cell["\<\
Many mathematicians seem to be frozen in the past.
Many of today's math courses actually look to others a lot like 1860 \
understanding of [math] looks to us.
We better learn to acknowledge that math is incredibly sloppy today, just as \
it was in 1860. For me, the daily use of computer algebra systems has opened \
my eyes; others may find other ways of waking up.\
\>", "Text"],

Cell["", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Jerry's favorites from the masters", "Title"],

Cell["Rene Descartes", "Subsection"],

Cell["\<\
The more it approaches intuition, the more reliable the deduction \
is.

Intuition has two distinctive features - it is an instantaneous act and it \
consists of clear grasp of an idea.

Intuition and deduction should be trustworthy processes which we can use to \
lead to genuine knowledge.
      
There are two ways of arriving at knowledge - through experience and \
deduction.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Gottfried Wilhelm von Leibniz", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
It is unworthy of excellent persons to lose hours like slaves in \
the labor of calculation.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Antoine Arnaud and Pierre Nicole", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Some defects ordinarily found in the method used by mathematicians:
Defect 1: To pay more attention to proof than to evidence, and to try to \
convince rather than enlighten the mind.
Defect 2: To prove things that do not require proof.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Blaise Pascal", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
[The normal student attempts to fix formal terminology] in his \
memory because it means nothing to his intelligence.

Never undertake to prove things that are so evident in themselves that one \
has nothing clearer by which to prove them.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Leonhard Euler", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
[Some facts] can be seen more clearly by an example than by a \
proof.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Augusta Ada Byron", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
 [A good calculating machine could] weave algebraic patterns just \
as the Jacquard loom weaves flowers and leaves.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" J.L. Lagrange", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
We must agree that the idea [of formal definition of limit] is not \
sufficiently clear to use as a basis for a science in which certainty must be \
founded on evidence, especially when presented to beginners.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Voltaire", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Nothing is more worthy of respect than an abuse dating from ancient \
times.
Dr. Pangloss in Voltaire's Candide.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Johann Wolfgang von Goethe ", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Is it life, I ask, is it even prudence,
To bore thyself and bore the students?\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\

All theory, dear friend, is grey, 
but the golden tree of actual life springs ever green.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Schopenhauer ", "Subsection"],

Cell["Thoughts die the moment they are embodied by words.", "Text"],

Cell[" Henri Poincare ", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
When a student commences seriously to study mathematics, he \
believes he knows what a fraction is, what continuity is, and what the area \
of a curved surface is; he considers evident, for example that a continuous \
function cannot change its sign without vanishing.  If [the teacher] says to \
him: No that is not evident; I must prove it to you, . . . what would this \
unfortunate student think? He will think that the science of mathematics is \
only an arbitrary accumulation of useless subleties; either he will be \
disgusted with it or he will amuse himself with it as a game and arrive at a \
state of mind analogous to that of the Greek sophists.

Can one ever understand a theory if one builds it up right from the start in \
the definitive form that rigorous logic imposes?  No; one does not really \
understand it . . .one retains it only by learning it by heart.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" W. B. Ford ", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
I am led to the idea which in substance is that the ordinary first \
course in calculus should be more largely graphical.  The question that the \
beginner desires answered is what is what is the calculus about - -what does \
it do? . . . Let us be satisfied with a rough definition of the derivative, \
allowing intuition and not rigor to be the chief factor in supplying it and \
therefore drawing very largely on the geometrical side. . .\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[" Alfred North Whitehead", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Elementary mathematics . . . must be purged of every element which \
can only be justified by reference to a more prolonged course of study. There \
can be nothing more destructive of true education than to spend long hours in \
the acquirement of ideas and methods that lead nowhere. . . . [The] elements \
of mathematics should be treated as the study of fundamental ideas, the \
importance of which the student can immediately appreciate; . . . every \
proposition and method which cannot pass this test, however important for a \
more advanced study, should be ruthlessly cut out.

The solution I am urging is to eradicate the fatal disconnection of topics \
which kills the vitality of our modern curriculum.  There is only one subject \
matter, and that is Life in all its manifestations. Instead of this single \
unity, we offer children Algebra, from which nothing follows. . .

Civilization advances by extending the number of operations we can do without \
thinking about them.  Operations of thought are like cavalry charges in a \
battle - they are strictly limited in number, they require fresh horses and \
must be made only at decisive moments.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Henri Lebesgue", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
There is a real hypocrisy, quite frequent in the teaching of \
mathematics.  The teacher takes verbal precautions, which are valid in the \
sense he gives them, but that the students most assuredly will not understand \
the same way.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\

Unfortunately competitive examinations often encouage [an educational] \
deception.  The teachers must train their students to answer little \
fragmentary questions quite well, and they give them model answers that are \
often veritable masterpieces and that leave no room for criticism.  To \
achieve this, the teachers isolate each question from the whole of \
mathematics and create for this question alone a perfect language without \
bothering about its relationships to other questions.  Mathematics is no \
longer a monument but a heap.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\

If the limit of the [polygonal areas] had been designated as the 'tarababump' \
of the circle, one would not be permitted to derive from it the value of the \
tarababump of the sector. . . We allow ourselves to do it because instead of \
the word tarababump, we used the word area! . . . imagine the inevitable \
confusion that will be caused by making students identify this new area with \
the areas to which they are accustomed.

Our teaching does not make full use of that historic event, which is probably \
the most important event in the history of science, namely, the invention of \
the decimal system of numeration.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["George D. Birkhoff", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
From the beginning Nature has led the way and established the \
pattern which mathematics, the language of nature, must follow.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Winston Churchill", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
Personally, I am always ready to learn, although I do not always \
like being taught.\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["Jacques Hadamard", "Subsection",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
The talent [of being able to rapidly make very complicated \
calculations in the head] is, in reality, distinct from mathematical ability. \
 Very few known mathematicians are said to have possessed it. . .

I insist that words are totally absent from my mind when I really think. . . \
. Even after reading or hearing a question, every word disappears at the very \
moment I am beginning to think it over; words do not reappear in my \
consciousness before I have accomplished or given up the research . . . and I \
fully agree with Schopenhauer when he writes, Thoughts die the moment they \
are embodied by words  I think it is also essential to emphasize that I \
behave in this way not only about words, but even about algebraic signs.  I \
use them when dealing with easy calculations; but whenever the matter looks \
more difficult, they become too heavy baggage for me.\
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The words or language, as they are written or spoken do not seem to \
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images which can be voluntarily reproduced and combined.

We will never solve the problems of the world from the level of thinking we \
were at when we created them.\
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At a great distance from its empirical source. . ., a mathematical \
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[Mathematics] must remain . . . as a unified vital strand in the \
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[The student] refuses to be bored by diffuseness and general \
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non-essential, and which for the sake of a systematic set of axioms, \
deliberately conceals the facts to which the growth of the subject [of \
calculus] is due.\
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It's all visual.  It's hard to explain. . . . Ordinarily I try to get the \
pictures clearer, but in the end mathematics can take over and be more \
efficient at communicating the idea of the picture.  In certain problems that \
I have done it was necessary  to continue the development of the picture as \
the method before the mathematics could really be done.\
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Many of the math books . . . are full of  . . . nonsense - of carefully and \
precisely defined words that are used by pure mathematicians in their most \
subtle and and difficult analyses, and are used by nobody else . . ..  The \
real problem in speech is not precise leanguage.  The problem is clear \
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Mathematics today is a vital, vibrant discipline composed of many parts which \
in mysterious ways influence and enrich each other . . ..  It is beginning to \
emerge from a self imposed isolation [from its sister disciplines] and listen \
with attention to the voices of nature.\
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\"As societies become more complex in structure and resources, the \
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and what is acquired in school.  This danger was never greater than the \
present time, on account of the rapid growth in the last few centuries of \
knowledge and technical modes of skill.\"\
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    CellMargins->{{24, 24}, {0, 10}},
    CellGroupingRules->{"SectionGrouping", 30},
    PageBreakBelow->False,
    CellFrameMargins->{{15, Inherited}, {Inherited, Inherited}},
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    TextAlignment->Center,
    LineSpacing->{1.4, 1},
    FontFamily->"Times",
    FontSize->24,
    FontWeight->"Bold",
    FontColor->GrayLevel[1],
    Background->RGBColor[0, 0.392187, 0]],
  
  Cell[StyleData["PrefaceTitle", "Presentation"],
    CellMargins->{{24, Inherited}, {60, Inherited}},
    TextAlignment->Center,
    FontSize->38,
    FontColor->GrayLevel[1],
    Background->RGBColor[0.596078, 0.65098, 0.0196078]],
  
  Cell[StyleData["PrefaceTitle", "Printout"],
    CellMargins->{{0, Inherited}, {0, Inherited}},
    FontSize->16,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]],
  
  Cell[StyleData["PrefaceTitle", "TwoColumn"],
    CellFrame->{{1, 1}, {0, 5}},
    CellMargins->{{0, Inherited}, {0, Inherited}},
    FontSize->16,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Special Body Text and Index", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Accident"],
    CellFrame->3,
    ShowCellBracket->False,
    CellMargins->{{24, 24}, {0, 10}},
    CellFrameMargins->{{15, Inherited}, {Inherited, Inherited}},
    TextAlignment->Center,
    LineSpacing->{1.4, 1},
    FontFamily->"Times",
    FontSize->24,
    FontWeight->"Bold",
    FontColor->RGBColor[1, 0, 0]],
  
  Cell[StyleData["Accident", "Presentation"],
    CellMargins->{{24, Inherited}, {60, Inherited}},
    TextAlignment->Center,
    FontSize->36],
  
  Cell[StyleData["Accident", "Printout"],
    CellFrame->2,
    CellMargins->{{0, Inherited}, {0, Inherited}},
    FontSize->16,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]],
  
  Cell[StyleData["Accident", "TwoColumn"],
    CellFrame->2,
    CellMargins->{{0, Inherited}, {0, Inherited}},
    FontSize->16,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["ContentsText"],
    CellMargins->{{50, 10}, {5, 5}},
    FontFamily->"Times",
    FontSize->16],
  
  Cell[StyleData["ContentsText", "Presentation"]],
  
  Cell[StyleData["ContentsText", "Printout"],
    FontColor->GrayLevel[0],
    Background->None],
  
  Cell[StyleData["ContentsText", "TwoColumn"],
    FontColor->GrayLevel[0],
    Background->None]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Special1"],
    CellDingbat->"\[EmptySquare]",
    ShowClosedCellArea->True,
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    FontFamily->"Times",
    FontSize->14,
    FontWeight->"Bold",
    FontColor->RGBColor[0.689998, 0.0899977, 0.119997]],
  
  Cell[StyleData["Special1", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["Special1", "Printout"],
    FontSize->12,
    FontColor->GrayLevel[0]],
  
  Cell[StyleData["Special1", "TwoColumn"],
    FontSize->12,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Special2"],
    CellMargins->{{6, 0}, {0, 0}},
    CellGroupingRules->{"SectionGrouping", 40},
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    TextAlignment->Center,
    FontFamily->"Courier",
    FontSize->10,
    FontColor->GrayLevel[0.333333]],
  
  Cell[StyleData["Special2", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["Special2", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0]],
  
  Cell[StyleData["Special2", "TwoColumn"],
    FontSize->10,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Special3"],
    CellDingbat->"\[GraySquare]",
    ShowClosedCellArea->True,
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    TextAlignment->Left,
    FontFamily->"Courier",
    FontSize->10,
    FontColor->GrayLevel[0.333333]],
  
  Cell[StyleData["Special3", "Presentation"]],
  
  Cell[StyleData["Special3", "Printout"],
    FontColor->GrayLevel[0]],
  
  Cell[StyleData["Special3", "TwoColumn"],
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Special4"],
    ShowClosedCellArea->True,
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    TextAlignment->Center,
    FontFamily->"Courier",
    FontSize->10,
    FontColor->GrayLevel[0.333333]],
  
  Cell[StyleData["Special4", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["Special4", "Printout"],
    FontColor->GrayLevel[0]],
  
  Cell[StyleData["Special4", "TwoColumn"],
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Special5"],
    ShowClosedCellArea->True,
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    TextAlignment->Center,
    FontFamily->"Courier",
    FontSize->10,
    FontColor->GrayLevel[0.333333]],
  
  Cell[StyleData["Special5", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["Special5", "Printout"]],
  
  Cell[StyleData["Special5", "TwoColumn"]]
  }, Closed]],
  
  Cell[StyleData["IndexEntry"],
    ShowCellBracket->False,
    CellMargins->{{15, 5}, {0, 5}},
    PageBreakBelow->False,
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    ParagraphIndent->-40,
    StyleMenuListing->None,
    FontSize->16],
  
  Cell[StyleData["IndexSubEntry"],
    ShowCellBracket->False,
    CellMargins->{{45, 5}, {0, 0}},
    DefaultFormatType->DefaultTextFormatType,
    DefaultInlineFormatType->DefaultInputInlineFormatType,
    ParagraphIndent->-40,
    StyleMenuListing->None,
    FontSize->16]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for License Agreement", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["LicenseHeading"],
    ShowCellBracket->True,
    ShowGroupOpenCloseIcon->True,
    CellMargins->{{24, 24}, {-1, 2}},
    CellGroupingRules->{"SectionGrouping", 40},
    PageBreakBelow->False,
    CounterIncrements->"Subsection",
    CounterAssignments->{{"Subsubsection", 0}},
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->12,
    FontWeight->"Bold",
    FontColor->RGBColor[0.4, 0.300008, 0.6]],
  
  Cell[StyleData["LicenseHeading", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["LicenseHeading", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]],
  
  Cell[StyleData["LicenseHeading", "TwoColumn"],
    FontSize->10,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["LicenseText"],
    CellFrame->True,
    ShowCellBracket->False,
    CellMargins->{{24, 24}, {5, -1}},
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->12,
    Background->RGBColor[1, 0.537743, 0.509071]],
  
  Cell[StyleData["LicenseText", "Presentation"],
    FontSize->18],
  
  Cell[StyleData["LicenseText", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]],
  
  Cell[StyleData["LicenseText", "TwoColumn"],
    FontSize->10,
    FontColor->GrayLevel[0],
    Background->GrayLevel[1]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Automatic Numbering", "Section"],
  
  Cell["\<\
The following styles are useful for numbered equations, figures, \
etc.  They automatically give the cell a FrameLabel containing a reference to \
a particular counter, and also increment that counter.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["NumberedEquation"],
    CounterIncrements->"NumberedEquation"],
  
  Cell[StyleData["NumberedEquation", "Presentation"]],
  
  Cell[StyleData["NumberedEquation", "Printout"]],
  
  Cell[StyleData["NumberedEquation", "TwoColumn"]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["NumberedFigure"],
    CellFrameLabels->{{None, None}, {Cell[ 
            TextData[ {"Figure ", 
              CounterBox[ "NumberedFigure"]}]], None}},
    CounterIncrements->"NumberedFigure",
    FormatTypeAutoConvert->False,
    FontFamily->"Times"],
  
  Cell[StyleData["NumberedFigure", "Presentation"],
    CellMargins->{{24, Inherited}, {20, Inherited}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["NumberedFigure", "Printout"],
    CellMargins->{{14, Inherited}, {Inherited, Inherited}},
    FontSize->10],
  
  Cell[StyleData["NumberedFigure", "TwoColumn"],
    CellMargins->{{14, Inherited}, {Inherited, Inherited}},
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["NumberedTable"],
    CellMargins->{{6, Inherited}, {Inherited, Inherited}},
    CellFrameLabels->{{None, None}, {Cell[ 
            TextData[ {"Table ", 
              CounterBox[ "NumberedTable"]}]], None}},
    CounterIncrements->"NumberedTable",
    FormatTypeAutoConvert->False,
    FontFamily->"Times"],
  
  Cell[StyleData["NumberedTable", "Presentation"],
    CellMargins->{{24, Inherited}, {20, Inherited}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["NumberedTable", "Printout"],
    CellMargins->{{14, Inherited}, {Inherited, Inherited}},
    FontSize->10],
  
  Cell[StyleData["NumberedTable", "TwoColumn"],
    CellMargins->{{14, Inherited}, {Inherited, Inherited}},
    FontSize->10]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Headers and Footers", "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontSize->10],
  
  Cell[StyleData["Footer"],
    CellMargins->{{0, 0}, {0, 4}},
    StyleMenuListing->None,
    FontSize->9],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Palette Styles", "Section"],
  
  Cell["\<\
The cells below define styles that define standard \
ButtonFunctions, for use in palette buttons.\
\>", "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, After]}]&)}],
  
  Cell[StyleData["Evaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["EvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Hyperlink Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making hypertext \
ButtonBoxes.  The \"Hyperlink\" style is for links within the same Notebook, \
or between Notebooks.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontSize->14,
    FontColor->RGBColor[0, 0.392187, 0],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontColor->GrayLevel[0],
    Background->GrayLevel[1],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["Hyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    Background->GrayLevel[1],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MEIHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontSize->14,
    FontWeight->"Bold",
    FontColor->RGBColor[0.650004, 0.680003, 0.0800031],
    Background->RGBColor[0, 0.392187, 0],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Come visit us!"}],
  
  Cell[StyleData["MEIHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    Background->GrayLevel[1],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["MEIHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    Background->GrayLevel[1],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["BasicsHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontColor->RGBColor[0.848096, 0.171878, 0.228321],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Go to Basics"}],
  
  Cell[StyleData["BasicsHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["BasicsHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["BasicsIndexHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontColor->RGBColor[0.848096, 0.171878, 0.228321],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2], 
        FrontEnd`SelectionMove[ 
          FrontEnd`SelectedNotebook[ ], Next, CellGroup], 
        FrontEndToken[ "SelectionCloseAllGroups"], 
        FrontEndToken[ "OpenCloseGroup"]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Link into Basics"}],
  
  Cell[StyleData["BasicsIndexHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["BasicsIndexHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["TutorialsHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontColor->RGBColor[0.0199588, 0.346716, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Go to Tutorials"}],
  
  Cell[StyleData["TutorialsHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["TutorialsHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["TutorialsIndexHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontColor->RGBColor[0.0199588, 0.346716, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2], 
        FrontEnd`SelectionMove[ 
          FrontEnd`SelectedNotebook[ ], Next, CellGroup], 
        FrontEndToken[ "SelectionCloseAllGroups"], 
        FrontEndToken[ "OpenCloseGroup"]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Link into Tutorials"}],
  
  Cell[StyleData["TutorialsIndexHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["TutorialsIndexHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GiveItaTryHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontColor->RGBColor[0.497459, 0.196094, 0.543877],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Go to GiveItaTry"}],
  
  Cell[StyleData["GiveItaTryHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["GiveItaTryHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GiveItaTryIndexHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontColor->RGBColor[0.497459, 0.196094, 0.543877],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2], 
        FrontEnd`SelectionMove[ 
          FrontEnd`SelectedNotebook[ ], Next, CellGroup], 
        FrontEndToken[ "SelectionCloseAllGroups"], 
        FrontEndToken[ "OpenCloseGroup"]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Link into GiveItaTry"}],
  
  Cell[StyleData["GiveItaTryIndexHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["GiveItaTryIndexHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["LiteracyHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontColor->RGBColor[1, 0.433326, 0],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Go to Literacy"}],
  
  Cell[StyleData["LiteracyHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["LiteracyHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["LiteracyIndexHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontColor->RGBColor[1, 0.433326, 0],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2], 
        FrontEnd`SelectionMove[ 
          FrontEnd`SelectedNotebook[ ], Next, CellGroup], 
        FrontEndToken[ "SelectionCloseAllGroups"], 
        FrontEndToken[ "OpenCloseGroup"]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Link into Literacy"}],
  
  Cell[StyleData["LiteracyIndexHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["LiteracyIndexHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["PreviewHyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->None,
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontColor->GrayLevel[0.250004],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2], 
        FrontEndToken[ "OpenCloseGroup"]}]&),
    Active->True,
    ButtonFrame->"None",
    ButtonNote->"Preview of Lesson"}],
  
  Cell[StyleData["PreviewHyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["PreviewHyperlink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"]],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["RefGuideLink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"]],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}],
  
  Cell[StyleData["GettingStartedLink", "TwoColumn"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["OtherInformationLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"]],
  
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