(* Content-type: application/vnd.wolfram.cdf.text *)
(*** Wolfram CDF File ***)
(* http://www.wolfram.com/cdf *)
(* CreatedBy='Mathematica 8.0' *)
(*************************************************************************)
(* *)
(* The Mathematica License under which this file was created prohibits *)
(* restricting third parties in receipt of this file from republishing *)
(* or redistributing it by any means, including but not limited to *)
(* rights management or terms of use, without the express consent of *)
(* Wolfram Research, Inc. *)
(* *)
(*************************************************************************)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 835, 17]
NotebookDataLength[ 33807, 856]
NotebookOptionsPosition[ 29431, 713]
NotebookOutlinePosition[ 31514, 786]
CellTagsIndexPosition[ 31360, 777]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["What is a Theorist?", "Title",
CellChangeTimes->{{3.493568928203*^9, 3.493568928876*^9}},
LineSpacing->{1.5, 2},
CellTags->"c:1"],
Cell["George Hrabovsky", "Author",
CellChangeTimes->{{3.493568933612*^9, 3.493568939712*^9}}],
Cell["MAST", "Institution",
CellChangeTimes->{{3.493568940932*^9, 3.4935689415690002`*^9}}],
Cell[TextData[{
Cell[TextData[StyleBox["1. ", "SectionNumber"]], "SectionDingbat"],
"Introduction"
}], "Section"],
Cell["\<\
Hello and welcome to this column. I hope to entertain and inform you with a \
useful resource relating both the methods and philosophies of theoretical \
physics.\
\>", "Text",
CellChangeTimes->{{3.408336454378544*^9, 3.4083365078153825`*^9}, {
3.493568982525*^9, 3.4935689835699997`*^9}},
LineSpacing->{1.5, 3}],
Cell["\<\
\tThe reason for this column is that there are plenty of articles on \
experiments and how to make observations and I thought it would be nice if \
there were a similar resource for those who seek to understand and explore \
theory. I will be presenting methods and ways of thinking about theory. I \
will also be adding material on mathematics.
\tThis column then has the role of acting as guide to the landscape of theory \
in general and theoretical physics in particular.
\tEach column after this one will begin with a statement of what was done in \
the previous column. Each column will then have an exposition. This may take \
up more than one section of the column. The exposition will be followed by a \
list of books that I like that are relevant to the subject of the chapter, \
along with comments about why I like the book(s) in question. Then you will \
find what is called The Theory Challenge; a question that I pose for you to \
attempt before reading the next column (where I will answer the Theory \
Challenge). Then I will include a study guide of what order to read \
supplemental material to get the most out of your experience and what sorts \
of things you need to be able to do to move on. The study guide may also \
suggest project ideas for expanding the material in useful ways. Finally, \
there will be a set of exercises that will help you to mastering the \
techniques in the column and to expand on it.\
\>", "Text",
CellChangeTimes->{
3.408333515813094*^9, {3.4083367176671343`*^9, 3.408336723996235*^9}, {
3.4935689996219997`*^9, 3.493569123282*^9}, {3.493569153891*^9,
3.493569155014*^9}},
LineSpacing->{1.5, 3},
FontSize->12],
Cell[TextData[{
Cell[TextData[StyleBox["2. ", "SectionNumber"]], "SectionDingbat"],
"Introduction to this Article"
}], "Section",
CellChangeTimes->{{3.5632136217165375`*^9, 3.563213629599988*^9}},
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:2"],
Cell[TextData[{
"The goal of this column is to help you to study theoretical physics and be \
able to apply it as the basis of our own individual scientific \
investigations. So, if we are interested in cell biology, we must keep in the \
back of our minds that we are looking for possible ways of applying what we \
are studying to that science.\n\tIn this column we will begin at the \
beginning. We will start with the study of mechanics. We will also develop \
the necessary mathematics as we go. We will cover the principles of \
conservation laws, harmonic motion, and rigid bodies before deciding to move \
on to the next subject. \n\tThe conservation laws of mechanics are the \
conservation of energy, the conservation of momentum, and the conservation of \
angular momentum. To understand the conservation of energy we will need to \
understand the geometry of motion, a subject called ",
StyleBox["kinematics",
FontSlant->"Italic"],
". That will be our actual starting point."
}], "Text",
CellChangeTimes->{
3.40833352156136*^9, {3.4935691612530003`*^9, 3.493569198249*^9},
3.493569239972*^9},
LineSpacing->{1.5, 3},
FontSize->12],
Cell[TextData[{
Cell[TextData[StyleBox["3. ", "SectionNumber"]], "SectionDingbat"],
"The Nature of Physics"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:2"],
Cell[TextData[{
"Physics is a science, perhaps the most fundamental. This means that we base \
all of our knowledge on nature, not simply on good ideas. When we have a good \
idea we must always compare that with nature. If our idea is not supported by \
nature then our idea must be discarded or changed to conform with nature. To \
compare with nature we must make measurements of nature and conduct \
experiments.\n\tAn experiment is a means of duplicating a natural phenomena \
in a laboratory. This can be our beginning point, we measure something in \
nature. If we measure enough things we will eventually be able to make \
general statements about what we are measuring.\n\tSo long as such general \
statements are based upon what is measured, they can be considered as true. \
Then we can make predictions using this assumption. These predictions can \
then be tested experimentally. This is called a ",
StyleBox["model",
FontSlant->"Italic"],
". These experimental tests are the ultimate test of any idea, and are the \
basis of scientific truth.\n\tIn physics, we begin by taking the simplest \
possible point of view for any phenomena. Then we study this simple model \
until we understand it. Once we understand it we can begin to make the model \
more realistic by adding complications that were removed by our \
simplification."
}], "Text",
CellChangeTimes->{3.408333525517048*^9},
LineSpacing->{1.5, 3},
FontSize->12],
Cell[CellGroupData[{
Cell[TextData[{
Cell[TextData[{
StyleBox[
CounterBox["Section"], "SectionNumber"],
StyleBox[". ", "SectionNumber"]
}], "SectionDingbat"],
"What is Theoretical Science?"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:2"],
Cell["\<\
To answer this, we begin with the theorist. A theorist is a scientist who \
specializes in finding patterns in experimental or observation data and then \
making predictions assuming those patterns to be reality. Every theorist, \
like every other scientist, has a slightly different approach. Despite this, \
there are some things common to all of us:\
\>", "Text",
CellMargins->{{Inherited, 20}, {Inherited, Inherited}},
CellChangeTimes->{3.408333530704507*^9},
LineSpacing->{1.5, 3},
FontSize->12],
Cell["\<\
A willingness to approach a problem from any direction that seems likely \
yield a solution.\
\>", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.408333554368534*^9}, {
3.4083340804149523`*^9, 3.4083340844407406`*^9}, {3.493569325809*^9,
3.493569325817*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["A sense of great excitement about what we are doing.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336412734976`*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["A willingness to work hard.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336437770977`*^9}, {3.4083337192055583`*^9,
3.408333719225587*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["An intuition about the subject of our research.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336437770977`*^9}, {3.4083337192055583`*^9,
3.408333723952384*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["A good amount of creativity.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336437770977`*^9}, {3.4083337192055583`*^9,
3.4083337294002175`*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["A sense of the great beauty in science.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336437770977`*^9}, {3.4083337192055583`*^9,
3.4083337338365965`*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["The feeling that doing science is fun.", "Item1Numbered",
CellChangeTimes->{{3.4083335494514637`*^9, 3.4083335570023212`*^9}, {
3.4083336412734976`*^9, 3.4083336437770977`*^9}, {3.4083337192055583`*^9,
3.408333735939621*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell[TextData[{
"But wait a minute! Don't all scientists have these traits?\n\tTrue enough; \
what makes a theorist different is not their attitude about \
science\[LongDash]rather it is in their approach. Instead of verifying that \
an idea is true the theorist often invents the idea to be proven. Of course, \
to an extent, all scientists do this. What the theorist brings is \
specialization. We are skilled at putting an idea into the right language to \
be tested. We also develop many of the mathematical and computational methods \
to make sure an idea is consistent with what we already understand to be \
true. Once a new idea can is shown to be both self-consistent and in keeping \
with what we believe to be true, it can then be tested experimentally.\n\tIt \
is important to realize that before an idea can be called a theory, it is \
subjected first to proof of internal self-consistency and then is shown to be \
consistent with the current body of scientific knowledge. Any inconsistencies \
must be identified and explained, otherwise the proposed theory must be \
considered to be unproven.\n\tAt the heart of science there is a fundamental \
connection between theory and experiment. Without an experimental \
verification theorizing is either pure philosophy or pure mathematics; \
neither of which are really science. Similarly, experimentation without a \
theoretical background is like a ship running full speed without a rudder.\n\t\
One difficulty that people experience when learning and doing science is the \
need for exact terms and precise ideas. We believe that ultimately the ideas \
of science can be expressed simply. The combination of the need for \
precision of expression and the fundamental simplicity we believe in allows \
us to use mathematics to express scientific ideas. One of my goals, then, for \
this book will be to provide some of these mathematical tools for you.\n\tOne \
of the startling things about science is how much of it is based upon \
approximations. The most useful type of approximation is a ",
StyleBox["model",
FontSlant->"Italic"],
". Almost all of science is based on the use of models. Some are physical, \
some chemical, most are mathematical, and many are performed on a computer. \
The theorist invents models to ask \"what-if\" questions of existing ideas. \
These lead to predictions, which in turn lead to experiments to test the \
predictions. These experiments lead to new data being collected, which can \
then be analyzed for new patterns, new models, to emerge. And science marches \
on..."
}], "Text",
LineSpacing->{1.5, 3},
FontSize->12]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
Cell[TextData[{
StyleBox[
CounterBox["Section"], "SectionNumber"],
StyleBox[". ", "SectionNumber"]
}], "SectionDingbat"],
"\[ThinSpace]How is Theory Done?"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:3"],
Cell["\<\
Now that we have explored what theory is, it is reasonable to ask the \
question, \"How is theory done?\"
\tTo actually do theoretical work you must decide on a problem to work on. \
Please, don't try to tackle impossibly difficult problems. There is simply no \
chance in the universe that you, an amateur theorist, are going to be able to \
adequately contribute to the cutting edge of quantum gravity, quantum \
cosmology, string theory, etc., without spending literally decades of your \
life on mastering difficult mathematics and physical concepts on a daily \
basis. Let's be reasonable here. You don't see amateurs trying to build large \
hadron colliders, or space telescopes, or the like. Anyone who claimed they \
were doing so would be viewed with, to put it mildly, some skepticism. It is \
no different for theorists; choose a problem that you have a chance of solving.
\tLet's say that you have, in fact, chosen a problem to work on. One that you \
think you can solve. How do you know that you can solve it? The smart-aleck \
answer would be to solve it and find out.
\tFor problems where you are trying to calculate something, or to derive a \
formula, ask yourself these questions:\
\>", "Text",
CellChangeTimes->{3.408335124155778*^9},
LineSpacing->{1.5, 3},
FontSize->12],
Cell[CellGroupData[{
Cell[TextData[StyleBox["Can you define the problem exactly?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.40833513663372*^9, 3.4083351366437345`*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell[TextData[StyleBox["Can you define what you are trying to find, or to \
derive?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.4083351381759377`*^9, 3.408335147389186*^9}}],
Cell[TextData[StyleBox["What are the fundamental constants involved with the \
problem?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.4083351538484735`*^9, 3.4083351564021454`*^9}}],
Cell[TextData[StyleBox["What are the variables?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.408335162320656*^9, 3.408335166236286*^9}}],
Cell[TextData[StyleBox["What variables do you know already?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.408335172955949*^9, 3.4083351759502544`*^9}}],
Cell[TextData[StyleBox["What variables do you need to find?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{{3.408335180647008*^9, 3.4083351815683327`*^9}}],
Cell[TextData[StyleBox["Can you think of a way of relating the unknown \
variables to those that are known?", "Item",
FontSize->12]], "Item1Numbered",
CellChangeTimes->{3.4083351872765408`*^9}]
}, Open ]],
Cell["\<\
If you can answer all of these questions then you can probably solve the \
problem. So go ahead and solve it. The next step after that is to verify that \
you have actually solved the problem. I can highly recommend Georgi Polya's \
book on problem-solving [2]. There are other good books on problem-solving \
too; [3], [4].
\tFor problems where you are trying to prove something to be true you need to \
get a little bit deeper:\
\>", "Text",
LineSpacing->{1.5, 3},
FontSize->12],
Cell["Can you define what you need to prove without ambiguity?", \
"Item1Numbered",
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
Can you make a list of all of your underlying assumptions? If so, do so. \
Justify each assumption with what is accepted as scientific fact.\
\>", "Item1Numbered",
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
Can you determine a direct path of logical reasoning that leads from your \
assumptions to what you need to prove? If so, do so. Justify each step.\
\>", "Item1Numbered",
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
If you assume that what you are to prove is false, can you show that your \
assumptions lead to a contradiction? Again, if so, do so while justifying \
each step.\
\>", "Item1Numbered",
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
There are numerous other strategies for making logical proofs. Look in some \
of the references listed below [5], [6], [7], [8].
\tIf you have an idea that you have demonstrated to be true, then you should \
use it to make some predictions. Change some of your variables and predict \
how this will change your overall results. Change your variables into other \
expressions and study how this changes the behavior of your whole system. \
These predictions form the basis for new experiments.\
\>", "Text",
CellChangeTimes->{3.4083352307390366`*^9},
LineSpacing->{1.5, 3},
FontSize->12]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
Cell[TextData[{
StyleBox[
CounterBox["Section"], "SectionNumber"],
StyleBox[". ", "SectionNumber"]
}], "SectionDingbat"],
"Bibliography"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:4"],
Cell[TextData[{
StyleBox["[1] M. S. Longair, 2003, ",
FontSize->12],
StyleBox["Theoretical Concepts in Physics",
FontSize->12,
FontWeight->"Bold"],
StyleBox[", Second Edition, Cambridge University Press. I used some of the \
notions in this wonderful book in this chapter.",
FontSize->12]
}], "Reference",
CellChangeTimes->{{3.493569472209*^9, 3.493569472217*^9}, {
3.563213794394414*^9, 3.563213795075453*^9}, {3.5632138302484646`*^9,
3.56321385569492*^9}, {3.563213886917706*^9, 3.5632138892568398`*^9}}],
Cell[TextData[{
"[2] G. Polya, 1973, ",
StyleBox["How to Solve It",
FontWeight->"Bold"],
", Princeton University Press. This is a wonderful book and one of the best \
on developing problem-solving strategies."
}], "Reference",
CellChangeTimes->{{3.493569472209*^9, 3.493569472217*^9}, {
3.563213794394414*^9, 3.563213795075453*^9}, {3.5632138302484646`*^9,
3.56321385569492*^9}, 3.563213886917706*^9}],
Cell[TextData[{
"[3] Wayne A. Wickelgren, 1974, ",
StyleBox["How to Solve Problems: Elements of a Theory of Problems and \
Problem Solving",
FontWeight->"Bold"],
", W. H. Freeman and Company (reprinted by Dover Publications, Inc. in 1995 \
under the title ",
StyleBox["How To Solve Mathematical Problems",
FontWeight->"Bold"],
"). An interesting book covering methods of problem solving and an attempt \
to craft a general theory of problem solving."
}], "Reference",
CellChangeTimes->{{3.4935694802869997`*^9, 3.493569488907*^9}}],
Cell[TextData[{
"[4] Steven G. Krantz, 1999, ",
StyleBox["Techniques of Problem Solving",
FontWeight->"Bold"],
", American Mathematical Society. This book describes problem solving \
techniques for a bewildering array of different classes of problems."
}], "Reference",
CellChangeTimes->{{3.493569495059*^9, 3.4935694968450003`*^9}}],
Cell[TextData[{
"[5] Bryan Bunch, 1982, ",
StyleBox["Mathematical Fallacies and Paradoxes",
FontWeight->"Bold"],
", Van Nostrand Rheinholt Company, New York (this book has been reprinted by \
Dover Publications, Inc. in 1997). A delightful book that will demonstrate \
the most common mathematical flaws in reasoning and understanding."
}], "Reference",
CellChangeTimes->{3.493569502924*^9}],
Cell[TextData[{
"[6] V. M. Bradis, V. L. Minkovskii, A. K. Kharcheva, 1959, ",
StyleBox["Lapses in Mathematical Reasoning",
FontWeight->"Bold"],
", Permagon Press, Oxford and London, and The Macmillan Company, New York \
(reprinted by Dover Publications, Inc. in 1999). This has the standard \
Russian mathematical take-no-prisoners attitude that I like. It deals only \
with high school level mathematics."
}], "Reference"],
Cell[TextData[{
"[7] Howard Eves, 1990, ",
StyleBox["Foundations and Fundamental Concepts of Mathematics",
FontWeight->"Bold"],
", PWS Kent Company, Boston (reprinted by Dover Publications, Inc. in 1997). \
An excellent survey of the mathematics important for theory, from the \
perspective of developing logic and reasoning ability. This book is not for \
the faint of heart."
}], "Reference",
CellChangeTimes->{{3.493569525705*^9, 3.493569525707*^9}}],
Cell[TextData[{
"[8] John P. D'Angelo, Douglas B. West, 2000, ",
StyleBox["Mathematical Thinking",
FontWeight->"Bold"],
", Prentice-Hall, Inc. This is a very modern book covering the ideas of \
problem-solving and proofs at an intermediate level. This book assumes some \
familiarity with calculus."
}], "Reference",
CellChangeTimes->{3.493569531218*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
Cell[TextData[{
StyleBox[
CounterBox["Section"], "SectionNumber"],
StyleBox[". ", "SectionNumber"]
}], "SectionDingbat"],
"Study Guide"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:5"],
Cell["\<\
The subject is too huge at this point to do much meaningful study. If you \
feel you must turn to some addition material and begin outside study, I can \
recommend:\
\>", "Text",
CellChangeTimes->{3.4083356910008607`*^9},
LineSpacing->{1.5, 3},
FontSize->12],
Cell[TextData[{
"[9] R. P. Feynman, Robert B. Leighton, Matthew Sands, 1964, ",
StyleBox["The Feynman Lectures on Physics",
FontWeight->"Bold"],
", Addison-Wesley (There is a new version published in 2006 by Benjamin \
Cummings). This is the set of books where I first learned physics back in \
the early-1970s. I think the treatment is wonderful, and Feynman was a genius \
of the first order; so many of his lectures contain really advanced concepts \
explained in understandable ways (mostly). Read through these and take \
copious notes. Be sure to ask yourself lots of questions! Then go ahead and \
try to answer all of them; make sure you can verify that your answers are \
right! If not, why not? For the subject of this chapter, read through \
chapters one to three of volume one."
}], "Reference",
CellChangeTimes->{{3.4935695478970003`*^9, 3.4935695542349997`*^9}},
LineSpacing->{1.5, 1.5},
FontSize->12]
}, Open ]],
Cell[TextData[{
Cell[TextData[StyleBox["8. ", "SectionNumber"]], "SectionDingbat"],
"Exercises"
}], "Section",
LineSpacing->{1.5, 1.5},
FontSize->16,
CellTags->"c:5"],
Cell["Do any or all of these that are of interest to you.", "Text",
LineSpacing->{1.5, 3},
FontSize->12],
Cell["Make a summary sheet for the concepts discussed above.", "Item1Numbered",
CellChangeTimes->{3.40833576178264*^9},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["Make a list of the new terms used and what they mean.", "Item1Numbered",
CellChangeTimes->{3.408335774470885*^9},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
Acquire a notebook. Should you need a source for scientific notebooks you can \
get them from the MAST storefront at www.lulu.com (online). The specific URL \
is http://stores.lulu.com/store.php?fAcctID=606172. In any case the pages \
must be prenumbered, or you may number them as you go. Do not tear any pages \
out. You should have at least one page for the title of the notebook (for \
example, \"Projects for 2008,\" \"Calculus,\" \"Building a Tornado Machine,\" \
etc.), include your name and the date you begin the notebook. You need not \
number the title page. Make sure that you must reserve at least one page (and \
I recommend at least two) for a table of contents. As you add relevant \
sections to your notebook, write down the section title and page into your \
table of contents so you can find it later. Here are some additional \
guidelines:\
\>", "Item1Numbered",
CellChangeTimes->{3.4083357868186398`*^9},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
Should you attend discussions, talks, or seminars note the title, date, and \
speaker as the Section Heading. You might want to take your notes on a pad \
during the talk, and then add them to the notebook later. This gives you a \
chance to think about the notes as you add them to the notebook.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When you read source material, note the question you are attempting to \
answer, the author of the publication, the date of publication, the title, \
the publisher or the name of the magazine or journal. Again, you might want \
to take the notes on a pad as you read and then transfer them to your \
notebook later on.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When you make observations in the field or the laboratory, title the \
observation (for example, \"Observing a thunderstorm video\"), note the date, \
the time, any relevant local conditions (temperature, light level, etc.) that \
might influence the observation. Note how the data is being taken. Then \
record the data into your notebook as it is taken. You should sign each page \
as you record the time for each observation. This is to establish and \
maintain the integrity of your data.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When making a calculation you must first title it, note all relevant \
assumptions you are making, note all units and constants in use, and then \
record each step in the calculation and its results.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When setting up an experimental apparatus first record the title of the \
experimental set-up, the date, time, local conditions that could influence \
the experiment, list all of the materials used, then list each step in the \
set-up as you perform it. If something unexpected happens, record that, too. \
Sign each page as you perform the set-up. This is to establish and maintain \
the integrity of the data.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When calibrating an apparatus or instrument record the title of it, the date, \
the time, all relevant local conditions, list all of the materials used and \
how you intend to perform the calibration and why you chose the method being \
used. Then record each step as you perform it. Record all data you collect as \
you collect it. This is to establish and maintain the integrity of the data.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When analyzing data record the title of the experiment or observation the \
data was drawn from, the method of analysis and its justification, the \
results of the analysis, and your estimate of the error in your analysis.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When making a model (physical, mathematical, or on a computer) record the \
title of the model, all assumptions that you are using, the method of \
modeling and its justification, and then record each step in your model and \
its results.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When performing a derivation or proof record the title of the work, all \
assumptions being used, all definitions, all theorems, all conjectures, and \
then each step and its justification and results.\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
When entering a practice problem and its solution, be sure sure to name the \
problem (For example, \"Problem Calculus - 1\"), write the problem clearly, \
begin the solution process by explaining what you intend to do and why before \
you do it, then record each step in the solution along with full \
justifications for the methods you use, verify your answer, and then think \
about how the answer to the problem will influence the remainder of your \
work, can you think of applications for the answer? Can you think of other \
ways to asnwer the same problem? Does this answer shed light on other \
problems you are working on? (More than one research project has been started \
in this way).\
\>", "Item2Paragraph",
CellDingbat->"\[FilledSmallCircle]",
CellMargins->{{40, Inherited}, {Inherited, Inherited}},
LineSpacing->{1.5, 1.5},
FontSize->12],
Cell["\<\
You will find that a scientific notebook is a great tool for not only \
recording your work, but for developing your ideas. It is the most important \
tool you will have. It is hard to keep a notebook like this, at first. Once \
you get into the habit, you will find it a valuable resource.\
\>", "Text",
LineSpacing->{1.5, 1.5},
FontSize->12]
}, Open ]]
},
PrintingStyleEnvironment->"Printout",
WindowToolbars->{"RulerBar", "EditBar"},
CellGrouping->Manual,
PageWidth->PaperWidth,
WindowSize->{1049, 740},
WindowMargins->{{334, Automatic}, {-78, Automatic}},
DockedCells->(FrontEndExecute[{
FrontEnd`NotebookApply[
FrontEnd`InputNotebook[], #, Placeholder]}]& ),
PrintingCopies->1,
PrintingStartingPageNumber->1,
PrintingPageRange->{Automatic, Automatic},
PageHeaders->{{Inherited, "Chapter One",
Cell[
TextData[{
OptionValueBox[""]}], "Header"]}, {
Cell[
TextData[{
OptionValueBox[""]}], "Header"], "Chapter One", Inherited}},
PrintingOptions->{"PrintCellBrackets"->False,
"PrintMultipleHorizontalPages"->False,
"PrintRegistrationMarks"->True,
"PrintingMargins"->{{72, 72}, {72, 72}}},
TaggingRules:>{
"PaginationCache" -> {{2006, 9, 19, 6, 57, 17.096816`8.985490180530087}, {1,
1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6,
6}}},
CellLabelAutoDelete->True,
LineSpacing->{1.5, 1.5},
FontFamily->"Garamond",
CounterBoxOptions->{CounterFunction:>Identity},
FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (October 6, 2011)",
StyleDefinitions->FrontEnd`FileName[{"Article"}, "JournalArticle.nb",
CharacterEncoding -> "WindowsANSI"]
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
"c:1"->{
Cell[1257, 32, 138, 3, 76, "Title",
CellTags->"c:1"]},
"c:2"->{
Cell[3724, 86, 258, 7, 46, "Section",
CellTags->"c:2"],
Cell[5143, 118, 183, 6, 46, "Section",
CellTags->"c:2"],
Cell[6796, 154, 251, 10, 46, "Section",
CellTags->"c:2"]},
"c:3"->{
Cell[12206, 273, 254, 10, 46, "Section",
CellTags->"c:3"]},
"c:4"->{
Cell[17064, 399, 235, 10, 46, "Section",
CellTags->"c:4"]},
"c:5"->{
Cell[20822, 503, 234, 10, 46, "Section",
CellTags->"c:5"],
Cell[22272, 543, 171, 6, 46, "Section",
CellTags->"c:5"]}
}
*)
(*CellTagsIndex
CellTagsIndex->{
{"c:1", 30792, 753},
{"c:2", 30862, 756},
{"c:3", 31059, 763},
{"c:4", 31134, 766},
{"c:5", 31209, 769}
}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[1257, 32, 138, 3, 76, "Title",
CellTags->"c:1"],
Cell[1398, 37, 94, 1, 42, "Author"],
Cell[1495, 40, 92, 1, 13, "Institution"],
Cell[1590, 43, 115, 3, 50, "Section"],
Cell[1708, 48, 326, 7, 43, "Text"],
Cell[2037, 57, 1684, 27, 381, "Text"],
Cell[3724, 86, 258, 7, 46, "Section",
CellTags->"c:2"],
Cell[3985, 95, 1155, 21, 268, "Text"],
Cell[5143, 118, 183, 6, 46, "Section",
CellTags->"c:2"],
Cell[5329, 126, 1442, 24, 358, "Text"],
Cell[CellGroupData[{
Cell[6796, 154, 251, 10, 46, "Section",
CellTags->"c:2"],
Cell[7050, 166, 514, 10, 89, "Text"],
Cell[7567, 178, 330, 8, 37, "Item1Numbered"],
Cell[7900, 188, 241, 4, 16, "Item1Numbered"],
Cell[8144, 194, 267, 5, 16, "Item1Numbered"],
Cell[8414, 201, 287, 5, 16, "Item1Numbered"],
Cell[8704, 208, 270, 5, 16, "Item1Numbered"],
Cell[8977, 215, 281, 5, 16, "Item1Numbered"],
Cell[9261, 222, 278, 5, 16, "Item1Numbered"],
Cell[9542, 229, 2627, 39, 651, "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[12206, 273, 254, 10, 46, "Section",
CellTags->"c:3"],
Cell[12463, 285, 1304, 21, 359, "Text"],
Cell[CellGroupData[{
Cell[13792, 310, 211, 4, 16, "Item1Numbered"],
Cell[14006, 316, 195, 3, 16, "Item1Numbered"],
Cell[14204, 321, 201, 3, 16, "Item1Numbered"],
Cell[14408, 326, 157, 2, 16, "Item1Numbered"],
Cell[14568, 330, 171, 2, 16, "Item1Numbered"],
Cell[14742, 334, 171, 2, 16, "Item1Numbered"],
Cell[14916, 338, 195, 3, 16, "Item1Numbered"]
}, Open ]],
Cell[15126, 344, 492, 10, 134, "Text"],
Cell[15621, 356, 124, 3, 16, "Item1Numbered"],
Cell[15748, 361, 214, 5, 37, "Item1Numbered"],
Cell[15965, 368, 221, 5, 37, "Item1Numbered"],
Cell[16189, 375, 236, 6, 37, "Item1Numbered"],
Cell[16428, 383, 599, 11, 134, "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[17064, 399, 235, 10, 46, "Section",
CellTags->"c:4"],
Cell[17302, 411, 523, 12, 32, "Reference"],
Cell[17828, 425, 414, 9, 32, "Reference"],
Cell[18245, 436, 541, 12, 77, "Reference"],
Cell[18789, 450, 339, 7, 47, "Reference"],
Cell[19131, 459, 397, 8, 62, "Reference"],
Cell[19531, 469, 429, 8, 77, "Reference"],
Cell[19963, 479, 459, 9, 62, "Reference"],
Cell[20425, 490, 360, 8, 47, "Reference"]
}, Open ]],
Cell[CellGroupData[{
Cell[20822, 503, 234, 10, 46, "Section",
CellTags->"c:5"],
Cell[21059, 515, 271, 7, 44, "Text"],
Cell[21333, 524, 924, 16, 185, "Reference"]
}, Open ]],
Cell[22272, 543, 171, 6, 46, "Section",
CellTags->"c:5"],
Cell[22446, 551, 106, 2, 20, "Text"],
Cell[22555, 555, 161, 3, 16, "Item1Numbered"],
Cell[22719, 560, 161, 3, 16, "Item1Numbered"],
Cell[22883, 565, 977, 16, 205, "Item1Numbered"],
Cell[23863, 583, 466, 9, 78, "Item2Paragraph"],
Cell[24332, 594, 488, 10, 78, "Item2Paragraph"],
Cell[24823, 606, 662, 12, 120, "Item2Paragraph"],
Cell[25488, 620, 369, 8, 57, "Item2Paragraph"],
Cell[25860, 630, 581, 11, 99, "Item2Paragraph"],
Cell[26444, 643, 563, 10, 99, "Item2Paragraph"],
Cell[27010, 655, 392, 8, 57, "Item2Paragraph"],
Cell[27405, 665, 408, 9, 57, "Item2Paragraph"],
Cell[27816, 676, 371, 8, 57, "Item2Paragraph"],
Cell[28190, 686, 867, 15, 162, "Item2Paragraph"],
Cell[29060, 703, 355, 7, 63, "Text"]
}, Open ]]
}
]
*)
(* End of internal cache information *)
(* NotebookSignature rx0bPfH3W899gBKIR3MJ3HH# *)