LAWS OF EXPONENTS - To multiply powers of the same base, add their
exponents.
Thus,
22 times 23 = 25
= 32
PROOF: 22 = 4;
23 = 8;
25
Therefore;
4 x 8
= 32
To divide powers of the same base,
subtract the exponent of the divisor from the exponent of the dividend.
(The dividend is on top / divisor is on the bottom)
Thus,
35
/ 33 = 32
= 9
PROOF: 35 = 243;
33 =
27; 32
Therefore;
243
/ 27
= 9
(Note: The above statement
corrected 03/13/00 by the sharp eye and compliments of Jason Rana, Ouachita
Baptist University. We appreciate anyone who brings errors to our
attention so we may correct them.)
Webmaster@ 101science.com
HANDY FORMULAS
AND
INFORMATION -
These should be memorized!
(-a)n = an, if n is even
(-a)n = -an, if n is odd
am * an = am+n
an / am = an-m
(ab)n = anbn
(a + b)2 = a2 + 2ab +
b2
(a - b)2 = a2 - 2ab +
b2
(a + b)(a - b) = a2 - b2
(a + b)3 = a3 + 3a2b +
3ab2 +b3
STATISTICS
SECTION
STATISTICS
Little
Handbook of Statistics
http://www.tufts.edu/~gdallal/LHSP.HTM
Online
Textbook explains statistics http://davidmlane.com/hyperstat/index.html
Probability
Tutorials - online
Electronic
Statistics Book http://www.statsoft.com/textbook/stathome.html
Online
Textbook http://davidmlane.com/hyperstat/index.html
Statistics
Lab http://www.ruf.rice.edu/%7Elane/rvls.html
REGRESSION ANALYSIS
Introduction
to Regression Analysis
Multiple
Regression
Regression
Analysis
CORRELATION
AND REGRESSION
[PDF] An
Introduction to Regression Analysis
Regression
analysis - Wikipedia, the free encyclopedia
Simple
linear and multiple regression
PA
765: Multiple Regression
Statistical
Analysis
Reliability
and Regression Analysis
Statistical
Analysis
Regression
Analysis
WPI
Global Perspective Program - Handbook for IQP Advisors and
KaleidaGraph
- scientific graphing, curve fitting, data analysis
Defense
Procurement and Acquisition Policy - Contract Pricing
Parametric
Cost Estimating Handbook - Regression Analysis
[PDF] Regression
analysis
LINEAR
REGRESSION
Java
Applet to figure normal distribution statisics for you http://playfair.stanford.edu/~naras/jsm/FindProbability.html
http://www-stat.stanford.edu/~naras/jsm/example6.html
http://www-stat.stanford.edu/~naras/jsm/
http://www.symynet.com/educational_software/teaching_resources/Statistics/normal_distribution/intro.htm
http://www.adamssixsigma.com/Newsletters/standard_normal_table.htm
http://stat-www.berkeley.edu/~stark/SticiGui/index.htm
Applied
Statistics Books
WEB PAGES THAT PERFORM
STATISTICAL CALCULATIONS
Indiana
University Statistics and Math Center
Fluid Dynamics
and Statistical Physics
Statistical Data Resources
Geospatial
and Statistical Data Center University of Virginia
CDC
Injury Statistics
CDC
Center for National Health Statistics
SSBR:
Health Statistics
Top 100 Applied Statistics Books for SaleMathematical
Statistics and Data Analysis
Mathematical
Statistics and Data Analysis
Probability
and Statistics - 101science.com - WWW Links page.
Statistics Links to TI-83 Programs you
can download to your calculator:
http://www.iserv.net/~gopat/ (General Statistics)
http://www.keycollege.com/workshopstatistics/vonoehse/ti83prgm.zipStatistics
http://silver.sdsmt.edu/~rwjohnso/Ggrant.htm
Statistics - CBL
Finding Mean and Standard Deviation with the TI-83
Mean and standard
deviation on the TI-83
[PDF]Using
the TI-83 to Find the Sample Mean and Sample Standard ...
TI-83
Instructions - Hypothesis Testing with one mean
TI 83 Instructions - Confidence Intervals for mean (small
samples ...
[PDF]TI-83/83
Plus: Confidence Interval for One-Sample Mean with s ...
[PDF]TI-83/83
Plus: Hypothesis Testing for Two-Sample Mean with s ...
[PDF]Calculating
Mean and Standard Deviation for a Sample with TI-83 Normal
probabilities on the TI-83
SettleBasics
TI-83
Instructions
Adolphe Quetelet (1796 - 1874)
QUOTE: "The
more progress physical sciences make, the more they tend to enter the domain of
mathematics, which is a kind of center to which they all converge. We may even
judge the degree of perfection to which a science has arrived by the facility
with which it may be submitted to calculation."
Adolphe Quetelet
Quoted in E Mailly, Eulogy on Quetelet 1874
Adolphe Quetelet received his first doctorate in 1819
from Ghent for a dissertation on the theory of conic
sections. After receiving this doctorate he taught mathematics in
Brussels, then, in 1823, he went to Paris to study astronomy at the Observatory
there. He learnt astronomy from Arago
and Bouvard and the theory
of probability under Joseph Fourier
and Pierre Laplace.
Influenced by Laplace
and Fourier,
Quetelet was the first to use the normal curve other than as an error law. His
studies of the numerical consistency of crimes stimulated wide discussion of
free will versus social determinism. For his government he collected and
analysed statistics on crime, mortality etc. and devised improvements in census
taking. His work produced great controversy among social scientists of the 19th
century.
At an observatory in Brussels that he established in 1833 at
the request of the Belgian government, he worked on statistical, geophysical,
and meteorological data, studied meteor showers and established methods for the
comparison and evaluation of the data.
Article by: J J O'Connor and E F
Robertson
Statistics
From Wikipedia, the free
encyclopedia.
Find out how you can help support
Wikipedia's phenomenal growth.
Statistics is a branch of applied mathematics
which includes the planning, summarizing, and interpreting of uncertain
observations. Because the aim of statistics is to produce the "best"
information from available data, some authors make statistics a branch of decision
theory. As a model of randomness or ignorance, probability
theory plays a critical role in the development of statistical
theory.
The word statistics comes from the modern Latin
phrase statisticum collegium (lecture about state affairs), from which came
the Italian
word statista, which means "statesman" or "politician"
(compare to status)
and the German
Statistik, originally designating the analysis of data about the state. It
acquired the meaning of the collection and classification of data generally in
the early nineteenth century.
We describe our knowledge (and ignorance)
mathematically and attempt to learn more from whatever we can observe. This
requires us to
- plan
our observations to control their variability (experiment
design),
- summarize
a collection of observations to feature their commonality by
suppressing details (descriptive
statistics), and
- reach consensus about what the
observations tell us about the world we observe (statistical
inference).
In some forms of descriptive statistics,
notably data
mining, the second and third of these steps become so prominent that the
first step (planning) appears to become less important. In these disciplines,
data often are collected outside the control of the person doing the analysis,
and the result of the analysis may be more an operational model than a
consensus report about the world.
The probability of an event is often defined
as a number between one and zero rather than a percentage. In reality however
there is virtually nothing that has a probability of 1 or 0. You could say
that the sun
will certainly rise in the morning, but what if an extremely unlikely event
destroys the sun? What if there is a nuclear war and the sky is covered in ash
and smoke?
We often round the probability of such
things up or down because they are so likely or unlikely to occur, that it's
easier to recognise them as a probability of one or zero.
However, this can often lead to
misunderstandings and dangerous behaviour, because people are unable to
distinguish between, e.g., a probability of 10-4 and a probability
of 10-9, despite the very practical difference between them. If you
expect to cross the road about 105 or 106 times in your
life, then reducing your risk per road crossing to 10-9 will make
you safe for your whole life, while a risk per road crossing of 10-4
will make it very likely that you will have an accident, despite the intuitive
feeling that 0.01% is a very small risk.
Some sciences use applied
statistics so extensively that they have specialized
terminology. These disciplines include:
Statistics form a key basis tool in business
and manufacturing as well. It is used to understand measurement systems
variability, control processes (as in "statistical process control"
or SPC), for summarizing data, and to make data-driven decisions. In these
roles it is a key tool, and perhaps the only reliable tool.
Links to observable statistical phenomena
are collected at statistical
phenomena
Regression--analysis
of variance (ANOVA) -- multivariate
statistics -- extreme
value theory -- list
of statisticians -- list
of statistical topics -- machine
learning
How do you solve a percentage increase
question?
- How do you calculate a
percentage increase? For example if your supply of apples increases from
206 to 814, what was the percentage increase?
We can see by subtracting 206
from 814 that the increase in the number of apples is 608. Remember we
started with 206, not zero.
Percentages are
fractions.
Dividing 814 by 206 gives approximately 3.951 and since we
started with one whole (100%) basket of 206 apples we must subtract one from
this percentage number. This is the step many people miss. So, 3.951
minus 1 equals 2.951. Multiplying this number by 100 to give percentage;
100 times 2.951 gives 295%
increase as the answer.
- Check your work. Does
this answer look correct? Well, if we had 200 apples increasing to 400
(double) that would be a 100% increase. So, increasing from 400 to
600 (another 200 apples) would be another 100% increase. So, increasing
from 600 to 800 (another 200 apples) would be another 100% increase. So
going from 200 to 800 represents an increase of 300%. 3 times our original
amount of 200 equals 600 which is equal to the increase (800 minus 200 =
600). So the answer to our problem should be close to 300%. Our
answer is 295% so it is close to what we would expect. Now let's do an
accurate check of our original problem. 206 times 2.95 equals 608 (the
number of apples increased) which proves our answer is correct.
Math Dictionaries
Math Dictionary:
http://www.blarg.net/~math/deflist.html
Definitions: http://userzweb.lightspeed.net/~barr/def.html
Math Words: http://www.geocities.com/poetsoutback/etyindex.html
Math Words for Middle Grades: http://mathcentral.uregina.ca/RR/glossary/middle/
A
VISUAL DICTIONARY OF SPECIAL PLANE CURVES - X. Lee For more information
see Xah Lee's Home Page
A
VISUAL DICTIONARY OF SPECIAL PLANE CURVES - X. Lee Xah Lee's Home Page
Some Examples from over 60 tutorials include
Inversion
Astroid
Parabola
!!!!!MATH
VIDEO TRAINING AVAILABLE
!!!!!
MORE WEB MATH LINKS
Find other great math sites - Click here - on the web.
Common Errors Made in Math: http://math.vanderbilt.edu/~schectex/commerrs/
Math Terms/Dictionary: http://www.blarg.net/~math/deflist.html
Lesson Plans: http://www.awesomelibrary.org/Library/Materials_Search/Lesson_Plans/Math.html
Understanding Math Sequences and their
Graphs http://jwilson.coe.uga.edu/emt669/Student.Folders/Jeon.Kyungsoon/document3/essay3.html
Dr. Math
Quasicrystals
Encyclopedia
Online
Note scroll down for the encyclopedia online.
Comprehensive Math
Tables
History of Mathematics
How to study Math &
Science
Chronological
List of Mathematicians
UNITS CONVERSION
CALCULATOR
Frank
Potter's Science (math) Gem's - Hugh collection
Ask
Dr. Math (K-12 Math questions answered)
MathNERDS
(Ask questions from K-5 through graduate college level.)
MegaMathematics ( Los Alamos National Laboratories)
The History of Mathematics (Great Site for Historical Information)
Mathematics
- From Wikipedia.
Find out how you can help support
Wikipedia's phenomenal growth.
Mathematics is commonly
defined as the study of patterns of structure, change, and space. In the
modern formalist
view, it is the investigation of axiomatically
defined abstract
structures using logic
and mathematical
notation. Mathematics is often abbreviated to math in North America and
maths in other English-speaking countries.
These specific structures investigated
often have their origin in the natural
sciences, most commonly in physics,
but mathematicians
also define and investigate structures for reasons purely internal to
mathematics, because the structures may provide, for instance, a unifying
generalization for several subfields, or a helpful tool for common
calculations. Finally, many mathematicians study the areas they do for
purely aesthetic reasons, viewing mathematics as an art
form rather than as a practical or applied science.
See the article on the history
of mathematics for details.
The word "mathematics" comes
from the Greek
μάθημα (máthema) which means "science,
knowledge, or learning";
μαθηματικός (mathematikós)
means "fond of learning".
The major disciplines within mathematics
arose out of the need to do calculations in commerce, to measure land and to
predict astronomical events. These three needs can be roughly related to the
broad subdivision of mathematics into the study of structure, space and
change.
The study of structure starts with numbers,
firstly the familiar natural
numbers and integers
and their arithmetical
operations, which are recorded in elementary
algebra. The deeper properties of whole numbers are studied in number
theory. The investigation of methods to solve equations leads to the
field of abstract
algebra, which, among other things, studies rings
and fields,
structures that generalize the properties possessed by the familiar numbers.
The physically important concept of vector,
generalized to vector
spaces and studied in linear
algebra, belongs to the two branches of structure and space.
The study of space originates with geometry,
first the Euclidean
geometry and trigonometry
of familiar three-dimensional space, but later also generalized to non-Euclidean
geometries which play a central role in general
relativity. Several long standing questions about ruler
and compass constructions were finally settled by Galois
theory. The modern fields of differential
geometry and algebraic
geometry generalize geometry in different directions: differential
geometry emphasizes the concepts of coordinate system, smoothness and
direction, while in algebraic geometry geometrical objects are described as
solution sets of polynomial
equations. Group
theory investigates the concept of symmetry abstractly and provides a
link between the studies of space and structure. Topology
connects the study of space and the study of change by focusing on the
concept of continuity.
Understanding and describing change in
measurable quantities is the common theme of the natural sciences, and calculus
was developed as a most useful tool for doing just that. The central concept
used to describe a changing variable is that of a function.
Many problems lead quite naturally to relations between a quantity and its
rate of change, and the methods to solve these are studied in the field of differential
equations. The numbers used to represent continuous quantities are the real
numbers, and the detailed study of their properties and the properties
of real-valued functions is known as real
analysis. For several reasons, it is convenient to generalise to the complex
numbers which are studied in complex
analysis. Functional
analysis focuses attention on (typically infinite-dimensional) spaces of
functions, laying the groundwork for quantum
mechanics among many other things. Many phenomena in nature can be
described by dynamical
systems and chaos
theory deals with the fact that many of these systems exhibit
unpredictable yet deterministic behavior.
In order to clarify and investigate the
foundations of mathematics, the fields of set
theory, mathematical
logic and model
theory were developed.
When computers
were first conceived, several essential theoretical concepts were shaped by
mathematicians, leading to the fields of computability
theory, computational
complexity theory, information
theory and algorithmic
information theory. Many of these questions are now investigated in
theoretical computer
science. Discrete
mathematics is the common name for those fields of mathematics useful in
computer science.
An important field in applied
mathematics is statistics,
which uses probability
theory as a tool and allows the description, analysis and prediction of
phenomena and is used in all sciences. Numerical
analysis investigates the methods of efficiently solving various
mathematical problems numerically on computers and takes rounding errors
into account.
- Mathematics may be defined as the
subject in which we never know what we are talking about, nor whether
what we are saying is true.
- -Bertrand
Russell
An alphabetical list
of mathematical topics is available; together with the "Watch
links" feature, this list is useful to track changes in mathematics
articles. The following list of subfields and topics reflects one
organizational view of mathematics.
Numbers
-- Natural
numbers -- Integers
-- Rational
numbers -- Real
numbers -- Complex
numbers -- Hypercomplex
numbers -- Quaternions
-- Octonions
-- Sedenions
-- Hyperreal
numbers -- Surreal
numbers -- Ordinal
numbers -- Cardinal
numbers -- p-adic
numbers -- Integer
sequences -- Mathematical
constants -- Number
names -- Infinity
Arithmetic
-- Calculus
-- Vector
calculus -- Analysis
-- Differential
equations -- Dynamical
systems and chaos theory -- Fractional
calculus -- List
of functions
Abstract
algebra -- Number
theory -- Algebraic
geometry -- Group
theory -- Monoids
-- Analysis
-- Topology
-- Linear
algebra -- Graph
theory -- Universal
algebra -- Category
theory
Topology
-- Geometry
-- Trigonometry
-- Algebraic
geometry -- Differential
geometry -- Differential
topology -- Algebraic
topology -- Linear
algebra -- Fractal
geometry
Combinatorics
-- Naive
set theory -- Probability
-- Theory
of computation -- Finite
mathematics -- Cryptography
-- Graph
theory -- Game
theory
Mechanics
-- Numerical
analysis -- Optimization
-- Probability
-- Statistics
Fermat's
last theorem -- Riemann
hypothesis -- Continuum
hypothesis -- P=NP
-- Goldbach's
conjecture -- Twin
Prime Conjecture -- Gödel's
incompleteness theorems -- Poincaré
conjecture -- Cantor's
diagonal argument -- Pythagorean
theorem -- Central
limit theorem -- Fundamental
theorem of calculus -- Fundamental
theorem of algebra -- Fundamental
theorem of arithmetic -- Four
color theorem -- Zorn's
lemma -- "The
most remarkable formula in the world"
Philosophy
of mathematics -- Mathematical
intuitionism -- Mathematical
constructivism -- Foundations
of mathematics -- Set
theory -- Symbolic
logic -- Model
theory -- Category
theory -- Theorem-proving
-- Logic
-- Reverse
Mathematics -- Table
of mathematical symbols
History
of mathematics -- Timeline
of mathematics -- Mathematicians
-- Fields
medal -- Abel
Prize -- Millennium
Prize Problems (Clay Math Prize) -- International
Mathematical Union -- Mathematics
competitions -- Lateral
thought
Mathematics
and architecture
Numerology
Old:
New:
- Davis, Philip J.; Hersh, Reuben: The
Mathematical Experience. Birkhäuser, Boston, Mass., 1980. A gentle
introduction to the world of mathematics.
- Gullberg, Jan: Mathematics--From the
Birth of Numbers. W.W. Norton, 1996. An encyclopedic overview of
mathematics presented in clear, simple language.
- Mathematical Society of Japan:
Encyclopedic Dictionary of Mathematics, 2nd ed.. MIT Press, Cambridge,
Mass., 1993. Definitions, theorems and references.
- Michiel Hazewinkel (ed.): Encyclopaedia
of Mathematics. Kluwer Academic Publishers 2000. A translated and
expanded version of a Soviet math encyclopedia, in ten (expensive)
volumes, the most complete and authoritative work available. Also in
paperback and on CD-ROM.
