Would you like to know everything about mathematics?
Do you think that is impossible? It isn't if you are willing to read and study many books. You can't learn everything from class lectures. The bulk of your mathematics learning will come from reading, working problems, and studying various books on your own. And you can do this at your convenience. Since there is no pressure, you can learn without stress. You can learn mathematics by studying the web links and information on this web page and in the books in the following list.
VERY IMPORTANT!! Use you browser's "Find on this page" capability to search for words on a page. Usually Ctrl + F will work.
Rule: 1. If no letter in front of a letter is of greater value, add the numbers represented by the letters. Example. XXX = 30; VI = 6
Rule 2. If a letter in front of a letter is of greater value, subtract the smaller form the larger; add the remainder or remainders obtained to the numbers represented by the other letters. Example. IV = 4; XL = 40; CXLV = 145
Now type in a number in the box below and press the translate button to see you number in Roman Numerals. (Note: Don't hit enter, press the button.)
An interactive site to help you explore and gain deep understanding of topics in mathematics. Online self tests and their answers are also included in the site.
A Math Refresher A short self-study course on algebra and trig, with history tidbits and some problems. Embedded in a larger course on astronomy, physics and space, it provides math tools used in the material and stresses intuitive understanding.
Calc98, a free scientific, engineering, statistical and financial calculator for Windows and PocketPC.Calc98 includes a vast range of units conversions, fundamental constants and physical property data, and other features including arbitrary base numbers, Roman numerals and a stopwatch feature and built-in Periodic Table of the Elements.
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
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
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.
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.
- 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.
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.
The word "mathematics" comes from the Greek μάθημα (mįthema) 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.
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.
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.
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.
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.
You are crazy if you don't have this book!, July 11, 2000 A reviewer from Los Angeles said: Great reference for formulas and identities that you have forgotten. Integral table is awsome. ......This is some of the best money I have ever spent. Used it all the time in my physics classes and ALWAYS carry it with me. How did I ever get on without it?