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Algebra Help It's a total bummer when you are working on an equation at three o'clock in the morning and you have nobody to ask for help. Never again will you be left mathematically stranded. On the Net you can always find the help you need. (Too bad you can't take the computer in with you when you have a test.) Web:
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American Mathematical Society The American Mathematical Society was established in 1888 in order to promote mathematical research. Since then, the mathematical world has changed more than anyone in 1888 could have imagined. However, the AMS is still around serving its thousands of members. Web: Calculus When I was a kid, one did not talk about calculus in polite society. I had to learn to differentiate and integrate the same place everyone else did -- in the street. Today you can enjoy these once-forbidden arts in the privacy of your own home. Connect to the Net and go wild. (Just remember, if your parents find out what you are doing, you didn't learn about it here.) Web:
Chance Server What exactly is a snowball's chance in hell? Check in at the Chance Server and you might find out. Get the Chance News, a biweekly report with popular news items that can be used in classroom settings to make teaching statistics and probability fun. (Not that it isn't normally fun, of course.) Teaching aids are also available. Web:
Chronology of Mathematicians Find out who came before whom by reading this lengthy list of mathematicians organized chronologically from 1700 B.C. to modern times. There are also links to some of the mathematicians who have available biographical information. Web:
Electronic Journal of Differential Equations This site is dedicated to all aspects of differential equations, integral equations, and functional differential equations and their applications. (Just don't forget to add the constant.) Web: Flatland "Flatland", written by Edwin Abbot, is a mathematical story in which a "person" who lives in Flatland tells us what life is like in his world. Flatland is completely two-dimensional -- that is, the whole world exists on a flat surface. Although this seems impossible to imagine, Abbot is such a good writer (and mathematician) that he makes the whole thing understandable and plausible. The most interesting thing is that "Flatland" is a lot more than a mathematical book; it is actually an extremely well-executed social commentary. If you have even the slightest skill in mathematical thinking, I suggest that you take a look at "Flatland". It will expand your thinking in more ways than one. Web:
Geometry Geometry is the branch of mathematics that studies the properties and relationships of various elements, such as points, lines, planes, curves, solids, surfaces, and so on. We all study geometry in school, but it is clear that some of us are more adept than others at visualizing in two and three dimensions. Here are some tools to help you, not only to visualize, but to explore the properties of many types of geometrical objects. Web:
History of Mathematics Get the real story of mathematics, the one your teachers never told you. Read these well-researched essays on various topics in the history of math as well as the biographies of several hundred mathematicians. Contemplate those yet-unsolved questions about prime numbers and whether Konigsberg burned his bridges behind him. Web:
Hub Mathematics and Science Center Take a few mathematicians and scientists, network them together, and suddenly you have The Hub, a service designed to help math and science researchers efficiently utilize telecommunications opportunities. The Hub offers a quarterly newsletter full of Internet usage tips and Internet and telecommunications resources. The Hub can also help you publish reports or requests for proposals. Web: Linear and Nonlinear Programming Linear and nonlinear programming are used to optimize mathematical quantities, subject to various constraints and relationships. With linear programming, the relationships are expressed as a series of linear equations. With nonlinear programming, generalized functions, not necessarily linear, are used instead. Both linear and nonlinear programming are part of operations research and, as such, are discussed in the sci.op-research Usenet group. Web:
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Logic To a civilian, logic describes the act of thinking clearly and rationally. ("My goodness, Clarissa, how can we discuss your mother's visit if you refuse to be logical?") To a mathematician, logic is a lot more. Traditionally, we consider the study of logic as originating with Aristotle, who recognized reasoning as being a science of its own. Modern logic began in 1854 when George Boole published a book in which, for the first time, logical reasoning was treated abstractly. In the twentieth century, much emphasis has been placed on symbolic logic or formal systems, in which mathematical symbols are manipulated according to certain rules. Four important areas of mathematical logic are: axiomatic set theory (what parts of mathematics can be formalized?), proof theory (what can be proved within a formal system?), model theory (how can mathematical logic be applied to algebraic problems?), and recursion theory (are various functions computable?). Web:
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Math and Philosophy Do you agree that even Frege can be faulted for insufficient tenacity in giving up his program after Russell's discovery of the eponymous paradox? Or do you think that ramified type theory, contextual definition of class abstracts, the doctrine of acquaintance, and the theory of proposition identity are just so much hot air? Sit in with people who really understand who shaves the barber (if the barber shaves everyone who does not shave himself). Just be careful to behave yourself: someone may prove that you do not really exist. Usenet:
Math Articles I love mathematics, and I like reading about it, so this is one of my favorite Web sites. This site contains a large collection of articles about various types of math. The articles are short enough so that you can read one at a single sitting. However, there will be plenty to think about. If you have a math background, you will know what I mean when I say there are probably whole areas of math that are strangers to you. Spend some time browsing this site, and you will be able to fill in some of the blanks. Web: Mathematical Association of America This is an organization of college and university mathematics teachers with the goal of advancing the mathematical sciences. This Web page has links to math preprints, publications, career opportunities and other math resources on the Internet. Web: Mathematical Quotations Server The next time you are going to a hot math party, be sure you are well equipped with some good icebreakers, like quotes by your favorite mathematicians. Quotations are sorted alphabetically so you can browse through them or you can do a fast search by keyword. Web:
Mathematics Resources The world of mathematics is so vast that, if there is any part of it you like, I guarantee you will find something to interest you on the Net. These resources are suitable for mathematicians and math teachers, but if you just want to browse, I bet you'll have a good time looking at puzzles and mathematical curiosities. Web:
Mathematics Talk and General Discussion There are discussion groups in Usenet where you can talk about all things mathematical. Now, you might think that unless you are specifically working on a particular research problem or you have a question, talking about math is a waste of time. What you are forgetting is that, traditionally, the most beautiful and intelligent women have always been attracted to the mathematically inclined. Remember, a man who knows his numbers is a man you can count on. Usenet:
Numerical Analysis It's amazing how many people still don't know a Tchebyshev polynomial from a fourth-order Runge-Kutte algorithm. Join the discussion with people who want more out of life than the simple L2 norm that seems to satisfy a whole world of mathematically disadvantaged social scientists. Web:
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Operations Research Operations research is the study of how to use mathematics to make decisions when the problem at hand is complex, and you have to decide how to balance various factors to optimize particular criteria. (If there is significant uncertainty in the outcome, you can say you are doing systems analysis and ask for more money.) Web:
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Pi (3.14159...) Here are some Internet sites celebrating the charm and elusiveness of pi, the irrational number that expresses the ratio of the circumference to the diameter of any circle. Would you like to see pi to many, many digits? Would you like to have your very own program to calculate pi? Would you like to experience pi in ways that normal people have never imagined? It's all here, waiting for you on the Net. (By the way, you may be wondering, is pi my favorite transcendental number? No, I have to admit that my favorite is e. However, I wouldn't kick pi out of bed for eating mathematical crackers.) Web:
Society for Industrial and Applied Mathematics The Society for Industrial and Applied Mathematics provides information about activities and issues of interest to applied and computational mathematicians, engineers, and scientists who use mathematics and computers. Web: Square Root of 2 When you've almost got it figured out and everyone keeps interrupting your thinking space, it's really aggravating. There's no sense in starting over again trying to recalculate the square root of 2. It's already been done: to a million digits. Web:
Statistics When you need a fuzzy clustering algorithm right away and the resident statistician has gone to the 7-11 for a 6-pack of Jolt cola, where do you turn for answers? Try the Net: just the place for people who are approximately right, some or all of the time. Web:
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Symbolic and Algebraic Computation The invention of symbolic and algebraic computation (SAC) programs has added a whole new set of tools to the arsenal of mathematicians, scientists, engineers and students. SAC systems manipulate numbers and symbols exactly, compared to floating point arithmetic, which is approximate. These resources will help you find a wide variety of SAC information, as well as the main Web sites for the major software packages. The Usenet group discusses such tools, as well as the related mathematical issues. Talk about Mathematica, Maple, Macsyma and Reduce. (My goodness, is Reduce still around? I remember using it back in the mid-1970s. Oh, how symbolic algebra makes one feel old.) Web:
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Turing, Alan Alan Turing, the man who brought you the Turing Test, the most popular after-dinner pastime of pre-television families of the early 1950s, has a site devoted to his life and work. Read his chronology, family origins and information about his early life. Discover who inspired him in his work and read about the Turing Machine, Turing's codebreaking work, early computer technology, his arrest, trial and eventual suicide. Web:
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