The alt.algebra.help FAQ ~~~~~~~~~~~~~~~~~~~~~~~~ Version 1, created 30th May 1996. First revision 6th June 1996. Second revision 31st July 1996. By Joe Chacko . Hello. This is a list of frequently asked questions. You get free answers with most of these questions. Please note, that the following are guidelines to make life easier for the denizens and newbies of AAH. To follow them would be polite, and to ignore them might cause unnecessary confusion. That is all. They are not rules, and the internet is a free medium. We are not insisting on anything, but making suggestions on how to do whatever you want to do. The aim of this FAQ is not to teach anyone mathematics. That is what the newsgroup is for. If you want to read a text on mathematics, buy a mathematics book. Questions ~~~~~~~~~ 1 What is this group for? 1.1 What is algebra? 1.2 Why would anyone subscribe to this newsgroup? 1.3 What topics are suitable for discussion? 1.4 Will someone do my homework for me? 1.5 Who is entitled to ask questions here? 1.6 Who is entitled to answer 2 How should I post a question? 2.1 How do I type expressions in ascii (text) form? [style guide here] 2.2 Can I use ASCII graphics? 2.3 Oh please can I use ASCII graphics, huh, huh can I? 2.4 What should I do if my articles don't appear? 2.5 Why does everyone hate me? 3 How should I answer a question? 3.1 What should I do if I am not sure of my answer? 3.2 Should I e-mail my answers? 4 Where can I get mathematics software? 5 Do you want to make money fast? 6 How can I remember all the formulae and formulas I need? 7 Are there any other newsgroups I should be aware of? Answers ~~~~~~~ Answer::1 What is this group for? Well, it is for the discussion of algebra. Mainly the algebra is from algebra classes. If you need help with algebra in whatever form, or want to help other people with algebra, this is a good place to do it. If you wish to discuss other mathematical topics here, feel free. Very advanced mathematics might be better suited to sci.math. Answer::1.1 What is algebra? To most people, algebra is the use of letters to represent unknown quantities in mathematical problems. 'Algebra' comes from an Arabic phrase. This referred to a particular type of mathematics that was mainly a leisure pursuit for rich men. Algebra has come a long way since then, and the algebra studied today is very far removed from the original kind. For interested mathematicians, or advanced students, algebra becomes a more abstract subject. It involves the study of formal number systems of which the systems we use in everyday life are just examples. The set of two-by-two matrices is an example of a less common number system. Answer::1.2 Why would anyone subscribe to this newsgroup? Students, and concerned parents subscribe for help with algebra. Teachers (and would-be teachers) subscribe to help people, to ask for help with algebra, or even to discuss teaching practices. Some people just tune in for the occasional challenge to stop their brains seizing up. These are just some of the reasons people have for using AAH. Answer::1.3 What topics are suitable for discussion? Anything you think might involve algebra, whether that be a school problem, a real life problem or a puzzle you are stuck on, is suitable for discussion on AAH. As well as this, we regularly discuss teaching methods, other branches of mathematics than algebra, mathematical conventions, numerical methods, prices of calculators, etc. Off-topic discussions are inevitable, but a mainly algebraic theme would be appreciated. ***** Answer::1.4 Will someone do my homework for me? No. Well, don't rely on it. No-one rates the importance of handing in your next assignment more than you or your parents do. The nice helpful people here would rather spend twenty minutes helping you understand a concept in algebra than 5 minutes doing your work for you. Even if someone does it once or twice, they are providing solutions for you to look through and understand, or answers for you to check your work against. You will not get enough homework solutions from this group to affect your end-of-term report, so don't think you've found the easy way out. There isn't one in the long run. Answer::1.5 Who is entitled to ask questions here? You are. Any on-topic question you ask will be well-received, and possibly even answered, unless you repeatedly ask us to provide complete solutions to your homework. If you only want to pose 'trick' questions, rec.puzzles might be a more appreciative audience. Please read section 2 of the answers for more details on how to ask a question. Answer::1.6 Who is entitled to answer? You are. If you have an answer, feel free to post it. If you only want to solve lots of problems, however, try going to the rec.puzzles newsgroup(s), rather than doing everyone's homework for them. This does not help students who need algebra help. Please refer to section 3 of the answers for more details on answering questions. Answer::2 How should I post a question? PUT MATHEMATICAL EXPRESSIONS ON SINGLE LINES. Use your newsreader software, and issue the command to write a new article. In the subject line, give an indication of what type of problem it is. Try to avoid very brief subject lines, since your article may appear as part of an existing thread of articles (if someone else has used the same subject line recently). This may result in your article being overlooked by many people. If you can't think of a better subject line than "Help!" or "Algebra Problems", then begin the subject line with your initials. ALWAYS REMEMBER TO write expressions on one line, [People with different newsreaders or fonts will have problems reading your post. There will be confusion.] give an indication of how old you are or what level of mathematics you have reached in your studies (or both), and [otherwise you may get a reply suitable for someone with much more or much less knowledge of mathematics than you.] include a brief description of what you have tried to do by way of solving the problem you are posting. [then others may be able to tell you where you went wrong, and what to do in future. Also, this will save people covering old ground in their replies. Lastly, there may be several ways to answer a problem, and your working will help others choose the best way for you.] Answer::2.1 How do I type expressions in ascii (text) form? The two most important things to bear in mind are clarity and lack of ambiguity. In other words, whatever you type should mean something, and should not mean more than one thing. This can most easily be achieved through the liberal application of parentheses(), brackets[] and common sense. Here are a few checks to make before you post an article... 1) Are your expressions on one line? 2) Could any expressions be read in more than one way? e.g. if you write "x^3/2" you could mean either "x cubed over 2", or "x, raised to the power of one and a half". You could remove ambiguity by writing either "(x^3)/2" or "x^(3/2)". More on this subject, "the order of operations", later. 3) Have you really posted a problem? e.g. if you post an article saying "Please help, I'm stuck. 5x + 2x + 3 - 2" we may guess what your problem is, but there is nothing to solve. What has been posted here is just an expression. It means something only when we plug a value for x into it. If you do not understand the question, reproduce it as faithfully as you can, and ask for help on how to interpret it. It is of interest that a large proportion of lost marks on tests are to do with a student's inability to express herself clearly. If you have a problem, make sure you know what is required as a solution. In the above example, the problem might well be "Simplify the expression...". What is required is a simplified expression. Simple! 4) If you are not sure whether your expressions are clear, then try to describe the problem in words. ***** [This is the style guide I mentioned.] However, here are some symbols to be going on with. They are arbitrarily chosen (shamelessly stolen) from a variety of conventions. Variables ~~~~~~~~~ x a variable, or unknown. x is the most commonly used letter (and not just in this FAQ) for unknowns, although there are a few conventions: v,w usually used for vectors x,y real numbers q,r rationals j,m,n naturals z complex number f,g,h functions, as in "f(x):= x^2 + 5" (f is a function of x, defined to be the square of x plus 5) Greek letters - For lower case letters, type name of letter in lower case. For upper case, type name in upper case. This should circumvent most problems. e.g. tau, TAU, alpha, beta, gamma, GAMMA. N.B. Pi and pi should be considered lower case. Only PI is upper case. This list is not complete. Where possible, try to use lower case single letters for variables. Capitals are usually used to refer to sets (and classes), matrices, and much much more. ***** Basic Symbols Examples ~~~~~~~~~~~~~ ~~~~~~~~ + plus 4 + 2 = 6 - minus 4 - 2 = 2 / divided by 4/2 = 2 * multiplied by 4*2 = 8 (Use when multiplying two numbers) [N.B. it is acceptable to contract things like "2*x" to "2x" and "x*y" to "xy", but not "2*5" to "25"] . multiplied by (2).(5) = 10 , x.y = xy = x*y [N.B. to avoid confusion, don't use this with digits, where it might represent a decimal point. e.g. "3.5" should represent "three point five" rather than "three times five"] ! factorial 4! = 24 | divides 2|4 (4 is divisible by 2) [N.B. for natural numbers m and n, m|n if and only if n divided by m gives no remainder.] : to (ratio) 4:2 = 2:1 = 2 ^ to the power of 4^2 = 16 (4 squared equals 16) = equals x = 4/x (this is an equation) ~ approximately equals 22/7 ~ 3.14 # is equivalent to if you don't know this, don't use it := is defined to be x := a/b (here's a definition) < is less than 2 < 4 > is more than 4 > 2 <> is not equal to x <> 2 =< is equal to or less than 2 =< 4 >= is more than or equal to x >= 2 ==> implies x >= 4 ==> x > 2 <== is implied by Alex is 21 <== It is Alex's 21st birthday today <==> implies and is implied by x = 2 <==> 2x = 4 sqrt() denotes the square root, or radical, of whatever is within the brackets. It is defined to be the positive square root. Should you wish to indicate both possibilities, use: +/- 'plus or minus' to indicate that both positive and negative values should be considered. Compare with: |x| absolute value of x (but not when x is a vector) xy juxtaposition (putting next to) is also used to indicate multiplication, i.e. "x times y" x(y) a tricky one. It could mean either "x times y" or "x (a function) of y". In fact the second meaning covers the first, but this is a technicality. The meaning should be inferred from context, but where possible, try to avoid any such ambiguity. The log function ~~~~~~~~~~~~~~~~ log() denotes a logarithm. ln() natural logarithm lg() log to the base 10 logx() log to the base x N.B. it is important that you know what base you are using, and why. If no base is specified, assume that we use a base of 10. Calculus ~~~~~~~~ f'() given that f() is a function, we take f'() to be the first derivative of f(). Similarly... F() is taken to be the anti-derivative of f(), including a constant of integration of course. dx "with respect to x" - always used in conjunction with derivative or integral symbols. _/~[] I just made this one up. It is an integration symbol. e.g. _/^ [(1/4)x^3 + x^2] dx = x^4 + (1/2)x^2 + c a_/~b[] Integration from a to b. e.g. a_/^b [x/2] dx = (b^2 + c) - (a^2 + c) = b^2 - a^2 dy/dx This is the derivative of y with respect to x. ***** Special numbers ~~~~~~~~~~~~~~~ pi The greek letter pi, defined to be the ratio of the circumference of a circle to its radius. e Euler's number(?). Used as a base for natural logarithms. ***** Trig functions (unless otherwise specified, x is in radians) ~~~~~~~~~~~~~~ Use standard abbreviations as in any textbook or as taught in class. e.g. sin(x), cos(), cotan() To show the inverse operation, use the prefix arc- e.g. arcsin() Remember, arc refers to the smallest positive answer. N.B. all arguments to trig functions are assumed to be in radians, unless explicitly stated otherwise. Set Theoretic Symbols ~~~~~~~~~~~~~~~~~~~~~ {} - the set of U - union c - is a subset of @ - belongs to ' - prime \ - without / - quotient : - such that ***** Order of Operations ~~~~~~~~~~~~~~~~~~~ [Help, please?] ***** Answer::2.2 Can I use ASCII graphics? No. You have to be very careful, and always bear in mind that other people's newsreaders may use different character sets and different tab lengths from the ones your editor does. Even if you master ASCII graphics, there are those on this newsgroup who cannot use monospaced fonts to read articles, so your article will look very strange to them. Also, various newsreaders have different line lengths. Extra care is required to make sure that your graphics can survive being quoted by someone else. The best idea is not to do it. Refer to the single-line equations guideline above. Answer::2.3 Oh please can I use ASCII graphics, huh, huh can I? It would be foolish of me to imagine that everyone who reads this FAQ will refrain from using multiple line expressions. If you must use ascii graphics, here are some guidelines:- Try to express any multiple line equations in words or as single line equations nearby in your article, for clarity. Use tabs only at the beginning of a line, or to tabulate items which are not longer than 3 characters. Usually using tabs will lead to trouble, so avoid it if you can. Use brackets around each line of a vector or matrix. e.g. (12 4 6) ( 3 11 9) (-2 1 3) Write a brief explanation of any diagrams in words. ***** Answer::2.4 What should I do if my articles don't appear? Do _NOT_ repost them. If the second lot get through, so will the first. People will shout at you for doing things like this. Contact your internet service provider, or your system administrator to find out why your articles have not appeared. It may be the case that you will have to wait as much as two weeks for the news to propagate around to the newsfeed you pick up your articles from. Be patient. As a last resort e-mail someone on AAH with details of your article, and ask them if they have seen it. Answer::2.5 Why does everyone hate me? Probably because you reposted an article seven times. No, seriously, if one or two people have written you e-mails which are harshly worded, they may not have meant to be hurtful or spiteful. Even if they did, they do not speak for anyone else. You have as much right to use this newsgroup as anyone else. If you really have been ostracized, then it is almost certainly because of persistently irritating behaviour on your part. An apology might be all that lies between you and free algebra help, should you want it. Answer::3 How should I answer a question? The general aim of people who answer questions from students on AAH is to tell the students how to approach a problem. If you have a way to solve a problem, post it. If you can put the emphasis on making the student understand what you have done, rather than just presenting her with an answer and some working, then so much the better. ***** Answer::3.1 What should I do if I am not sure of my answer? If you are unsure of your answer, feel free to post it, but make it clear that you are not sure of your answer. If consider it relevant, please indicate what level of mathematics you have attained (what class you are in). Teaching is often the best way to learn. Also, if you guess an answer to a problem, you will help yourself more than if you just ignore the question. Even if you answer incorrectly, you are developing your intuition, one of the most vital tools for any mathematician. Answer::3.2 Should I e-mail my answers? If your answer is right, then yes. It will surely reach the person (who asked the question) faster. However, make sure that the person you send the e-mail to is the same person that asked the question. Also, please post the answer to the group, and mark both your e-mail and your news article with "[e-mailed and posted]" or somesuch. Answer::4 Where can I get mathematics software? This is a very frequent question. I have no answers yet, but I'm sure some of you who read this will send me answers to put in this FAQ. Please send name of software, brief description, and URL of any web page. Also, please send any copyright notices. We probably have to include them. ***** I have yet to see teaching software that actually makes mathematics fun, whatever it claims. There are no real shortcuts to learning mathematics, either. If you want to learn mathematics, or help your children learn mathematics, you are going to have to put some time in yourself. The best thing to do is to get a book. Once you have used a book, it will be easier to refer back to. Books are more portable in general. Books are easier to learn from. Books are often cheaper (especially second hand). If you want interactive mathematics help, then try a newsgroup. ***** As for mathematical software tools, this is what computers were designed to do in the first place. There are plenty of very good mathematical tools around. ***** Answer::5 Do you want to make money fast? Yes. However, your scams will neither work nor fool anyone on AAH. Just go away. Note for newbies: there exists at least one person with access to usenet whose scruples are few (less than epsilon). This person, and any others such, occupy their time posting articles with lurid, irrelevant and even illegal schemes for gaining money. These schemes are mathematically unsound, and help to waste bandwidth and server disk-space. If you are irritated by these articles, then write a letter of warning back to the sender, and a letter of complaint to the sender's postmaster, and to the sender's service provider. Don't bother complaining within the newsgroup, as the sender is not usually listening in. Answer::6 How can I remember all the formulae and formulas I need? There are very few regular users of this group who would not agree that mathematics is not really about learning formulae, or even formulas. It would be much better for you to learn how to work things out from first principles. This is an easier way to learn, and imparts a better understanding of the mathematics involved. If you are young, this could make the difference between being able to do mathematics for the rest of your life, or for the next few weeks/months. The simple answer to the memory problem is... ...PRACTICE. Memory aids _can_ help, but only as part of a controlled mathematics diet. Answer::7 Are there any other newsgroups i should be aware of? Yes. sci.math - advanced, rigorous mathematics, definitions, semantics rec.puzzles - er...puzzles Discretion is a usefool tool in deciding whether to post something here or to take it elsewhere. Please read the FAQ of any group you post to.