why should one study abstract algebra if it has no real life applications?
605311
chemistry, quantum mechanics...
620299
programs that do algebra are not that common.\nI know two names: Maple and Mathematica. \n\nHowever learning to use them might be harder than learning high-school math.
168376
It really depends on what you will do in the future. Many careers involve Algebra. Other than in some careers, you don't need to use it that much in your everyday life, but it is handy to use in some sticky situations. Algebra is not needed all the time, but it is good to have.
159293
Depends on what you are analyzing.  Matrix algebra is used extensively in communications and signal processing applications.  Not very much, though, in financial applications.
1074474
For a carefully structured, coherent, and comprehensive course of discrete mathematics, the approach is traditional, deductive, and straightforward, with no unnecessary abstraction. It is self-contained including all the fundamental ideas in the field. It can be approached by anyone with basic competence in arithmetic and experience of simple algebraic manipulations. Students of computer science whose curriculum may not allow the study of many ancillary mathematics courses will find it particularly useful. Mathematics students seeking a first approach to courses such as graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra will also enjoy a clear introduction to these more specialized fields. You will want to present descriptions of numerous algorithms on a form close to that of a real programming language. To enable students to develop practical programs from the design of algorithms. Students of mathematics and computer science seeking an eloquent introduction to discrete mathematics should see the the source for further information.
658021
Upper division math courses may be more theoretical - theorems and proofs rather than computations.  But not always.  There is still plenty of calculation type problems in some upper division math courses.\n\nIf you are good in calculus, keep going on - you may like it.
226634
I don't know if this counts as an application, but it can simply be a fun exercise for a person who loves number to just sit down and do the math.  That probably seems silly to people who are more goal oriented, since they just let the computer do all the work.\n\nI love numbers, and it's more fun than just sitting around twiddling my thumbs(or doodling, since I use paper and pencil)
3783
Actually, that's untrue.  You don't need to be a mathematician to need to use algebra.  Algebra helps you calculate many things and solve problems relating to groceries, finance, construction and much more.  I agree, it is tough and often boring to learn, however it is quite useful.
969538
Disagree.  It solves some problems in evolutionary theory where selective pressures are subtle.  The mathematics are highly refined and led to new insights, but it's application in the real world is limited.
328121
Analytic and Algebraic Number Theory contain easily stated theorems with extensive wide-spanning proofs that require knowledge from almost every area of mathematics, including topology and category theory. As such, I would say this area of study is the most difficult, as one that requires the most mathematical experience to tackle. \nAlgebraic topology, on the other hand, can easily be taught in its basic form to motivated high schoolers. It doesn't even require knowledge of calculus, though such knowledge enriches the subject when one gets to cohomology and applications to vector fields and differential equations. These topics can be saved for a college course.
117795
You are taking the expression too literally. "Imaginary" numbers is just that .. an expression to diffeerentiate them from "real" numbers.\n\nIt's hard to understand now, at this point in your life, but you shouldn't worry "if you'll ever use it." That's not the way to go about learning because, as fate would have it, you have no way of knowing what you will or will not need in the future. Imaginry numbers are critical to electrical systems and electrical engineers use them on a daily basis. Also, if you take differential equations, you will use them in order to solve such equations.\n\nTry to learn as much as you can, because you never know when you'll need it. This is something I have learned the hard way. I wish, in some areas in school, I'd paid more attention.
213762
Not directly!! You're not going to go work for some company, go to a meeting, and say, "according to the Remainder theroem ..."  However, because those theorems work, other, more advanced theorems work, in Calculus, complex variables, differential equations, advanced algebra, ect.  And those definetly have practical application in virtually all fields.
818849
looks like straightforward algebra, and isn't really relevant whether the formulas are electrical
821101
Unfortunately I have the same reaction when I tell people I chose to study maths as a degree-people look at me as if I'm crazy!  I think that it is possibly due to the fact that to do and understand maths, you have to understand the language in which it is written, and unfortunately, that language can look rather confusing!  \n\nAlso, I think that maths can be very intense-if you compare a maths book to a novel, there will be much more information per page in the maths book than the novel, and I think that sometimes people are put off by this, which is a real shame!\n\nAlso, sometimes maths can be counter intuitive, and I guess this also discourages people!  Like for example "a minus times a minus is a plus".\n\nIt's such a shame that people do seem to be put off of maths and numbers, because it is such a great subject!  I include a link below to a magazine called Plus, which is published on the web for free, and which has fun articles, aimed at mathematicians and non-mathematicians alike, on all sorts of maths related topics.
599732
Algebra and all the Maths that one learns at school and college are tools which are ultimately used by Scientists, engineers, doctors, and almost all the people who have something to do with science. Even social scientists like historians and sociologists use it. \n\nIt may seem abstract but Maths is the underlying machinery of the Universe.
10912
The idea behind this is that understanding what they are doing is more important than taking up time performing routine arithmetic.  \n\nI think that's fine when you hit more advanced math classes in high school.  If you are learning algebra your time is better spent concentrating on the algebra rather than doing mundane calculations you've already mastered in years past. If I have to take time to factor 1334025 by hand to find that its square root is 1155, that's going to be a huge distraction when I'm trying to solve an equation.\n\nOn the other hand, calculator use is, in my opinion, introduced way too early these days, when a lot of kids do not have strong calculation skills of their own.
766099
Get a book from your library on applied math.\n\nInternate must be full of such applictions.