Unfortunately, the people who post basic algebra problems have not taken enough math to know what "Linear and Abstract Algebra" means. They see only the word "Algebra"!
Lately there have been a ridiculous amount of off-topic threads put in this subforum, so I want to take the time to remind everyone that this is a very specific subforum meant for advanced algebra only. Basic algebra questions should be placed in the pre-university subforum. If your algebra question isn't part of an assignment or topic from at least a 2nd or 3rd year university course, chances are it shouldn't go here. Also, this is not the generic place to put any advanced question. If you have a question about analysis, please put it there. That's why we have an analysis subforum! If it's about topology, put it there! Again, that's why we have one.
Cliffnotes: Only put advanced algebra questions in this subforum. Those who can't follow this simple guideline will be warned, then infracted, so please don't do it.
Best,
Jameson
Most non-mathematicians seem to think that "algebra" means replacing numbers with letters.
Actually, algebra is the study of sets which are structured by one or more binary relations.
If you don't know what a group or a ring or a field is, this is not the place for your post
I disagree to using that as an excuse. People should read the whole sentence. Even though they may not know what "linear algebra" is, they should at least recognize the fact that they themselves are not familiar with the term. If you dont know what a term means, why would you pretend to and make decisions based on those false presumptions?
Think about it. You may not know what a term is... but how can you not know that you do not know what a term is?
People are not in the right for acting on their own ignorances. In my opinion. At least if they are intellectually capable enough to recognize the fact that they are ignorant. You can appreciate the fact that you are ignorant of something and choose to refrain from making presumptions about it. This is basic ethics. Its basic reasoning skills
I will however add that the phrase "advanced algebra" is a relative term. A ninth grader undoubtedly believes himself more advanced than an eighth grader. Unfortunately, a lot of the phrases we use... "advanced", "pre-", are abstract and ambiguous terms which are in no way indicative of a particular curriculum. I think if the administration is going to be picky about what goes where, they should explicitly list that topics associated which each category. To precision.
After all, what makes us good at math is our ability to reason critically, rigorously, without making assumption, and our appreciation for specificity and our reluctance to operate under ambiguity. Those of us who can help know where to look, those of us who need the help dont know where to post.
Very little isnt algebra. Combinatorics is algebra. Calculus is algebra. Algebra is a very wide field... another ambiguous term in and of itself.
I, myself, just got done posting a combinatorics problem in the discrete math category, not the probability/statistics or the advanced algebra. Even though it could arguably fit into either.
I dont know what constitutes an advanced algebra topic. Rings? Fields? What about finding the root to a cubic or a quartic polynomial using Cardanos method? Finding the roots to an arbitrary cubic was something I had to look up. Im midway through a masters in math and I have never been taught this before. Its certainly not learned at the community college level, and especially not at the high school level. And yet, the topic and the subject matter are both pretty trivial. So would it belong in advanced algebra or in basic algebra?
Indeed, I find the segregation of "college" math and "baby" math to be offensive. There are students at the college level learning basic algebra and there are students at the high school level learning multivariate calculus. Grade-level has nothing to do with course, curricula, or subject matter. Categorizing it as such is offensive because it puts an "intelligence" or "academic" quality on a category where it is not deserved or warranted. Suddenly the category "algebra" no longer has a basis in subject matter but a basis in the students capacity to perform.
I have actually been to math forums where basic algebra was placed in the "elementary school" section, subjects up to multivariate calculus and advanced statistics were all placed in the "high school" section. Pretty much the only subjects in the "college" section were subjects that I, as a math major, had only just begun to learn even so much as existed. If the forum is for the layman who needs help, why go out of your way to offend them and turn them off by associating their need with their subject matter?
CAN ANYONE PLEASE TELL ME ABOUT
Cauchy–Schwarz inequality
1. WHAT IT MEANS ACTUALLY I KNOW FORMAL DEFINITION BUT I WANA INSIGHT CONCEPT WHY PRODUCT OF INDIVIDUAL VECTORS IS ALWAYS> AND EQUAL THAN INNER PRODUCT
2. SPECIFY THE CASE WHEN PRODUCT OF MAGNITUDES OF IND.VECTORS IS = MAG OF INNER PRODUCT
MAY THIS HELPS ME TO GET INSIGHT CONCEPT
I AM NEW TO THESES FORUMS IF ANYONE CAN EMAIL ME IT WILL BE GREAT FOR ME...
THANKX.
E-MAIL ADRESS:
junaidanwar194@gmail.com
It seems to me there's a lot of gray area. For instance, a familiar theorem says that the diagonals of a parallelogram bisector each other. An elementary proof is easy to find, and I assume all of us do this some time in high school. But suppose you want to prove it using vectors. That we might not learn until we take linear algebra. And linear algebra does belong in this forum. I think. Maybe we could use another forum about linear algebra.
I'm working through Norman Wildberger's WildLinAlg videos now (so far as I know, this video series is not used in any credit classes anywhere, but it's a very interesting treatment of the subject). He includes a lecture on 3D geometry. I'm thinking of asking a question about one of his exercises. Since it's part of a linear algebra program, I figure I should post it in this forum. Would I be right to do so?