In complex analysis |z| is called the the modulus. Since the complex field is not well ordered (meaning we can't say stuff like 3<5) then we cannot generalize the real value absolute value into the complex field. Instead we define |z| = Sqrt[x^2 + y^2]. This is consistent with the real valued...
Oh this stuff happens. I once had probability greater than one and didn't notice it until 2 weeks later when a friend of mine says, it all makes sense until here (the 5th equation i wrote.) Sometimes you have lapse in judgement. Get up start again and hope for the best.
Be careful with this attitude. Doing work you don't want to do is important so that you may do the work you want too. There are to many stories of kids who were really bright but never worked hard so when they hit University they just fumbled around after a while. I suggest along with working...
So that is 2 math classes per semester for your sophomore year? Sounds about right. As for if you should take complex analysis before or after topology, that really depends. Each school teaches that course differently. At my school, it depended on real analysis. If people at your school say...
1) presence of researchers working in a subject of interest.?
This was the most important factor for me. A strong research group had to be present with well known people in the field.
2) supportive grad program
This was also key. I wanted to feel that the program was behind me and that I...
I did math at the UT- Austin, so i'm bias. Out of the three schools listed, which one would benefit you the most is a tough question to answer. It really depends on what you value more, and what you expect. I choose UT over Princeton for two reasons: 1)I was a big fan of Austin 2)I hate...
Math GRE is over hyped. I tend to agree with mathwonk's assessment of the test . It is essentially a cutoff point.
mrb if you feel you will one day be able to dominate the GRE than you should relax a bit. I believe Mathwonk was simply saying that if you can't do well on the GRE then you...
heh....you don't. You take it all, you learn it, you say how much it sucks but by the end of the semester you know some cool stuff and it makes it all worth wild.
Really, it's just about reading the book, asking questions in lecture, and doing the homework. When you learn these theorems, you need to sit there and think about what it means and if you really want to get ahead think about what more theorems the the theory or definition implies. It's...
Copying examples is fine for lower division math classes, but as you move up to more abstract classes, then it becomes little use. It's more helpful in the long run to learn definitions, learn theorems and see why they are true, and then apply those theorems and definition to problems. The...
Yep, let's break this down into parts:
1)Assume Ax = b has a solution, then b can be written as a linear combination with the vectors from the columns of A. Since the span is the linear combination of the vectors a1 a2 a3 ... an then b is in the span. So then use your definition.
2)Now work...
You need to show your ideas, so we can work together and get the solution, so let's start with the basics:
If this is true, why would it be true? How many possible incomes are possible?
Come on, this is a pretty fundamental question. If you want to find the row space, you are going to want to row reduce the matrix and use all the nonzero rows as a basis.
To find the null space, set Ax = 0 and solve [ A 0] and right the solution in parametric form. Take the vectors you have...
Let's go back to the definition of L.I and L.D.
If I can write c1* f1 +c2* f2 +c3* f3 = 0 for some scalar c1 c2 c3, and not all of them are zero, then we found L.D. So, can you think of anything? Here's a hit, two of the scalars are the same number.
Linear algebra is pretty important subject. The more you know from it, the better you'll be for it. If you feel your course in it was weak, then go study it independently. You'll find that many linear algebra concepts will be applicable to abstract algebra, so studying for linear algebra can...
Why don't you just get a masters at a moderate school, and then go on to a PhD at a better one? A friend of mine went to a small school in Missouri for his masters and then went off to a top 10 school (world) for his PhD and now is a professor at a pretty good school.
Trying to get a...
It isn't the material is extremely difficult, it's that there are a lot of different things that Calc II needs to do, such as methods of integration, series, and parametric equations. Methods of integration and the information about series is pretty straightforward, but it the work can be...
Minor correct, it isn't to hard if you are from Texas (due to the top 10% rule) but since many people from in-state come, they are a bit more selective from out-of-state. But I do suggest them for engineering or Texas A & M.
You must be reading a different post than I am. I read, pure math is the way to the underground... with no reference to any other field. Anyways, it doesn't matter, let's just say it was one huge misunderstanding!
I have a question though. Does anyone know where I can find good information...
I think some of you guys are reading a bit to much into Mer's post.
What she wrote is pretty much common sense. If you understand the root of a subject you will probably understand the subject a lot more. I'm not exactly sure how any of you guys got that she is knocking applied. I study...
Let a and b be two real numbers.
Let x = ab + (-a)b + (-a)(-b)
x = ab + (-a)[ b + -b]
x = ab + (-a)*0
x = ab
Now once again let x = ab + (-a)b+ (-a)(-b)
x = (a - a)b + (-a)(-b)
x = (-a)(-b)
By the transitivity
ab = (-a)(-b)
Note ab = (-1)(-1)ab, let x = ab and you get x = (-1)(-1)x which...
That's irrelevant. It's like asking, "how hard is it to run the 100 meter dash, and then answered with not as hard as winning a marathon." Regardless if you are right or wrong, it doesn't matter. The skills and purposes are different, even though both events require legs.
Physics is hard. Maybe not at first, but it will become hard and that challenge is what draws quite bit of people. Prepare to work at using those concepts you learn to solve actual problems and then extend those results to new ones.
Mathematics isn't simply about deriving stuff. I don't think a computer, on it's own, can solve all existences, uniqueness, and a myriad of other problems mathematicians solve. It's a useful tool, no doubt, but mathematicians do more than deriving functions.
The other day I derived a...
If you take linear algebra with differential equations you will most likely only see linear algebra and how it used to solve certain differential equations. However, linear algebra has many more applications and useful theorems than simply to differential equations. If I had the choice, I...