1. Homework Statement
here's the picture and it's the second part of question 5:
http://imgur.com/ybSW4v4
2. Homework Equations
N/A
3. The Attempt at a Solution
so by intuition, I suspect that b = sup{a_n: n is in the natural numbers}
If we can show that, then it will...
When you've complete the math degree, did you feel like you got your education's worth and money's worth?
I have a few goals in mind that i would like to complete in math:
Start from axioms and build up geometry
Construct the real numbers
know what's happening in calculus in a deeper...
I don't do well by just reading a proof and internalizing it. I need problems to solve and would LOVE to internalize epsilon delta proofs by practicing 100s of them. It's how I got decent at integrals. It's how anybody gets good at math and music and in general your craft right?
I Don't know a...
One of my life goals is to really just learn how a computer works. I want to learn all the mathematics it takes to understand how a computer works, i want to know the history of it, i want to basically go back to first principles of how a computer works and understand how it evolved into it's...
Like what are the big conjectures or problems that if proven will yield great results in mathematics? Where is topology and abstract algebra now? Is analysis finished? Is linear algebra finished? Is 2d geometry finished? At the frontier of mathematics, what are the most important questions that...
I've often wondered this myself. Is it just a convention? Is it because in a way, all the orders of operation are just "addition" ? addition is addition, subtraction is adding negative numbers, multiplying is addition, dividing is multiplying.
But then if this were true, it would only work...
Like are we talking about just as well as a mathematician or does he have to know the properties of structure in math that he's studying. Not really the rigour but more like what properties it has and what it can do.
Question about "if and then" statements. IE implication statements.
1. Homework Statement
When something is for example asking for:
if |x-3|<δ, prove that |x+3| <δ + k (where k is a constant)
are they supposing it's true? Like are they giving you a hypothesis? How do implication...
1. Homework Statement
From the definition of the derivative, prove that, if f(x) is differentiable at x=c, then f(x) is continuous at x=c.
2. Homework Equations
f'(c) = lim [f(x)-f(c)]/(x-c) This is the definition for a function to be differentiable at
x->c...
Here's my situation. In the math program now. Finding it's ok.. Not the best. Just ok.. I'm wondering if i should just join the army instead. Alot of my time, i think about getting laid or how to get into a girl's pants. I'd rather be doing jiu jitsu, mma and salsa than math sometimes.
If i...
1. Homework Statement
if |x-3| < ε/7 and 0 < x ≤ 7 prove that |x^2 - 9| < ε
2. Homework Equations
3. The Attempt at a Solution
So ths is what I did so far.
|x+3|*|x-3| < ε (factored out the |x^2 - 9|)
|x+3|*|x-3| < |x+3|* ε/7 < ε (used the fact that |x-3| < ε/7)...
Where you just study the graphs of equations but more abstractly. Don't you think that intuitively the cartesian coordinate system makes sense but at the same time, it's arbitrary? We coulda made the left hand side the positive numbers and the right hand side the negative numbers.
Graphs...
1. Homework Statement
http://people.math.carleton.ca/~mezo/A8math1102-11.pdf
1b) please
1. Suppose F is a field, A ∈ Mmn(F), b ∈ Fm and v ∈ Fn is a particular solution to the equation Ax = b. Let S0 ⊆ Fn be the solution set to
the (homogeneous) equation Ax = 0, and S ∈ Fn be the solution...
How long does it take for newly discovered math material or physics material to be standardized into the math undergrad curriculum? Just wondering about hilbert space as well. When did hilbert space first go into the undergrad curriculum?
What's the process like? I've heard there are many exams to write and they are quite difficult. Is it possible to be prepared in writing the actuarial exam by taking a 3 year general math degree? Would you guys recomend a statistics degree instead of a math degree? What classes should i be...
I mean when we're getting into higher level courses and real life, what are the more applicable subjects in math for mechanical engineering?
I'm not asking for myself but for a friend. He wants to get into Computational Fluid Dynamics and would like to prepare himself better during his...
1. Homework Statement
http://people.math.carleton.ca/~mezo/A6math1102-11.pdf
number 2a)
2. Homework Equations
3. The Attempt at a Solution
I just need help knowing what Re means. I've never seen it before and the prof didn't mention it.
Or does calculus rely heavily on graphs for it's discovery to occur? Would it be possible to have looked at the functions on the graph as sets mapping from one A --->B? Or would a mathematician have to have insane intuition and crazy in them to discover this?
I'm sick of still not getting this. I bombed the epsilon delta part of my mid term. A site where it gives many problems on epsilon delta and solutions would be amazing.
1. Homework Statement
Question 5.
http://cg.scs.carleton.ca/~michiel/1805/assignment1.pdf [Broken]
2. Homework Equations
3. The Attempt at a Solution
I arrived here:
Exist X, All Y (P(x,y) and NEGATION (Exist z: NEGATION Q(x,y,z))
I have no idea how you guys do the...
1. Homework Statement
Question 1.
http://people.math.carleton.ca/~mezo/A2math1102-11.pdf
2. Homework Equations
r1 = a modn
r2 = b modn
r = (a+b) modn
3. The Attempt at a Solution
I used the division algorithm
So:
a = (q1)n + r1
b = (q2)n + r2
(a+b) = (q3)n + r
i isolated for r1...
I'm getting bombarded with trying to understand the epsilon delta proof. I'm also getting killed in fields and proving things in that class. The only ones i feel like i have any chance are my computer science classes and discrete math class. What do you guys recomend me? I'm not particulalrily...
I got confused reading spivak's calculus book and couldn't understand why. They said something like
"if you add ab to both sides, you get (-a)(-b)=(ab)"
It's on the 7th page at the bottom. I believe it's the older version of the textbook.
Who are the current greats that will go down as "Gods equal to Gauss, Euler, etc.)?
Each generation of mathematics (dunno how long a generation is) have great mathematicians. Last generation was Hilbert, Poincare, cantor, and prolly 1-2 more. Alot of the works that these mathematicians have...
I don't know much about this P vs NP debate at all but what happens if they assume P = NP or P=/=NP? What does it mean when somebody resolves the debate? Why are there tons of mathematicians and computer scientists who are split between the two?
And what's considered modern mathematics? I always thought it was 1960s+. Around 50 years ago till now is what i considered modern math.
Anyway, how important is topology? I've heard people say "the idea of evolution to biology is the same as the ideas of topology to mathematics." So is it...
Should one who is trying to be a statistician supposed to know ALOT about computer science?
Should i take up to 2nd year courses on computer science? Would they need to take design and analysis of algorithms or computable functions
Does higher level mathematics like stochastics, analysis, topology apply to software engineering?
Do software engineers even use statistics/probability?
Can I be a software engineer with a computer science degree?
My friend said to be a software engineer, you need a software engineer degree...
I want a timeline for trigonometric function and how it was developed. Just like who created it and stuff like that. Did the greeks know about trigonometric functions? Is a tangent in calculus the same as a tangent in trigonometry and the function os a trigonometry? How do trigonometric...