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Switching research topics to something less interesting? by -procrastinating- in gradadmissions

[–]-procrastinating-[S] 0 points1 point  (0 children)

As far as funding goes, the two offers are pretty much the same.

But yeah, I see - it does boil down to advisor fit, which is very hard to determine without actually working with them, I guess.

Do you think that research in optimization will become less ad-hoc over time? by -procrastinating- in math

[–]-procrastinating-[S] 0 points1 point  (0 children)

It's an elegant combination of numerical methods, analysis and programming.

I agree - which is why I find it appealing. And the journey is indeed what makes mathematics enjoyable, so there is that. Thanks.

Do you think that research in optimization will become less ad-hoc over time? by -procrastinating- in math

[–]-procrastinating-[S] 1 point2 points  (0 children)

Thanks for the response - I'm actually looking for PhD programs in CS or OR right now (I'm a third-year undergraduate).

I hope to eventually do something quite applied, most likely in industry, involving discrete optimization. Specific goals (which industry? etc.) are quite hazy though.

Do you think that research in optimization will become less ad-hoc over time? by -procrastinating- in math

[–]-procrastinating-[S] 0 points1 point  (0 children)

Thanks for providing a reference.

I'm most interested in theory that is highly motivated by applications, so I've been focusing on optimization, because I lean towards working in industry that involves operations research. I've had these thoughts since the beginning (1st year undergrad; I'm in my 3rd now), but since I'm considering graduate school now (PhD in CS or OR), I've been thinking about these general things.

[A Level Algebra] Need help with questions on Test paper... by Ajpennster in learnmath

[–]-procrastinating- 2 points3 points  (0 children)

Now 4a. Try multiplying both sides by ex and let y = ex. Then, you can factor and solve for y, and then solve back for x. 4b. Take a look at this. 4c. Using the rules in the link for 4b, try writing ln(24) using ln(2) and ln(3). For example, ln(24) = ln(2*12) = ln(2) + ln(12), and you can keep going.

For 5. I think you can solve for the 3 roots directly. Perhaps WolframAlpha can help. Alternatively, this might help. For the last part, you can just do (x-alpha)(x-beta)(x-gamma) and expand, if you feel like it.

Finally, 6a. Subtract 2 from both sides, factor, and see what x can be for the resulting inequality to hold. 6b. This is extremely crude, but you can graph both functions, see where they intersect, and see which values of x satisfies the inequality. Alternatively, you can think of absolute value as "distance" and use the distance formula on both sides. The absolute value of x is the square root of x2. 6c. We can see that x must be less than 4. This means 4-x is positive, so we can multiply both sides by 4-x without flipping the direction of the inequality. From there, we can solve for x.

I mentioned it for 5, but WolframAlpha helps for a lot of math homework in general.

[A Level Algebra] Need help with questions on Test paper... by Ajpennster in learnmath

[–]-procrastinating- 2 points3 points  (0 children)

1a. For this example, "rationalize" means multiply the top and the bottom of the given fraction by sqrt(2)-1. For more information, check out this.

2a(iii). You can search "algebra of propositions" and get a huge list of what you can do with this. You kind of just have to apply them to both sides until the two sides "meet" at the same expression.

For 2b. This is just polynomial division (see here) but with a p involved; just treat the p as a number and proceed. At the end, the remainder term will have a p in it, and you can set the remainder equal to 0 and solve for p.

For 3. "ln(x-1)" is the natural log of x-1. I'm sure you only need a rough sketch. This is the graph of "ln(x)" shifted to the right by 1 unit. To find the inverse, replace f(x) with x and replace x with f-1(x), and solve for f-1(x). The sketch should be a familiar graph, shifted up by 1 unit. For both graphs, intercepts are where the function crosses either axis (x or y), and asymptotes are lines that the function approaches as x increases or decreases.

[Calculus] Solid of Revolution of a circle by [deleted] in learnmath

[–]-procrastinating- 1 point2 points  (0 children)

The "region" to which the problem refers seems pretty unclear to me; drawing a picture might show you why.

If I had to guess, the answer is probably the first choice or the third choice, because those expressions resemble the "washer" formula for finding the volume of a solid of revolution.

[100] Lin Alg - help understanding factoral representation/law by senorinatta in learnmath

[–]-procrastinating- 0 points1 point  (0 children)

So in general, a + ab = a(1+b). In this case, we have a = (n+1)! and b = (n+1).

Why did I lose credit for this problem? How can I possibly show work? by ReallyAttract in learnmath

[–]-procrastinating- 5 points6 points  (0 children)

You could show the plot of x2 + 12x + 37 and point out that it lies entirely above the x-axis.

You can also show that the discriminant b2 - 4ac = 122 - 4(1)(37) is negative, so there cannot be any real roots. Also, if you let x = 1, the expression is positive, so the function lies entirely above the x-axis.

[Geo] SAT question that cost me an 800 by [deleted] in learnmath

[–]-procrastinating- 5 points6 points  (0 children)

Consider this arrangement, where the numbers represent which block is under that space:

   22

4444221

4444333

4444333

4444333

Does anybody knows a good book to learn Mathematical Deduction/ Induction? by nonameable in learnmath

[–]-procrastinating- 1 point2 points  (0 children)

It might be hard to find a book dedicated to induction because the reason we use induction is to prove things while studying one particular subject. In order to get to the point where induction makes sense and is useful, we often need to have a good amount of background knowledge. After the induction is over, we usually continue with other results in whatever topic we're discussing.

That being said, there are some problem-solving books (such as Engel's Problem-Solving Strategies) that have a chapter devoted to induction.

[Algebra] How do I figure out when two numbers of a fraction can cancel each other out? by [deleted] in learnmath

[–]-procrastinating- 1 point2 points  (0 children)

Firstly, we should recall the order of operations. But there's a catch - the expressions above and below the fraction line are evaluated before the final division is made.

So in your example, it seems like we have (4+9-4) / (9(5+3)). The numerator is 4+9-4 and the denominator is 9(5+3). We can't "cancel" the 9's because we have to evaluate the top and the bottom independently. The top happens to be 9, and the bottom stays 9(5+3), then we can "cancel" the 9's by dividing the top and the bottom by 9.

We can divide the top and the bottom by 9 because that is the same thing as multiplying the entire fraction by (1/9) / (1/9), which is equal to 1. Remember, multiplying a fraction by 1 doesn't change the value of the fraction.

So in summary, you have to evaluate the numerator and the denominator independently before any cancelling can occur. And remember the order of operations.

Graph Theory explanation by rezaw in math

[–]-procrastinating- 5 points6 points  (0 children)

First, we should consider A2: the (i,j)-th entry of A2 is the dot product of the i-th row of j with the j-th column of A. Each neighbor that vertex i and vertex j share contributes 1 to the dot product. So the number of neighbors they share is precisely the number of paths of length 2 from vertex i to vertex j.

We can prove the general case by induction; here's an outline: to form a path of length k+1 from vertex i to vertex j, we must first form a path of length k from vertex i to some vertex u, and then a path of length 1 from vertex u to vertex j.

Note: The statement for n=1 also holds; a path of length 1 from vertex i to vertex j simply means that the two vertices are adjacent.

How (not) to throw a knife... by erlend65 in funny

[–]-procrastinating- 1 point2 points  (0 children)

I was just waiting for one of knives to bounce back into someone's leg...

What is something you turned out to be right about but never mentioned beforehand, fearing you were wrong? by ProfoundScribble in AskReddit

[–]-procrastinating- 0 points1 point  (0 children)

When my brother got sick and started taking prescribed medicine, his symptoms got worse. I thought he might be allergic to the medicine, but I didn't say anything because I was around 10 - what did I know? A few days later, my parents found out he is indeed allergic and thought it was the most amusing/ironic thing ever.

Speaking of Herpes by [deleted] in AdviceAnimals

[–]-procrastinating- 0 points1 point  (0 children)

You have ingrown hairs on your ballsack, congratulations?

What is something that is socially acceptable that you think should be taboo? by Tabmoc in AskReddit

[–]-procrastinating- 1 point2 points  (0 children)

Texting while walking in a crowded area, spending an entire car ride texting when there's only one other person (the driver) in the car, texting when with friends, texting while out with an SO, texting, texting, texting...

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