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# Salary concerns for Engineers (Degree Level Matter ?)

• Engineering
I am not sure if this would deem another thread but I wanted to ask if school and/or degree level (BS, MS,PhD) has meaningful bearing on starting salary with electrical engineering. I know that there are people who can make 100k with BS and people who make 50k with MS. However there is a difference between possibility and probability. I am basically asking how salary correlates with degree level in the most practical sense for engineering careers.

Higher degrees get higher salaries; that's how the two correlate.

Not sure what you are really asking.

I felt that was the general case. However I have heard of cases where people make more with just a BS degree. I guess what I am really asking about is what causes some people to be "special cases" in which they only have a BS degree and make as much as the corresponding masters degree.

Staff Emeritus
One's salary is not a reward for doing well in school. One gets a salary of $X because one's employers would rather have you working for them than an extra$X profit at the end of the year. Simple as that - it's all about how much money you can make for your employer. Some people do that better than others.

JakeBrodskyPE
Thanks Vanadium. That does put things into a better perspective. Then in that case, should one apply for positions that specifically state that graduate degrees are preferred in order to get the advantage for a salary. Or rather should one use their skill set to increase the net profit for the company.

The only off part of this ideology is that generally, MS people tend to make more on average....unless that is the result of increasing company profit.

Higher degrees get higher salaries; that's how the two correlate.

Not sure what you are really asking.

No, they don't. There are several reasons for this.

First, Engineering is a very practical field. What matters most is PRACTICE, not education. If you're trying to build something truly revolutionary, of a sort that nobody has ever tried before, then yes, more education may help. However, practical experience usually are the engineers with gray hair who have seen what works, how it works and when it doesn't work. THEY are the people making those big salaries.

Second, those with education tend to seek less common, more unusual endeavors. The intellectual challenge is what intrigues them. However, those jobs are few and far between. There is a lot of competition for those sorts of positions. They tend to make LESS money.

Third, Engineers are always studying new things. You don't just go to school and then stop learning so that you can practice what you learned. So your claim about the value of higher education is somewhat mystifying to say the least.

I know lots of people, some with Ph.D educations, who make less than I do. It is not about education. It's about the capabilities you bring to the table.

Let me leave you with this, lest you get the wrong idea about what I'm saying here: You go to school to study. You scratch an intellectual itch. And then, having scratched it, you go out in to the real world and try to make something of yourself and your community. There are many ways to do this. But above all you must NEVER stop learning. Educational institutions are supposed to instill a love of learning and an ability to teach yourself more. Getting a higher education isn't necessarily better. It merely means you studied more in a formal class-oriented atmosphere.

I have studied many things outside the confines of a university. I have learned a lot from many people in many walks of life. That's why they pay me the salary I get.

jackyl_83sg
Jake. I understand what you are saying and honestly I feel that experience is worth it's weight in gold for engineering. You also made valid points. My only concern is if what you say is prevalent, why is it cited on multiple job statistics like BLS that masters of engineering make more on average. Also I have seen different job postings where MS were preferred for hiring, despite the fact that the position formerly was for BS people.

Not to imply that this is the case for you, but if your only interest is money, then engineering is not a career for you. You will make far more with far less work by heading towards finance or business.

That said, no. A graduate degree alone does not command a higher salary. The problems you study in school will provide you with knowledge and theory, they will not provide you with experience in the real world. Classes cannot prepare you for the world that engineers actually work in. They won't teach you things like how to negotiate with manufacturers or salespeople, they won't teach you how to work in multi-disciplinary teams (at least not directly), and they don't always emphasize many secondary skills that employers of engineers value like foreign languages or finance.

However, there is still value in an advanced education in that it can open certain doors for you. You'll be able to tackle more unusual problems that require a deeper knowledge of certain subjects. If the idea of doing unusual work that few other people have done appeals to you, then that's what you need. And at the end of the day, if you love your work the money will come on its own.

And speaking of money. If your goal is to be rich or at least financially comfortable, then you should be focused on saving and investing rather than earning a high salary on paper.

J My only concern is if what you say is prevalent, why is it cited on multiple job statistics like BLS that masters of engineering make more on average.

Many people do not pursue their Master's degree or PhD until they are older. This means they may have their own firms or have advanced to leadership positions, or they've moved into consulting work. Also, I'm not sure that counts people with Master's degrees who are not working in positions that require them.

Staff Emeritus
Let me say it again, because I don't think it sunk in the first time. One's salary is not a reward for having done well in school.

JakeBrodskyPE
OK. Jack, you made some even more valid points. And to answer your inquiry, I'm not involved in engineering just for money. I really do have a passion for my field of study. My bigger concern has been gaining experience to match what I want to practice.
That said , I understand that no guarantees come with a BS or MS and that no matter how a class is taught, it doesn't mean your pay or experiences will be the better for it [giving respect for what vanadium has stated]. I am trying to do what I want because I'm passionate in learning more about it and become more skilled with it. That why I am in grad school.

No, they don't. There are several reasons for this.

That wasn't the question. It wasn't about what matters more; degree or experience.

The question was how degree and salary correlate. There's three possibilities. They correlate, positively. They correlate, negetively. Or there is no correlation at all.

Obviously a degree is being looked at. So there must be correlation.
All things else being equal, do you really believe someone with an MSc makes less than if that person would have had a BSc?

Apparently we are talking about engineering, but surely even with engineering, being less educated doesn't make you a better engineer, right?

Obviously a degree doesn't fix your salary for life and we all believe you truly make a sickening amount of money, but all that wasn't really relevant.

That wasn't the question. It wasn't about what matters more; degree or experience.

The question was how degree and salary correlate. There's three possibilities. They correlate, positively. They correlate, negetively. Or there is no correlation at all.

Obviously a degree is being looked at. So there must be correlation.
All things else being equal, do you really believe someone with an MSc makes less than if that person would have had a BSc?

Apparently we are talking about engineering, but surely even with engineering, being less educated doesn't make you a better engineer, right?

Obviously a degree doesn't fix your salary for life and we all believe you truly make a sickening amount of money, but all that wasn't really relevant.

Engineering is not like scouting where you earn merit badges and then move on to other things. It is a practice. Yes, there are bureaucratic toads who look only at merit badges and think that this must mean they're more competent.

Those motivated to work on a Master's degree tend to be those who would work heavily on technical things. But Engineering is more than that. If you think that people will see that MSc and decide to throw more money in your cubicle just because you have one, keep dreaming. Thanks to utterly blind HR policies, an MSc graduate may start off with more money, but that's no guarantee that you'll continue to improve your income. I'm sure you've seen the economics equations on compound interest...

The reason why people think an MSc is a good investment is because many HR departments are looking for differentiation methods to weed out some applicants. Thus, you do see a lot of positions where MSc degrees are preferred or even required. This is particularly the case for Civil Engineering.

However, the actual performance on the job does not require advanced degrees. There are no secret decoder rings that they hand out to MSc graduates that enable them to unlock the magical salary buckets filled with technical proficiency money to take you to the next level.

Oh and another thing: I make a middle class salary. It's probably closer to upper middle class, but it is still a middle class salary. The reason I'm still practicing engineering is because I enjoy it and I don't mind the lifestyle. If I wanted money, I'd have probably gone for a degree in business, accounting, or some other degree that gets you in to boardrooms these days. I've seen what executive life can do to people. Some handle it better than others. I'm not one of them.

billy_joule
Jake. I understand what you are saying and honestly I feel that experience is worth it's weight in gold for engineering. You also made valid points. My only concern is if what you say is prevalent, why is it cited on multiple job statistics like BLS that masters of engineering make more on average. Also I have seen different job postings where MS were preferred for hiring, despite the fact that the position formerly was for BS people.

Bureaucracy is a funny thing, isn't it? If you were in charge of an HR department and you had no idea how to screen applicants in an open, easily reviewable, "transparent" manner, what would you do? You'd look for more education. So that's what they do. Does it work? I don't think it hurts. But it doesn't help.

Basically, if the job market is thin and you don't think you can find a job right away, an MSc may help pad your resume or CV to get you an interview.

However, once you hit the real world, all that becomes irrelevant. But for one case, I have not seen consistent evidence that someone with an MSc in Engineering will outperform someone else without one. The best case I have seen is that Civil Engineers tend to have a lot of higher math courses in a Master's degree than they'd get in a Bachelor's degree. However, most Bachelor's Degree Mechanical and Electrical Engineering students get those classes early in their Bachelor's Degree studies.

Those who tend to worship proficiency in mathematics might think that a Master's degree is almost essential for Civil Engineering. And for some disciplines of Civil Engineering, such as Structural Engineering, that math really is essential. But that's only one case out of many. Since you were asking broad questions about all engineering, the general answer is no, it really doesn't seem to make much difference in most cases.

So jobs where you need a minimum of five years of education pay less than jobs that require three years of education?
Or you lose skills you learned in those three years in the two years of the MSc, making you lose employability.

You are typing a whole lot but I don't see why a lower degree is better than a higher degree. Why not get a job without even a BSc and make even more money?

Apparently you have a BSc and think you did well. That's all fine, but what does performance on the job have to do with your degree? Obviously a guy with an MSc that never even shows up for his job is going to get fired and make less. No one is going to keep him around 'because he has an MSc'. But that's not the point. No one is saying that an idiot with an MSc will do better than a model employee with an BSc.

Obviously employers look at your degree, so it must have an effect. So does it lower your salary or increase your salary? You say you will earn less with an MSc? So you should never put it on your cv and never mention it? (But secretly use those skills on the job (or are you saying it is all a complete waste of time?))

I know that the US kind of has a strange system where you earn a BSc as a terminal degree. Where I live you start at the BSc level knowing you will do an MSc and the level of math and pace is uniform across those 5 years.
There are other studies where the BSc is a terminal degree. Those studies are completely different in nature, while similar to US BSc degrees. But no one here would ever equate these two education tracks as anyone who has come into contact with either knows they really differ a lot.
The remainder of Europe should be very similar.

Are you really saying that in the US the average MSc is just a glorified BSc? If so, something is wrong with US education.

I know that in the US you can be an engineer with a BSc. Here, you need a 5 year academic education with an MSc as terminal degree to be a true engineer. With a BSc you start out as a glorified technician but with more oppertunities.
Surely you can do really well or really bad during your career. But upgrading your level of math and abstraction while you are doing your job, does that really happen in engineering?

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Quantum Defect
Homework Helper
Gold Member
Look at publications from the Professional Societies if you want more data. In Chemical Engineering, the American Chemical Society publishes salary information (broken up by academia/government/industry) as a function of terminal degree (BS, MS, PhD).

Engineering is a very big field.

billy_joule
So jobs where you need a minimum of five years of education pay less than jobs that require three years of education?
Or you lose skills you learned in those three years in the two years of the MSc, making you lose employability.

You are typing a whole lot but I don't see why a lower degree is better than a higher degree. Why not get a job without even a BSc and make even more money?

You're reading things in my comments that aren't there. I'm not saying you'll earn less. I'm just saying that a Bachelor's degree with two years experience is just as good in most Engineering fields as a Master's degree. So why would one get a Master's degree? Well, for a very few engineering endeavors, such as structural engineering, it is necessary because the standard curriculum does not cover it.

However, in most Engineering endeavors, A BSc and two years experience is about equal to an MSc. In other words, unless you're trying to scratch an intellectual itch of some sort, or you have some specific endeavor in mind that is primarily theoretical, there is usually not much to be GAINED by spending the extra time and money on a Master's degree. And if you're thinking about a Ph.D in Engineering, you must be looking to teach others because honestly, there isn't much that a Ph.D in Engineering is BETTER for.

In a practical field like this, educational foundations are important. However, practical experience is what you bring to the table when negotiating salaries.

donpacino
Gold Member
@OP. There has been a lot of talk about what makes a good engineer and how much your degree level effects LONG TERM salary. That being said there is a truth that i don't think anyone has pointed out yet.

On average out of college with no experience phd makes more than MS makes more than BS. Period.
after you are in the work force for a few years this is not necessarily true.

for example at my company entry level engineers with no experience come in at pay grade 8 if they have a BS and pay grade 9 if they have a MS. there is a lot of variation in the bands, but at the end of the day the MS people will make more than the BS people.

That being said there is a truth that i don't think anyone has pointed out yet.

On average out of college with no experience phd makes more than MS makes more than BS. Period.

That has, in fact, been pointed out. However, it isn't meaningful. The question isn't whether an MS makes more than a BS right out of college. The question is whether an MS right out of college makes more than an entry level BS with 2 years of experience. Or whether a PhD right out of college makes more than a BS with 5 years experience.

billy_joule
A little reminder: comparing salaries is a terrible way to compare the financial value of two careers or career paths, as it doesn't take into account the time value of money or opportunity cost.

So I question whether the OP is really asking the question they mean to ask.

donpacino
Gold Member
@OP. There has been a lot of talk about what makes a good engineer and how much your degree level effects LONG TERM salary. That being said there is a truth that i don't think anyone has pointed out yet.

On average out of college with no experience phd makes more than MS makes more than BS. Period.
after you are in the work force for a few years this is not necessarily true.

for example at my company entry level engineers with no experience come in at pay grade 8 if they have a BS and pay grade 9 if they have a MS. there is a lot of variation in the bands, but at the end of the day the MS people will make more than the BS people.

QuantumPion
Gold Member
It is also interesting to note that in some industries it may be actually harder to get a position with a MS as opposed to just a BS. The reason being that having a MS generally commands a higher starting salary, but someone with an MS is usually no more productive than someone with a BS for the same experience level, so the value to the company is less.

Where I live people with an MSc will have a different mentality and background because the place where they do their BSc is completely different from where BSc terminal degree people do their degree. There are many more high achievers and you get an academic background, and much more well-versed in math and fundamental theory. Everything is rigorous and no short-cuts are taken while at the BSc terminal degree programmas it is all about getting the job done and filling in the skillsets-profile your profession/future employees require.

I think that in the US it should also be the case that only top students go on to get an MSc, right? But otherwise it is similar?
So yes here, an MSc will make it easier to get a job that is usual done by a BSc. But that doesn't mean you get paid more.
Often I see vacancies with "8-10 years of experience for BSc, 4-6 for MSc", almost always the experience gap is bigger than the additional time spend in university.

Also, comparing someone with a BSc and 2 years of working experience to someone with a fresh MSc degree is no more fairer than comparing both just out of school, for many reasons.
They both start getting salary at a different point in time, they both start off at a different salary, but they also both have different salary curves throughout their career.
This is obvious when you add a third case of someone with no degree whatsoever. When he has 5 years of working experience he probably earns the most out of all 3. Yet no one in his right mind would suggest that not having an education at all makes you more money.

Also, when you take a BSc graduate and add 2 years of valuable working experience you are already skewering the comparison because not everyone, BSc or MSc, will have a job giving valuable working experience right out of university.

And when it come to the US, and some other places, we aren't taking into account maybe the most important factor; how much debt did one take out to get that degree.

Only when you come at PhD level employee's may feel you are overqualified; they will think you have no long-term interest in the mundane job profile they have to offer you. In that case they rather have an BSc or MSc take the job, leading to better continuity.

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Also, comparing someone with a BSc and 2 years of working experience to someone with a fresh MSc degree is no more fairer than comparing both just out of school, for many reasons.
They both start getting salary at a different point in time, they both start off at a different salary, but they also both have different salary curves throughout their career.
This is obvious when you add a third case of someone with no degree whatsoever. When he has 5 years of working experience he probably earns the most out of all 3. Yet no one in his right mind would suggest that not having an education at all makes you more money.

All of these supposed issues can be solved by considering the time value of money and the cost of education.

So in the case of the BS vs Masters, find the net present value of the BS's earnings at 2 years into their career. Then find the NPV of the masters at start date and subtract the PV cost of the MS.

That is absolutely a fair way to compare those two. The same process can be done for the no degree case.

You can use some model from finance or economics, but in the end it is just another opinion.


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# 1.1 – Types of Numbers

## Section 1 (Apex Pg 1 – 8)

Objectives

• Organize collections of numbers into mathematical sets.
Keywords
• Set – a collection of objects.
• Subset – a set that is part of a larger set.
• Element – an element is an individual item of a set.
• Counting Numbers / Natural Numbers – the numbers used to count: {1, 2, 3, 4, 5, …}.
• They go on forever; they are infinite, positive integers.
• Whole Numbers – the counting numbers (positive integers) and also zero:  {0, 1, 2, 3, 4, 5, …}.
• They go on forever.
• WhOle numbers have a zerO in them!
• Integers – whole numbers and their opposites:  {…, –3, –2, –1, 0, 1, 2, 3, …}.
• Positive Integers – these are the counting numbers / natural numbers.
• They are greater than zero:  {1, 2, 3, 4, 5,…}.
• Negative Integers – the integers that are less than zero.
• They are the opposites of the positive integers  {…, –3, –2, –1}.
• Opposites – two numbers that are equally far from zero in opposite directions along the number line.
• Adding a minus (or negative) sign to a positive number creates its opposite.
• Removing the minus (or negative) sign from a negative number creates its opposite.
Examples
1. Months
• Set – all of the months of the year
• Subset – winter months { December, January, February ]
• Element – December
2. Numbers
• Set – all numbers
• Subset – positive, even integers: {2, 4, 6, 8, 10,…}
• Element – 4

Notes

• A set is often shown by listing its elements within curly braces, sometimes called brackets { }.
• The ellipses (…) show that these numbers go on forever.

## Section 2 (Apex Pg 9 – 19)

Objectives

• Convert fractions to decimals to percent.
Keywords
• Fraction – a part, or parts, of the whole.
• Numerator – the number of parts being considered.
• Denominator – the total number of parts in the whole item.
• Decimal – you can write every fraction as a decimal by dividing the numerator by the denominator.
• Terminating Decimal – a number that ends
• Repeating Decimal – a number that keeps on going forever
• Percent – “per one hundred”
• The symbol that represents percent is %.
• Convert a decimal to a percentage by moving the decimal point two places to the right and putting % after it.
Notes
• The symbol ≠ means “is not equal to.”

## Section 3 (Apex Pg 20 – 32)

Objectives

• Define rational and irrational numbers, and explore their properties.
• Characterize numbers as fractions, exponents, and square roots.
• Show the relationships between numbers with a number line and inequality symbols.

Key Words

• Real Numbers – a set made up of all the numbers on the number line.
• Any real number is either a rational or irrational number.
• Rational Numbers – the set of all numbers that can be written as a fraction (which is a ratio of two integers, where the denominator is not zero).
• The rational numbers are a subset of the real numbers.
• Irrational Numbers – numbers that cannot be written in the form , where a and b are integers.
• Irrational numbers cannot be written as terminating decimals or repeating decimals.
• Proof by Contradiction – a method of proving that a proposition is true by showing that an assumption is false.
• Proposition – a sentence that is either true or false.
• Assumption – a statement that is accepted as true at the beginning of a proof.
• Exponent – a small raised number that tells you how many times to multiply the base number by itself.
• Base – a number in exponential form. It appears beneath the exponent.
Notes
• Squares and Square Roots are inverse (opposite) operations
• Rational Numbers
• Terminating (ending) numbers such as 4.5, 3.75, 2, 1/4, 2
• or Repeating numbers such as 0.222…, 3.876587658765…, 0.7777…
• Irrational Numbers
• They go on forever
• and they do not have any pattern
• Examples
• π
• √2, √3, √5, √7, etc.
• e
• Ratios make up Rational Numbers
• Examples
• 3/5 = 3:5 = 3 to 5
• 2/7 = 2:7 = 2 to 7

## Section 4 (Apex Pg 33 – 39)

Objectives

• Show the relationships between numbers with a number line and inequality symbols.

Key Words

• Number Line – a line that uses equally spaced marks to represent numbers.
• Numbers to the right of zero are positive, and numbers to the left of zero are negative.
• The greater a number is, the farther to the right it is placed on the number line.
• Comparison Symbols – Symbols used to compare two numbers or expressions.
• Comparison symbols include:

> (greater than)
< (less than)
≥ (greater than or equal to, at least)
≤ (less than or equal to, at most)
= (equal to)
(not equal to)

• at least : a number or more
• at most: a number or smaller

format: plain


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# Calculate $$cot 270°$$

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Calculate $$cot 270°$$

I use extensively Windows calculator, and right now I'm studying trigonometry.
So I wanted to calculate $$\cot 270°$$ in Win calc, but so far I don't know how. I would appreciate I you show me.
(Note: I could use $$\cos270°\csc 270°$$.)
Thank you.
KarimTef

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### Re: Calculate $$cot 270°$$

cot (360-90) = (cot(360)cot(90) + 1)/(cot(90) - cot(360)) and cot(x) = cos(x)/sin(x)

ten2match

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### Re: Calculate $$cot 270°$$

My question was: what was the keys in win calc that when pushed give the answer to the question. Apparently, it's just calculating cos 270, put it in the memory, and then calculate sin 270, and then perform the division cos 270/ sin 270.
FWIW, I wasn't and I'm not doing any ads for anyone, but I was really stuck.
KarimTef.

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# Weierstrass Substitution

## Definition

In integral calculus, the Weierstrass substitution or tangent half angle substitution is a method for solving integrals, which converts a rational expression of trigonometric functions into an algebraic rational function, which can be easier to integrate. The Weierstrass substitution is very useful for integrals that involve a simple rational expression with sine and/or cosine in the denominator.

### Struggling with math?

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# How use probability distribution to generate a binary array with k number 1s acording a range of lower and upper bounds

I need to generate a binary array of size N with K numbers 1 and (n-k) numbers 0 on it,does not matter in which position. The amount of K numbers 1s belongs to an interval Min <= K <= Max , and Max <= N .

Since these values is represented by a binary variable, the probability of array position has 0 is P(x=0) = 0.5 and it has 1 is P(x=1) = 1-P(x=0) = 0.5.

Let's suppose an array size of N=100 must have K numbers 1s on it according 20 <= K <= 30 ,i.e. Min=20 and Max=30.

My first idea to use a probability function to generate the values for this array was developed according to the following considerations, which I'm not sure if it is correct :

(1) for the MIN constraint K>=20, since the probability of 1s is P(x=1)=0.5 and it is required that at least 20 positions been filled with 1s then , at least 20/100 =20% , (Min/N) positions must have 1s, However, for a random binary variable P(X=1) = 0.5 , so how to combine this with the constraint of 20% must be 1 ?

(2) for the MAX constraint K<=30, it means that the (100 - 30) remaining positions must be 0, i.e. 70/100 = 70%, (1 - Max/N) positions must have zero. However, for a random binary variable P(X=0)=0.5, how to combine this with the constraint of 70% must be 0 ?

(3) the interval 20 <= K <= 30 , can be either 0 or 1, i.e. (30 - 10)/100= 20% , (Max - Min)/N positions can be filled 0 or 1.

After found the probability of 1s "prob_one", I'd like to write my code using a "rand" function (which returns a random number between 0 and 1) to fill each position of the binary array like this :

"if rand <= prob_one then myarray[position] := 1 else myarray[position] = 0" .

My Questions :

Q1) Do considerations (1) , (2) and (3) make sense ?

Q2) Is there any probability distribution function that can solve this problem and give a direct answer like P(X=1) = prob_one and P(X=0)= prob_zero ?

I appreciate solutions, explanations, examples and material references on how to solve this.

• Is there anything wrong with choosing p=(lower limit+upper limit)/2, in this case p=25%, with rethrows if the number fails? – JMP May 2 at 19:42
• This array must have at least lower limit of 1s . So I think there could be an option to have (L+U)/2 number 1s. But I'm searching first the probabilistic formula. Thanks or now ! – JRG May 2 at 19:52

The number of arrays which contains exactly $$k$$ times the digit $$1$$ is given by:

$$n(k) = {N \choose k} = \frac{N!}{k!(N-k)!},$$

where $$a!$$ is the factorial of the number $$a$$.

If you want to find the number of arrays with $$20 \leq k \leq 30,$$ then you must evaluate:

$$\sum_{k=20}^{30} n(k) = ...$$

In order to arrive to the same result using a probabilistic approach, you should first notice that the number of $$N$$-arrays composed by "0" and "1" digits only is $$2^N$$. Moreover, the probability that one of these array contains exactly $$k$$ digits $$1$$ is given by the binomial distribution:

$$P(k) = {N \choose k}p^k (1-p)^{N-k},$$

where $$p = \frac{1}{2}$$ is the probability of having a $$1$$. Therefore, the number of arrays which contains exactly $$k$$ times the digit $$1$$ is given by: $$n(k) = 2^N \cdot P(k) = 2^N {N \choose k}p^k (1-p)^{N-k} = 2^N {N \choose k} \left(\frac{1}{2}\right)^k \left(\frac{1}{2}\right)^{N-k} = {N \choose k} 2^{N - k - N + k} = {N \choose k},$$

which is exactly the same result presented at the beginning of this answer.

If you want to find the probability to extract one array with $$20 \leq k \leq 30$$, then you should evaluate:

$$\sum_{k=20}^{30} P(k) = \frac{1}{2^N}\sum_{k=20}^{30}n(k) = ...$$

• tks for the prompt reply. I'm not sure if I clearly described my point or if you didn't got he point> I'm NOT looking for the the number of arrays which has 20<=K<= 30 numbers of 1s whithin , as your answer proposed. I'm interested in a single array only that has 20<=K<=30 number 1s on it and I want to find the probability of such K . In other words given a single array of 100 positions, I want fill K positions of this single array with number 1, considering Lower <= K <= Upper . What is the the probability of having K number 1s in one single array of size N ? – JRG May 2 at 20:13


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# How can I prove it is a martingale when there is a jump process

Let $N_t$ be a Possion process, $M_t=N_t - \lambda t$ we can easily show that $M_t$ is a martingale.

Now $\int_0^t\Phi_udM_u=.....=\sum_{i=1}^{N(t)}\Phi_{\tau_i}-\lambda\int_0^t \Phi(u)du$

$\tau_i$ is jumps time of the poisson process $N_t$.

The question is how to prove $\int_0^t\Phi_udM_u$ is a martingale?? You may give any extra conditions to $\Phi$ if needed. (I am more interested in the ideas to cope with this question instead of this question itself.)

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Hi I think you should add more inforamtions about properties of $\Phi$ if you want to get an answer. Best regards –  TheBridge Jan 25 '13 at 16:21
If we want to easily show that $M_t$ is a martingale, we might better define it as $M_t=N_t-\lambda t$. –  Did Jan 25 '13 at 21:07
Did: Thank you. That is a typos. –  XXX11235 Jan 26 '13 at 16:33
TheBridge:I have editted the question. You may give any conditions if needed. Thanks. –  XXX11235 Jan 26 '13 at 16:34
Any ideas to solve this question? –  XXX11235 Jan 29 '13 at 19:16

## 1 Answer

We can prove rigorously that $(\tau_1, \tau_2....)$ given N(t)=n is uniformly distributed in $[0,t]^n$ space. Then the question can be solved easily.

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# Thread: [SOLVED] Integration by Parts Help

1. ## [SOLVED] Integration by Parts Help

Does anyone know how to do the integral of "4x arcsin(x)dx" ? Help is much appreciated.

2. Originally Posted by GreySweatshirt306
Does anyone know how to do the integral of "4x arcsin(x)dx" ? Help is much appreciated.
Use integration by parts $u = \sin^{-1}x,\;\;\;dv = 4x\,dx$

3. $
\begin{gathered}
I = \int {4x\arcsin (x)dx} \hfill \\
u = \arcsin (x) \Rightarrow du = \frac{1}
{{\sqrt {1 - x^2 } }} \wedge dv = x \Rightarrow v = x^2 \hfill \\
\end{gathered}
$

$
I = x^2 \arcsin (x) - \int {\frac{{x^2 }}
{{\sqrt {1 - x^2 } }}dx}
$

Now

$
\int {\frac{{ - x^2 }}
{{\sqrt {1 - x^2 } }}dx} = \int {\frac{{1 - x^2 + 1}}
{{\sqrt {1 - x^2 } }}} dx = \int {\sqrt {1 - x^2 } } dx + \int {\frac{1}
{{\sqrt {1 - x^2 } }}dx}
$

Can you continue?

4. Correction:

$\int\frac{-x^2}{\sqrt{1-x^2}}\,dx=\int\frac{1-x^2-1}{\sqrt{1-x^2}}\,dx=\int\sqrt{1-x^2}\,dx-\int\frac{1}{\sqrt{1-x^2}}\,dx.$

5. Originally Posted by Scott H
Correction:

$\int\frac{-x^2}{\sqrt{1-x^2}}\,dx=\int\frac{1-x^2-1}{\sqrt{1-x^2}}\,dx=\int\sqrt{1-x^2}\,dx-\int\frac{1}{\sqrt{1-x^2}}\,dx.$

Always I happened me that

thank you


text:
# Let X be a random variable uniformly distributed on the interval [−1, 1], and Y = |X| [closed]

Let X be a random variable uniformly distributed on the interval [−1, 1], and Y = |X|. Find the density function and the distribution function of Y .

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What have you tried? –  Brett Frankel Apr 18 '12 at 3:21
Hint: You can solve this with no calculation whatsoever. No pen, no paper. –  cardinal Apr 18 '12 at 3:26
Let $Y=|X|$. We want to find the cumulative distribution function $F_Y(y)$ of $Y$. By definition, $F_Y(y)=P(Y \le y)=P(|X|\le y)$.
It is clear that $F_Y(y)=0$ if $y\le 0$, and that $F_Y(y)=1$ if $y>1$. For $0<y<1$, we have $$F_Y(y)=P(|X|\le y)=P(-y \le X\le y)=\frac{2y}{2}.$$ This is because the interval $[-y,y]$ has length $2y$, and the density function of $X$ is $\frac{1}{2}$ on the interval $(-1,1)$. So on $(0,1)$, we have $F_Y(y)=y$, and therefore $f_Y(y)=1$. The random variable $Y$ has uniform distribution on $(0,1)$. This is intuitively almost obvious. We went through some formal calculations as preparation for handling more complicated problems of a similar type.


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# Content tagged Physics

Bill Nye to Visit Creation Museum for Debate - ABC News
posted on 2014-01-04 01:46:27
Multiple Cursor Mode
posted on 2013-09-26 15:35:00
In case you haven't already tried it, Multiple Cursor Mode for emacs is awesome. I actually got chills the first time I used it to edit multiples lines of work on a physics problem. All those repeated lines of LaTeX code, and now I can change them all at once!

It's in Marmalade, so go try it out!
My First Appearence in the Media
posted on 2013-03-16 21:41:50
A friend sent me a link today to something I took part in and had nearly forgotten about.  Nearly two years ago, my undergraduate adviser Kiko Galvez invited me back to Colgate because he had two people from Scientific American coming to make a short film about quantum entanglement, which we studied in the lab there.  They finally published that video today on their website.

I'm in the video only when they come to Colgate, where they shot Kiko and I shaking their hands and saying hello.  I'm nowhere near the educator and scientist that Kiko is yet, so I didn't manage to say anything as clearly as he did, and I seem to have ended up on the editing room floor, as they say.  Despite that, it's my experimental setup that I built and debugged that gets showed off, although it's set up with a nicer laser than I got to use.

If you're interested in entanglement and quantum physics, give it a watch.  Kiko's great at explaining things, and does a wonderful job in the video!
Science as told by comedians
posted on 2013-02-22 20:37:08
Lately, I've had the good luck to find a number of science shows trying to bring modern research and understanding to a wider public than the scientific communities.  I've been suffering through a long dearth of employment that I'd like to write about as soon as I understand it better myself.  Yesterday, I went on a search for new podcasts to fill my copious free time and found this! It's sort of in the same vein as Dara O'Brien's Science Club, and Neil DeGrasse Tyson's Star Talk.  Like Science Club, it's out of Britain, but has a tone more like Star Talk.

The format that all of these shows have in common is that some scientists and comedians try to make science more accessible and present. Billy Bragg, a legendary British punk who wrote many songs about labor movements and sexual politics, was in an episode I just listened to, which was exciting for me, as a fan of his music.  Unfortunately, part of his contribution to the episode was making the science as a type of faith argument, which I find very dull and not at all worthwhile.  That said, I hope to sort my feelings on that out into words sometime soon and put it up here.  Some of the episodes of these shows are naturally better than others, and I am grateful to the astronauts and scientists who take the time to go on them and be excited about their present work.  Getting to hear the cutting edge of science from the people who do it makes it all the more real.

Map Take 2: The Slicening
posted on 2012-11-30 22:05:50

It's been a while since I wrote about my scientific computing library for lisp: map.  Map is a great exercise for me -- in learning Lisp and learning algorithms and optimization.  Since I'm between jobs and not yet in grad school, the time has been ripe to work on the library with some toy cases and try to make it as usable as possible by the time I get back in a position where I could use it for real work.

Because of my copious free time, a lot has been changing lately, including the addition of matrix slices, which were important, and such important features as matrix inversion.  I'm also looking at adding parallelization at some point, as well as a matrix-defining macro in the style of the #v() one for vectors.

In any event, here's what's new:

Reflections on a year of Job-Hunting
posted on 2012-11-15 21:28:49
The past year has been one of unending frustration and despair.  I've had jobs, sometimes even jobs in Physics, which is my favorite kind of job, but even those have paid little, been short-term only, and sometimes been in very unwelcoming environments. I feel a lot of anger and frustration, because I feel like a lot of people misled me.  I don't think they did it on purpose, and I think a lot of it is disconnection with some parts of life both on my part and the parts of others.  I think my professors didn't know what sort of world they were sending me into, and I think they generally assumed either that my classmates and I wouldn't be continuing with Physics, or that we would be going right to graduate school.

I do think many of my classmates jumped off the Physics ship as soon as they got done with college.  But I know I've felt rather lost in the last year, which feels like it has been far longer, with some significant help from my research adviser, Kiko Galvez, in terms of names to talk to and introductions, but by and large, the year feels like a random walk experiment.

Map
posted on 2012-08-22 21:26:44

For a while now, I've wanted to make some of the great functionality of things like Octave (and it's parent Matlab) to Common Lisp.  Mostly, I want things like the slice assignments (arrays with ranges in the indices) and matrix math.  Also, it never hurts to make higher mathematical functions available in simple ways.  So, I started writing Map, which I hope will do just that.

Lately, I've been working in singular optics, largely with Spatial Light Modulators, which are like very tiny LCD screens in front of a mirror. They're cool because they can transform the wavefront of a laser beam into any sort of beam you'd like!  We use a fair bit of math to pump out the right images to put onto the SLM, and I'd been wanting to make a more general interface for that for a while.  I'm not there yet, but I'd like to share the few things I've done so far.

## Vectors

In Octave, you can type

[1:10]
and it will automatically be expanded to
[1 2 3 4 5 6 7 8 9 10]
.  This is great notation and can be used both for generating a vector or setting a range.  In map, I've implemented those with
#r(1 10)
, which creates a 'range' class that just keeps track of the numbers, and #v(1 10), which will expand to
#(1 2 3 4 5 6 7 8 9 10)
, like the Octave code.  This means you can do things like
(reduce #'+ #v(1 100))

To add up the numbers 1 to 100.  That, of course, isn't hard, especially when Gauss came up with a much easier way, but you get the picture.

One further thing that's special, is that you can apply a function to the vector you're generating by passing another argument (you can also pass a step size by entering three numbers).

(reduce #' #v(1 .1 10 #'sin))

will give you the sum of the sine of the numbers 1, 1.1, ..., 9.9, 10!  Moving on...

## Differential Equations

This is a much more meaty section, and was really fun for me, since I hadn't really implemented a ODE solver before (that I remember).  Map now contains a Runge-Kutta Feldberg 45 solver, which is supposed to have an adaptive step size, and currently doesn't seem to, so I didn't do everything right, but it works to a certain accuracy.

Here's a demonstration of finding the angular position and velocity ($\theta, \omega$) of a damped, driven pendulum, taken from some of my old computational physics notes.

(defun damped-pendulum (ti yi)        (declare (type double-float ti)                 (type (array double-float 2))                 (ignore ti))        (vector (+ (* -1d0 (sin (elt yi 1))) (* -1d0 .5d0 (elt yi 0)))                (elt yi 0)))
(map::mute (multiple-value-setq (ts ys)         (map:rkf45 #'damped-driven-pendulum                #r(0d0 1d-7 4d1)            #(0d0 1d0) 1d-10)))

Now, ts holds the time values, and ys is a 2x(length ts) array of position and velocity values!  Once I implement array slices, it'll be easy to graph them, but for now, you need to manually extract one of the rows of ys to plot against ts. There's still a lot of work to be done. Anyway, the resulting graphs are:

Thanks for reading, I'll probably post more once I've got slices sorted out.

In with the out crowd
posted on 2012-07-13 16:39:31
I was skimming through Planet Fedora today, and came across a post by Mairin Duffy, one of the designers at Red Hat. She was writing about a conference called Ada Camp, which exists to support women in the IT industry especially in open-source software.  I always jump on these sorts of posts because I care about equality in life and, not being a woman, I don't get to have (maybe even can't have) the sorts of conversations that happen at these things.  I was, therefore, very interested in what she and the other women had to say.  While I'm more of an enthusiastic onlooker (and user) to Open Source, I believe there are parallels to any other field where women (or any other group) are a minority, such as my beloved physics.
D-Wave's Lightswitch Game
posted on 2012-03-03 18:35:25

Suzanne Gildert is a scientist at D-Wave, which claims[1] to have created the first quantum computer. They currently have sold one to Lockheed Martin, and at least rent time on one to Google, even though the scientific community doesn't know if they're really selling a quantum computer or not.

One of the reasons that all of the scientists have such trouble saying whether what their machine does is quantum computing or not is because their computer could be doing either one of two different things, and getting very similar results.  They are either performing Quantum Annealing or Simulated Annealing which are very similar techniques, and there is certainly no reason their computer shouldn't work regardless of what they're doing, and will be quite good at solving any problem that can be expressed by the equation $$U = \sum_i h_i S_i - \sum_{<i,j>}J_{ij}S_i S_j, \quad (1)$$

which are much more numerous than you might think[2]. The big prize at stake, though, is being able to claim that you made the first reuseable quantum computer, which is naturally a huge claim to fame in the realm of quantum computing research.

Both quantum and simulated annealing work by minimizing Eq. 1, in which all of the $$S_n$$'s represent what physicists like to call "two-level systems."  That is, something with two main states -- eg. spin, which is up or down or polarization which can be reduced to being horizontal or perpendicular to a plane -- which can form a quantum equivalent to the binary 1 and 0 we're all used to now.

In annealing, the overall group of two-state systems will have different amounts of energy when some of the parts are in different states. So the equation will be minimized when the parts are in the correct combination of 1's or 0's.  Suzanne wrote up a nice blog post about that for D-Wave, so I'll just send you off to that.

The important difference between quantum and simulated annealing lies in how the group of objects goes from a starting state, say all spins pointing down (we'll call it 111 in binary) to whatever the lowest energy state is.  In the picture, I made up a system where the x-axis shows three two-state systems and what state they are in (i.e. '010' means particle one is up, particle two is down, and particle three is up) and the y-axis is the energy of the group of three in that state.  As is common, we start in state 111, at the very rightmost point of the graph.  In both cases we hope the system will end in 100, the lowest energy state (See? It's the lowest point on the graph).

## Quantum Annealing

In quantum annealing, we use the phenomenon called quantum tunnelling. Tunnelling is the quantum property by which a system can move from a low energy state to a lower energy state by skipping over an intermediate, higher-energy state.  In macroscopic terms, it would be like a ball on the ground next to a well suddenly being inside the well.  We don't expect it to end up in the well because it would need to raise itself up the side of the well first, something which would take energy to do, and since the ball was just sitting there, nicely, we wouldn't expect that at all.  Quantum objects do this all the time and the effects just don't add up to much on the scale of our ball.  Nevertheless, there's a calculable probability that all of the atoms in the sun will jump simultaneously to right where Earth is, but it's so small that its chances of happening before the universe ceases to exist are on the order of you winning the lottery a few times while getting hit by lightning and dying in plane crash simultaneously (please don't check that statement mathematically).

In the quantum world, we can take that graph and turn it upside down in our heads.  Now we're imagining a sort of probability distribution representation of the system.  The quantum way of thinking about it is that if we measure the state of the three particles over and over, we'll find them in state 100 most of the time, because that is the loest energy state, but then we'll also find it in states 011 and 111 sometimes, since they're more energetic than 100, but not by much and so are the next most likely states.

This method is dependent on maintaining coherence among the particles -- a special quantum property where the properties of the particles are interrelated.  One of the hallmark measurements of quantum computing is the coherence time of the qubits, which determines how long you have to do quantum-style work with them before they turn back into regular old pumpkin particles.  This is one of the big criticisms of D-Wave -- they haven't published these numbers, and so nobody can say for certain that they're doing quantum annealing as opposed to, say...

## Simulated Annealing

Which is not quantum at all!  Simulated annealing serves the same purpose, though, and, by analogy, uses a balloon instead of a ball, and hopes it deflates over the well and falls in.  In this case, the system is exposed to some energy, so it can travel up and down the slopes of the graph as it likes, and is slowly cooled (or some equivalent, energy-removing operation) in the hope that, as it cools, it will fall into that low energy state.

### Behind Closed Doors Does Not a Community Make

While I certainly don't like the method of keeping all of your cool research to yourself, I do think that D-Wave is doing cool research.  That said, I think their marketing department is probably stretching the truth if not outright lying about what they actually are selling.  As I was attempting to say, though, simulated annealing will get the job done in any event, I think most academics are just upset they're building something even remotely quantum while most of the rest of us are spending hours adjust delicate equipment in labs, trying to get a handful of qubits to do anything while they're claiming hundreds.  If you're interested in some of the controversy, you can spend a while reading Scott Aaronson's very interesting blog.

[1] D-Wave only publishes select information to the scientific community at large, and, as of the last time I really looked into it (a few months ago), they hadn't published anything that anyone had taken as definite results.
[2] Google seems to be using this for training image recognition software.

Maxwell's Sheep
posted on 2012-01-31 17:26:17

In the late 1700s, James Maxwell came up with a dilemma that, although just meant as a though experiment, was a troublesome idea to physicists.  He came up with a clever arrangement of systems of matter at different temperatures that might possibly violate the second law of thermodynamics, which would be troubling because, well, it's supposed to be a law, and we don't like nature going around breaking its own laws, since when that happens, it means we got the law wrong in the first place.

The experiment is as follows:

1. We have two systems of different temperatures that are isolated from each other and any other system they could exchange heat with.  Since the energy has nowhere to go, they will remain at this state. (This is in accordance with the first law)
2. We bring the two systems into contact and have a small door, guarded by a small demon, which only allows heat to flow one direction. That is, the demon checks if a particle moving from one system to the other is one of the 'hot' particles and allows it to move through in one direction on that condition.

Here we have to stop a minute and realize, as many did after him, that the situation where this demon requires no energy to do its census and rearranging of every molecule in the systems is impossible.  Measuring the particles requires interacting with them, and so the demon itself is part of the large system here and the energy it uses sorting is part of the overall equation.  This is where my experiment today is different!

I am performing this demonstration in Minecraft, which is a made up world that very clearly marches to the beat of a different Grand Unified Theory, and so I can create a zero-entropy demon.  My demon will be played by a fence gate and a pressure plate.

Here we can see a set of two sheep pens with my wonderfully rainbow-colored sheep in them.  All but the red sheep are in pen two (the further pen) representing a system at higher energy than pen one (the nearer), where there is just one sheep.  In the Middle is the gate with a pressure plate which will cause the gate to open located on the side of higher energy (read: more sheep).  This means that energy (sheep) can only flow from the higher energy to the lower energy pen1. This may seem obvious, but it's also the situation Maxwell tried to set up in his famous experiment.

Let's see what happens!

Long story short, it worked! I left the sheep alone for a little while, as the time of day change demonstrates nicely, and when I returned they were all stuck in the near pen. In case it was in any doubt, this says some strange things about the state of entropy in Minecraft. Perhaps things like cheap cold fusion are easy in this world. Maybe I just need to wait for a hydrogen block and a deuterium block...

[1] I have chosen to ignore second-order sheep effects, like a sheep stepping on the plate and allowing another sheep from the lower energy side to pass back into the higher energy side.

New job again!
posted on 2011-09-11 17:13:48

Well, the summer ended and it was finally time to move out of central New York. I managed a whole two weeks of work at the Air Force, but met some nice people. Now, though, I am relocating!

When looking for an apartment in New York City, there is a strange dance to be done. First, one would want an apartment, right? I sure did. Apparently, though, you need to be able to prove you can pay for it before you can move in (if you can find one at all) which means you need a job before you can rent an apartment. Of course, it would be nice to live near that job in the city that you're paying for the apartment with, wouldn't it? You can't do that until you have the job. I don't know how most people deal with this. After a few weeks job and apartment hunting, I'm guessing a lot of people just don't.

In any event, I got a job with the Wong Group at Columbia University.  This is quite new to me!  At this point, most every new job is a completely new experience for me, but in this case, well, this is probably my first real job.  I worked in a public library for 2 years, so, I guess that probably counts as a real job, too, but that was during high school and this is in a field I studied in College.

On my first day of work (Wednesday) I was given a budget code, told to order what I needed and left to do what I would in the lab with a laser that cost a quarter of a million dollars.

Then, I reminded myself that I was, in fact, qualified to use the equipment and got about learning how the particular equipment that they use in this lab works.  It's certainly a very free-form environment, working at a University instead of a government lab.  People are in and out whenever, and my introduction to the equipment took place at 8:30PM.

As usual, I've gotten myself into an unusual situation.  I'm working in the Mechanical Engineering department, where they're big on building things, and people at talks get their degrees listed along with what companies they've started.  I have yet to understand a talk given by another person in my lab (and I've already seen a few) so I'm hoping I can return the favor in a few weeks when it's my turn.

I'm working on checking some of the devices they work on.  Right now, I'm just checking some bulk BBO crystal to make sure it's creating the right entangled state (the $$|\Psi^+\rangle = \frac{1}{\sqrt{2}}\left(|HV\rangle + |VH\rangle\right)$$ state), by quantum state tomography.  Apparently, the group is (in part) working on entangled photon sources on a chip, and so once I've shown I can do QST, I'll be doing it to the outputs of a fiber and chip based device!

Wir tauschen Zeit für Geld (und hoffen lass mich jetzt nur so weit sein)
posted on 2011-06-16 02:27:10
Man, I've had a blog for how many months and haven't included a song in a title in some way?  These first two weeks have been my introduction to the life of a working physicist -- specifically a government-employed physicist.  Even more specifically, as I found out today, most of whose co-workers are computer scientists.

The lessons I learned today are two-fold: Never go to a set of 5-minute talks.  You will not remember anyone who spoke (ok, maybe one or two) and 5 minutes of talking means nobody gets to explain anything.  Also, they will go over 5 minutes trying, but still not really manage to talk about much, and you won't want to listen because of all of the other talks lined up after them.  Those were some of the dullest 4 hours I have lived through, my friends.  Wow.

On the brighter side, I am doing work now!  It's a lot nicer than sitting in a cubicle all day doing nothing.  Now I read books and articles, and try and make octave do math.  I'm even getting plausible numbers!  Today, I also experienced my first research group meeting, which was new and neat.  Getting a bunch of people together who are working on a common project and hearing ideas, suggestions, etc, was rather exciting, and certainly made me feel more a part of something.  I think a lot of people come in and out of the group, so people don't really go hugely out of their way to welcome newcomers, which makes sense, but didn't make me feel very at home very quickly.

That said, everyone's very friendly and accessible, and it's fun learning new personalities and seeing how they interact.  Unfortunately, I don't think I'll be writing much about my day to day research, as sharing what I'm doing is discouraged, but I'm already looking for the next thing to do and I'll make sure there are no problems sharing it.  That's what science is about, after all.
Working for the Gub'ment
posted on 2011-06-06 22:36:07
Well, now I'm out of school, and the tradition is to find a job. One way or another I ended up with a job and now, much to my surprise, I'm working for the air force. This also makes for the first time I've moved somewhere for a reason other than to take a class. I've been to Germany, to Rhode Island, and Hamilton, but they were all for school reasons, now I'm in Utica for work.

It's been pretty strange moving into a city all alone. I only managed to find an apartment here two days before I moved in, and I was pretty lucky for that. That said, I'll probably have a roommate soon, which will be a little different. Especially since I don't get to choose who. The apartment feels sort of middle of nowhere, although I'm pretty close to the Matt's Brewery, not that that means I get free beer or anything. It's hard to express, though, how strange being here alone is. I'm very glad I know some people nearby, and that my friend Dan was able to come up yesterday. The first night was pretty lonely. There are so many new places to learn, grocery stores to find, neighbors to meet or become comfortable with not seeing, parking arrangements to sort out.

So far, the job hasn't been great either. I had my first day today, and felt like I got nothing done. I wasn't expecting much, but today was something especially dull. I spent all day trying to get my security badge, but was behind other people in line until late in the day, when everyone who could sign my forms had, apparently, gnone home. So, I needed to have people escort me all over the building, because I wasn't allowed to be un-chaperoned. I even needed someone to walk me to the bathroom.

That aside, I'll be glad to be doing some research work, and look forward to meeting more of the people, because so far, the scientists have been exceedingly nice.

My First Magnetism Lesson
posted on 2011-04-24 22:51:30
So, I'm taking a class on science and math education this semester because I think they're important things for people to know, because so much of our modern world depends on them, and they often run so counter to our intuition.  Even as someone who has been taking physics courses for the last six years, I often find myself not completely sure of how things work, or at least unable to explain them to people when the chance arises.  For this class, I've been visiting a local high school and sitting in on their physics class.  I get to help out a little, and I'm slowly learning a bit about the craft of teaching.  While the part I'm most afraid of is classroom management (Not necessarily the best and handling conflict) I can only learn that from experience, and to get experience I have to plan some lessons...

Rochester Symposium
posted on 2011-04-24 22:15:24

I'm already two weeks late on this (and less late on other things) but two weeks ago I got the chance to present my senior research at the University of Rochester.  For those who haven't already read about it, I've been working on quantum optics with professor Kiko Galvez at Colgate.  I got to start working on this back in September, and being only a senior in college, I can say with little doubt this is the subject I know the most about in physics.  Since then, I've become attached to the subject, and was really excited to get to talk about it in front of an audience.  Furthermore, since the conference was titled the Rochester Symposium for Physics (Astronomy & Optics) Students (emphasis mine), I figured I'd probably be talking to an audience that knew something about what I was talking about.

This is how the world begins, not with a bang, but with a... collision of multi-dimensional manifolds.
posted on 2011-03-23 05:59:11
The Physics and Astronomy department at Colgate hosts weekly lectures by professors from other institutions about their research or interests.  This week we had the pleasure of hosting Professor Adam Frank of the University of Rochester, who studies stellar outflows, and how they affect start formation.  I was really surprised to learn that was what Professor Frank studies, because his talk today was about cultural perceptions of time.  He has, in fact, written a book about this (which isn't yet published, so here's a link to another one of his).

While he has obviously read a lot about the subject, and taught me a few things (e.g. first sleep), I was most interested in the talk we had afterwards over lunch with the physics club and professor Bary who also joined in.  The discussion went about the idea of energy sustainability, mostly, and how oil has given us a 'free energy' card to play for the last hundred years that allowed us to live in ways that we probably couldn't have otherwise.  This notion of a free oil energy card was new and unusual to me.  It was based on the extreme energy-freedom we have now because of all of the energy we use from oil.

Oil is (like most earthly energy sources) mainly stored solar energy, in a potent form.  Over millions of years, plant and animal matter has been pressed down into the stuff and collected in pockets in the Earth.  Because we only found out about how much energy it had recently, we've had millennia's worth of energy to draw on, and we've drawn most of it in the last hundred years.  This allows us the cars we're all so used to, the sprawl, the easy consumption, but imagine a world with a lower energy budget.  What if we could only afford to run the washer once a month? Or to drive only on the longest of trips because the energy to power these things was so rare that we actually only had enough to use it sometimes. I'm pretty sure I can barely even conceive of that

Also discussed was the failings of modern string theory to explain the so-called fine-tuning of the standard model.  The fine-tuning problem is that there are a number of constants in the standard model describing forces and the like that just seem to be from the universe itself.  We don't really have any reason they should be what they are, other than that they make the equations describe our universe.  The other strange part is that they could only be pretty much exactly what they are to get anything like our universe to exist.  Some people like to use this sort of thing as a rationale for a god of some kind, but that's just not seeing the pavement for the puddle.

Boxcar2d
posted on 2011-02-13 23:09:09

In the last few days, I've spent a lot of time zoning out and watching this play. It uses genetic algorithms to design cars out of combinations of wheels and vertices. For the first few generations, it's usually pretty stupid, and then gets a lot better as time goes on. Really fun to watch in any event. The website is here.

Dawn of a New Semester
posted on 2011-01-13 06:48:47

It's now officially Thursday, which means there are only 3 more days before the new semester starts.  If all goes according to plan, I'll be taking Intro to Quantum, a class on teaching math, and a German theatre/plays course.  My fourth course slot will be filled by independent research, because I got asked if I would like to try for honors in physics, and I certainly would!

Things exploding
posted on 2010-09-02 02:07:00

Back in America and classes are starting again. While I've definitely learned to better manage time and get things done, running two clubs effectively and gettting school work done will be a challenge. I've already been running around like a chicken with my head cut off trying to get clubs up - hopefully more people will step up to the plate soon so more can get done without my direct supervision.

TGA - Started up nicely, lots of new, enthusiastic freshmen - capture the lighthouse went quite well.

BSA - No students, but the new rabbi is interested and one polisci professor is quite into it and has a really neat meditation timer.

Physics Club - Working on organizing talks/lunches. Need to plan events with fire and nitrogen and shotting things out of other things...

Classes - Will computational mechanics be cool or hideously boring? Signs are pointing to boring. Geography of SE Asia may be interesting, but nobody seems to have said anything concrete yet.. Thermo should be new and interesting and research will be something about coherence of photons and storing images on them.

Unless otherwise credited all material by Matt Novenstern


text:
The coefficient of
Question:

The coefficient of $x^{7}$ in the expansion of $\left(1-x-x^{2}+x^{3}\right)^{6}$ is :-

1.  – 144

2. 132

3. 144

4.  – 132

Correct Option: 1

Solution:


text:
# Math Help - Optimization

1. ## Optimization

A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 3.5. What are the dimensions of such a cylinder which has maximum volume?

2. ## Re: Optimization

Express the radius of the cylinder as a function of its height. Thus express the cylinder's volume as a function of its height. Then find the maximum of the volume by differentiating.


text:
# Find Hybridizations

Covalent bonding uses so-called "hybrid" orbitals to form tetrahedral, octahedral, etc. formations out of the s, p, and sometimes d orbitals. Their naming conventions are pretty much the concatenation of the component orbitals; for example, the hybridization of the s orbital and one p orbital would be the two sp orbitals, and the hybridization of the s orbital, all three p orbitals, and 2 of the 5 d orbitals would be the 6 sp3d2 orbitals. Real-life hybrid orbitals rarely go beyond this, but of course we'll do it anyway.

# The Challenge

Write a program that takes in the number of orbitals needed and outputs the name of the hybrid orbital as a string such as sp3d4. Superscripts can be omitted.

The standard orbitals, ordered by the order in which they're hybridized, are as follows:

letter   # orbitals
s           1
p           3
d           5
f           7

No orbital should be used unless all lower orbitals have already been consumed. For example spd2 is not a valid orbital hybridization because there is still a p orbital that is not used.

If you go beyond the f orbital, then use the angular momentum quantum number (the zero-indexed position in this series: 0 is s, 1 is p, etc.) in parentheses. For example, 27 would be sp3d5f7(4)9(5)2. The number of orbitals for each set should continue with the pattern of "twice the angular momentum quantum number plus one".

Also, don't list the number of orbitals used in the output if that would be 1. It's sp3d, not s1p3d1.

# Test Cases

1 => s
2 => sp
3 => sp2
5 => sp3d
12 => sp3d5f3
36 => sp3d5f7(4)9(5)11

# Victory

The winner will be the shortest answer in bytes.

## JavaScript (ES6), 75 bytes

f=(n,l=0,r=n>l*2?l*2+1:n)=>n?("spdf"[l]||(\${l}))+(r-1?r:'')+f(n-r,l+1):''

## JavaScript 121 bytes

Works thanks to Stephen Leppik :)

o="";a=["s","p","d","f"];i=0;while(x>0){i<4?o+=a[i]:o+="("+i+")";b=Math.min(2*i+1,x);b>1?o+=b:z=0;x-=b;i++}console.log(o)

Here is the not golfed version :

o="";
a=["s","p","d","f"];
i=0;
while(x>0){
i<4?o+=a[i]:o+="("+i+")";
b=Math.min(2*i+1,x);
b>1?o+=b:z=0;             //z : useless assignment
x-=b;i++;
}
console.log(o);

• Also, 93 bytes. – Nissa Dec 21 '17 at 13:55


text:
# Topology optimization for reinforced concrete

Questo articolo è disponibile in:
Topology optimization is one of IDEA StatiCa Detail features which helps you with the design and alignment of reinforcement in concrete structures.
$$Topology optimization is a perfect tool for models with complex geometry, non-standard loading, or unusual placement of the element in the whole structure.The result of this calculation is a topology of compression fields and areas in tension. Based on the calculation result, you can decide where and how to modify reinforcement in your model.The topology optimization calculation included in our innovative CSFM (Compatible stress field method) uses an effective volume of the structure (20%, 40%, 60% or 80%), and in several iterations, places this volume in a way so the created topology is the stiffest possible.Watch our video webinar recording to learn how to utilize topology optimization in IDEA StatiCa Detail for reinforcing a concrete column with a bracket. Put IDEA StatiCa to the test Start your FREE trial and enjoy 14 days of the full version!$$


text:
# What is a suspension in chemistry?

Jul 7, 2018

A $\text{suspension}$ is an inhomogeneous mixture of a solvent and FINE particles.

#### Explanation:

or to quote wiki...

$\text{a mixture in which particles are dispersed throughout the bulk}$ $\text{of a fluid.}$

….and a course a fluid could be either a liquid or a gas.

Most of the time, chemists try to avoid suspensions, given that the SMALL particle size, makes the suspension hard to separate, and the particles occlude a lot of solvent molecules.


text:
Metapost crashes when adding tex labels

I am using Miktex 2.9 (64-bit) and TexnicCenter when compiling Metapost (version 1.504). My files will compile fine without labels. When I try to add a tex label, metapost crashes. I NEED HELP PLEASE!

Also, when compiling it is generating files with filenames like'mp755048' which have a .tex, .dvi, and .txt associated with the filename. The .dvi file contains the latex label by itself. The text file contains:

This is TeX, Version 3.1415926 (MiKTeX 2.9) (preloaded format=tex 2012.3.18)  1 FEB   2013 16:44
**mp755048.tex
("C:\Users\Documents\Research\Thesis - Paper 2\Graphs\mp755048.tex"
! Undefined control sequence.
l.2 \documentclass
{article}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., \hobx'), type I' and the correct
spelling (e.g., I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.3 \begin
{document}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., \hobx'), type I' and the correct
spelling (e.g., I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

[1] [1] )
Output written on mp755048.dvi (2 pages, 340 bytes).

A minimal example that fails:

prologues :=3;
verbatimtex
%&latex
\documentclass{article}
\begin{document}
etex

beginfig(1);
label(btex $x$ etex, origin);
endfig;
end;

-
Welcome to TeX.sx! I get an error regarding the misplaced word "vertices" (that I believe should go before etex), but once corrected I have no problem. –  egreg Feb 1 '13 at 21:30
I had a feeling my code would work for others. I think there is something wrong with the programs files. I have already re-installed Miktex. Any other suggestions? –  Jonelle Feb 1 '13 at 21:41
Can you try making a really minimal example that fails? The shorter is the code, the easier is to find the problem. –  egreg Feb 1 '13 at 21:43
Yes. Even this crashes: prologues :=3; verbatimtex %&latex \documentclass{article} \begin{document} etex beginfig(1); label(btex $x$ etex, origin); endfig; end; –  Jonelle Feb 1 '13 at 21:44
@jonelle: and is the generated output correct? –  Aditya Feb 2 '13 at 4:56


text:
# Looking for a better algorithm for finding the slope of an input signal

I've got an input signal that while sloping up, approximately bounces off an imaginary line. I'm looking for the equation to that imaginary line. I have a method, but is very brute force and it takes too long. I'm looking for ways to optimize my approach or hopefully learn about a completely different more efficient method. I've written a script in Octave that will do what I want, but it takes 3-10 seconds (with an input signal of 1800 samples) depending on how many iterations I run.

My brute force algorithm in Octave:

  x = 0:1:1800;
for i = 1:200
p = polyfit(x, input, 1);  % p gives the slope and offset
output= polyval(p, x);
input = clip(input, output);
endfor

the clip function clamps the input to the output. Clamps the input signal to the linear approximation.

  for i = 1:length(input)
if(input(i) > output(i))
input(i) = output(i);
end
endfor

To better explain what I'm looking for, I've included the rough image below. Of course, the red signal is the input and I'm looking for the equation of the blue line.

Thanks for taking a look.

I hope I understand what your'e asking correctly

To get the minimum slope of the image I would run an calculate the slope at each point (should be fast enough) and than take the minimal one.

For example :

x = 1:.05:3000;
y = 100+x + 300*sin(2*pi*x/1000);
origin = [0 0] ; % or origin = [ x(1) y(1) ];
slope = (y - origin(2)) ./ (x - origin(1));
[ minslope , minidx ] = min( slope ) ;
angle = atand( minslope );
figure;plot( x,y ,'-');
hold on;
plot([ origin(1) x(minidx)] , [origin(2) y(minidx)] ,'-r');

Will give you this slope:

Best of luck!,


text:
# The following is not a potential benefits of an EHR

###### Question:

The following is not a potential benefits of an EHR

### Simplify each product. write in standard form. 29. (w + 1)(w + 12) 31. (3r - 2)^2 33. (7q + 2)(3q +

Simplify each product. write in standard form. 29. (w + 1)(w + 12) 31. (3r - 2)^2 33. (7q + 2)(3q + 8)...

### Under which theme of geography does humans' use of earth's natural resources fall? a) environment b)

Under which theme of geography does humans' use of earth's natural resources fall? a) environment b) uses of geography c) world in spatial terms d) place and region...

### How do the densities of the jovian and terrestrial planets compare?

How do the densities of the jovian and terrestrial planets compare?...

### 5 A school has 20classrooms, One-fourth of the classrooms orefor kindergarten and firstgrade. Twice as many arefor second and third

5 A school has 20 classrooms, One- fourth of the classrooms ore for kindergarten and first grade. Twice as many are for second and third grade. The rest are for fourth and fifth grade. what percent of the classrooms are for 41 or 5 graders...

### Under the articles of confederation which of the following established thy new states would be created

Under the articles of confederation which of the following established thy new states would be created from new lands? a)jays treaty b)treaty of paris c)land ordinance d)northwest ordinance...

### Jessica retired at age 65. On the date of her retirement, the balance in her traditional IRA was $218,000. Over the years, Jessica had made$21,800 of

Jessica retired at age 65. On the date of her retirement, the balance in her traditional IRA was $218,000. Over the years, Jessica had made$21,800 of nondeductible contributions and $69,000 of deductible contributions to the account. If Jessica receives a$68,000 distribution from the IRA on the da...

### The following is an example of what type of sequence? 3, 11, 19, 27, 35… a. geometric c. ratio b.

The following is an example of what type of sequence? 3, 11, 19, 27, 35… a. geometric c. ratio b. arithmetic d. difference...

### Order the list of numbers from least to greatest. 8.8 x 10^21, 6.2 x 10^2, 2.8 x 10^21, 1.5 x 10^2, 5.1 x 10^12

order the list of numbers from least to greatest. 8.8 x 10^21, 6.2 x 10^2, 2.8 x 10^21, 1.5 x 10^2, 5.1 x 10^12...

### Coates writes of schools that “were not concerned with curiosity. They were concerned with compliance” (p. 26). How does the author

Coates writes of schools that “were not concerned with curiosity. They were concerned with compliance” (p. 26). How does the author see the education system as complicit in dividing America into two separate worlds? Does this description of American schools resonate with you?...

### Two rectangles have a perimeter of 16 inches name two possible answers for each rectangle

Two rectangles have a perimeter of 16 inches name two possible answers for each rectangle...

### Has the world's tenth-largest reserves of natural gas and the sixteenth-largest reserves of oil.

has the world's tenth-largest reserves of natural gas and the sixteenth-largest reserves of oil....

### The densest ocean water forms in the area

The densest ocean water forms in the area...

### Simplify (-7d3+5d+5d2-6d4)-(8d+5d2+2d4+3d3)

Simplify (-7d3+5d+5d2-6d4)-(8d+5d2+2d4+3d3) $Simplify (-7d3+5d+5d2-6d4)-(8d+5d2+2d4+3d3)$...

### There are no results for IN an Ap if the sum of the first m terms is equal to n and that of the first

There are no results for IN an Ap if the sum of the first m terms is equal to n and that of the first n terms is equal to m, then prove that the sum of the first (m+n) terms is -(m+n)...

### Evaluate 8x when x = 3.12

Evaluate 8x when x = 3.12...

### Which is a logical appeal for increasing the time of the school day for more standardized test preparation?

Which is a logical appeal for increasing the time of the school day for more standardized test preparation? in standardized test preparationsteve dawsona) extending the time of the school day clearly will cost a lot of money. b) schools have an obligation to make sure students do not lose any time ...

### What is the derivative of 2500x-x²?

What is the derivative of 2500x-x²? ...

### Facts and details that the author writes clearly in the text are called what? Hint obscure = not well known

Facts and details that the author writes clearly in the text are called what? Hint obscure = not well known...


text:
# Techniques Of Electromagnetic Cloaking

Author
Hemant
View Count
16440
AbstractHow to conceal objects from electromagnetic radiation has been a hot research topic. Radar is an object detection system that uses Radio waves to determine the range , angle, or velocity. A radar transmit radio waves or microwaves that reflect from any object in their path. A receive radar is typically the same system as transmit radar, receives and processes these reflected wave to determine properties of object. Different organizations are working onto hide object from the radar in outer space. Any confidential object can be taken through space without being detected by the enemies. This calls for necessity of devising new method to conceal an object electromagnetically.