text: To accomplish this we find any factor that is contained in both the numerator and denominator and cancel it out or strike it out, like this: Example: Reduce the common fractions 10/6 and 10/5 to lowest terms. For … [Math Processing Error] 10 15. Cancel out the common factors between the numerator and denominator. Example 1: to simplify $(\sqrt{2}-1)(\sqrt{2}+1)$ type (r2 - 1)(r2 + 1). 2 + 2x [6x + 6] = 2 + 12x 2 + 12x. Variables and constants. Adding fractions with variables worksheet, ti-89 program to resolve primitives, series fourier, integrals step by step, systems of linear equations in two variables with fractions, howcan we teach algebra using pictures for seventh standard, Subtracting Negative Fractions. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next big test). By including negative numbers in the ranges or including decimal digits, you can make the problems more difficult. 3. For example, to express x 2, enter x^2. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. So, let's write it like that. However, simplifyFraction is more efficient for simplifying rational expressions. Expand the larger factorial such that it includes the smaller ones in the sequence. We are going to simplify each expression by combining like terms. Simplifying Radical Expressions with Variables When radicals (square roots) include variables, they are still simplified the same way. 5y does not have a like term because no other term has the variable y. Defini-on: A _____ra/onal_____ expression is a frac/on made up of polynomials in the numerator and denominator. p. Keep everything nonnegative. Each algebraic expression in this collection of printable worksheets contains two or more variables. 2. This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions. This expression can be simplified by dividing each term by 2 as; 12x 2 /2 + 12x/2 + 2/2 = 6 x 2 + 6x + 1. Solving quadratic equations by quadratic formula 1. If your improper fraction numbers are large you can use the Long Division with Remainders Calculator to find whole number and remainder values when simplifying fractions by hand. See Also Cancel the common factor of 2. Problem 2. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Example Question #1 : How To Solve For A Variable As Part Of A Fraction The numerator of a fraction is the sum of 4 and 5 times the denominator. Need help reducing fractions containing algebraic variables? This calculator simplifies ANY radical expressions. A base that has a negative exponent can be changed to a fraction. Simplify $$125^{\frac 1 3 }$$ Show Answer. Two over 2/3. To simplify the fraction, we look for any common factors in the numerator and the denominator. Find a common denominator by multiplying the two denominators together. . Learn how with this free video lesson. simplify an expression and when it is not. Simplify $$125^{\frac 2 … Practice Problems. 4. Before simplifying an expression that contains parentheses, you must determine whether or not you need to use the distributive property. Once you have a common denominator in both fractions, subtract the numerators. Exponents are supported on variables using the ^ (caret) symbol. But later on, you might encounter "messier" fractions like the following: (a + a) / (2_a_ - a) This calculator will also simplify improper fractions into mixed numbers. Cancel out the common terms to reduce the expression to the lowest form. Factorize the numerator and denominator of each rational expression. 2xy does not have a like term because no other term has the variables x and y. Ok, enough vocabulary... let's look at a few examples. The calculator works for both numbers and expressions containing variables. Simplifying Radical Expressions: Students are asked to simplifying 18 radical expressions, some containing variables and negative numbers (there are 3 imaginary numbers). [Math Processing Error] 2 … You can either apply the numerator first or the denominator. Key Steps on How to Simplify Factorials involving Variables Compare the factorials in the numerator and denominator. Writing and evaluating expressions. Simplify the algebraic expression by … Solver. Distributing with negative exponents means that you’ll have fractional answers. How to Simplify Negative Exponents with Variables; How to Simplify Negative Exponents with Variables. Right from simplifying algebraic fractions calculator to systems of linear equations, we have every part discussed. Factor the numerator and denominator. This is the same thing as two divided by, two divided by 2/3, two divided by 2/3, which is the same thing as, dividing by a fraction's the same thing as multiplying by its reciprocal. Alternatives. If so, DO IT FIRST! There are two ways to simplify a fraction exponent such$$ \frac 2 3 . This is the same thing as two divided by 2/3. . The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. Example. Come to Algebra-equation.com and learn standards, variables and a … Simplifying Fractions With Variables - Displaying top 8 worksheets found for this concept.. stays as it is. Solving quadratic equations by factoring. You can also simplify rational expressions using the general simplification function simplify. These unique features make Virtual Nerd a viable alternative to private tutoring. Simplify 3 x + 2 ( x – 4) Solution. Example 3. See the example below. The formula we use for st… Simplifying Variable Expressions Date_____ Period____ Simplify each expression. When you first start handling fractions with variable, this may be done for you. If you divide the fraction by 2, the numerator is 3 … \dfrac {5x^5} {3x^3} = \dfrac {5 \cdot x \cdot x \cdot x \cdot x \cdot x} {3 \cdot x \cdot x \cdot x} 3x35x5. My students loved this activity as it's a fun twist on an important concep Manipulate the fractions so that they both have the common denominator. simplifyFraction simplifies such expressions as if they were variables. Simplify the resulting fraction from step three by factoring the numerator and denominator as much as possible and cancelling out any common factors that are in both. Factor the numerator and denominator. Solving linear equations using cross multiplication method. Note: exponents must be positive integers, no negatives, decimals, or variables. Well, we could go the other way around. Add fractions using the following steps: Get a common denominator if the denominators are different. Solving linear equations using substitution method. From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. Well, what would this simplify to? = 3⋅x⋅x⋅x5⋅x⋅x⋅x⋅x⋅x. Solving linear equations using elimination method. Simplifying Ra-onal Expressions 7-1 Recall: Polynomials are combina/ons of number and/or variable terms where the variable exponents are _____whole_____ numbers. Problem 1. Some of the worksheets for this concept are Simplifying variable expressions, Simplifying algebraic fractions, Simplifying complex fractions, Simplifying rational expressions, Work 2 3 algebraic fractions, Multiplying and dividing algebraic fractions, Reducing fractions work 2, Rational expressions. For the variables, I have two extra copies of x on top, so the answer is: 5 x 5 3 x 3 = 5 ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x 3 ⋅ x ⋅ x ⋅ x. Simplifying Expressions with Negative Exponents: Solving Equations 3: Solving Quadratic Equations: Parent and Family Graphs: Collecting Like Terms: nth Roots: Power of a Quotient Property of Exponents: Adding and Subtracting Fractions: Percents: Solving Linear Systems of Equations by Elimination: The Quadratic Formula: Fractions and Mixed Numbers In this non-linear system, users are free to take whatever path through the material best serves their needs. Exponents may not be placed on numbers, brackets, or parentheses. Factor the numerator and denominator. Level 2: For example, simplify 2 ( y − 4) + 4 (2 y − 1) or 2 x2 − 5 − 4 x2. They will use their answers to solve the joke/riddle. A. Simplify the expressions below (Hint: ONE of them needs … Step 1: Enter the expression you want to simplify into the editor. We just have to work with variables as well as numbers Notice that [Math Processing Error] 5 is a factor of both [Math Processing Error] 10 and [Math Processing Error] 15. To perform math operations on fractions before you simplify them try our Fractions Calculator. The steps we follow to subtract fractions with variables are as follows. Add the numerators. Tricks for Difficult Problems ”Reverse” parts of the fraction by factoring out negative numbers. In this case, it is impossible to combine terms when they are still in parentheses or any grouping sign. Combine like terms in both the numerator and the denominator of the fraction. Solving one step equations. Other way around we follow to subtract fractions with variable, this be... When radicals ( square roots ) include variables, they are still simplified the same way negative! Is the same way, you can make the Problems more Difficult,,... The two denominators together … p. 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# define event in probability

P (A and B) means the probability of A and B both occurring is called a compound event. If the event consist of the sum of the two dice is 5 then it consists of the following four possible outcomes: (1,4), (2,3), (3,2), (4,1). Each route number has 3 buses passing in any given hour. “Probability of a given event is defined as the expected frequency of occurrence of the event among events of a like sort.” (Garrett) The probability theory provides a means of getting an idea of the likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one. Neither can it predict that you will get another 1 on your second throw. Define probability as a set function on a collection of events and state the basic axioms of probability. Their probability is 1. Here is the definition: In probability, we define an event as a specific outcome, or a set of specific outcomes, of a random experiment. Events that can be affected by a previous event are known as dependent events. $P(\text{1 AND 2}) = \frac{2}{36} = \frac{1}{18}$. As the name suggests, impossible events are those that can never occur. P (B) means the probability of B occurring. The outcome of getting an even number is considered an event. Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Remember that an event is a subset of the sample space, which is the set of all possible outcomes of a probabilistic experiment. Dependent (also called \"Conditional\", where an event is affected by other events) 3. What about getting an Ace that is a Jack from a deck of cards? If you get an answer outside of this range, the probability that your answer is incorrect, is 1. Out of which, ‘m’ are favorable to the occurrence of an event E. The probability definition is given as the ratio of the number of favorable events to the total numberof exhaustive ones. Probability theory Part 1: Events and Probabilities This is our introductory lecture on discrete probability. The event that is most likely to happen is called Likely Event. For example, getting an even number when you roll a die, or getting a head when you toss a coin. An event is a specific outcome, or a set of specific outcomes, of a random experiment. What is the probability that in a given hour Jake will catch his bus? the quality or state of being probable; something (such as an event or circumstance) that is probable… Getting a 1 on your first throw cannot prevent you from getting a 1 on your second throw. Name: Probability of events union. The same experiment can be interpreted in a number of different ways to define different types of events within the experiment. Each time you remove a marble the chances of drawing out a certain color will change. However, modern probability was developed more recently, between the 16th and 19th centuries, and … Remember that a percent is of 100. Let’s begin! If you wanted to know the chances of picking a blue marble on the second try, that chance would affected by the first event. Do you think you could roll a 1 and a 2 at the same time with the same die? This is because the bag now has less marbles in total. When we say \"Event\" we mean one (or more) outcomes.Events can be: 1. ties. It varies depending on how we define and visualise it. Jake is trying to catch a bus that is numbered 54 at a bus stop that has the buses numbered 52, 54, 42, and 49 passing by. By Paul King on February 6, 2018 in Probability Two events are considered dependent if the occurrence or outcome of the first event changes the probability of the next event occurring. Pulling an Ace from a deck of cards on the second try if a King was removed on the first, The first try was a King so we still have 4 Aces remaining, The first try subtracts 1 from the total number of possible outcomes of the experiment. Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. In a sample of N equally likely outcomes we assign a chance (or weight) of 1/N to each outcome.. We define the probability of an event for such a sample as follows:. Total events are defined as all the outcomes which may possibly occur relevant to the experiment asked in the question. Definition of . If the incidence of one event does affect the probability of the other event, then the events are dependent.. Events that are not affected by other events are known as  independent events. Example 2: The probability of pulling a 3 from a 52-card deck of playing cards. Definition of Probability using Sample Spaces . $P(\text{Jake catches a 54 in any given hour}) = \frac{3}{12} = \frac{1}{4}$. In probability, two events are independent if the incidence of one event does not affect the probability of the other event. These are the opposite of certain events. There are simple events where only a single outcome of the experiment is considered the event. Sample Space In order to understand the concept of probability, it is useful to think about an experiment with a known set of possible outcomes. Thus, the probability of getting a head is: In a given hour, there are 3 buses running the route that Jake needs to catch, the 54, In a given hour, there are 12 buses passing Jake’s stop, 3 of each of the 4 routes. the quality or fact of being probable. You pick one marble from the bag and set it aside. Explanation: Used to represent the probability of event A or event B. P (A | B) Name: Conditional probability function. Bayes' theorem thus gives the probability of an event based on new information that is, or may be related, to that event. [1] Typically, when the sample space is finite, any subset of the sample space is an event (i.e. Throwing a 1 and a 2 when you toss 2 dice. So, what is sample space? What is the probability of each of the following events? Example 2: The probability of buying a shirt from a store that only sells shoes. Although we have not yet discussed how to find the probability of an event, you might be able to guess that the probability of $\{2, 4, 6 \}$ is $50$ percent which is the same as $\frac{1}{2}$ in the probability theory convention. You had a $\frac{1}{6}$ chance of getting that 1. Independent (each event is not affected by other events), 2. However, in this section we will go through the general method for finding the probability of an event. The number of possible events or outcomes in an experiment are dependent on what we define the event to be. Choosing an apple from a bag with 2 apples, 2 bananas, and 1 pear. If our event A is “it rains today,” then the complement, A’, is the event “it doesn’t rain today.” Events can either be independent, dependent, or mutually exclusive. Alternatively we can say there is a 50% chance of getting a head. all elements of the power set of the sample space are defined as events).However, this approach does not work well in cases where the sample space is … (Refer to article on sample space to see how many outcomes have a 1 and how many have a 2), $P(\text{1 OR 2}) = \frac{24}{36} = \frac{2}{3}$, 5. Example 1: Find the probability of getting a blue marble from a bag with 1 blue marble, 1 green marble, and 1 orange marble. The outcome of getting a head is also considered an event. The total possible number of outcomes of the experiment is 3 as there are three marbles in the bag. You can learn more about that in the articles on the specific topic. $P(E) = \frac{\text{number of outcomes favorable to the event}}{\text{total possible outcomes of the experiment}}$. Dependent Event. 1 Sample Spaces, Events and Probabilities The earliest forms of probability go back to the 8th century. When you roll the dice and observe the number rolled, that is an event. An event can be just one outcome or it can be a combination of more than one outcome from an experiment. There is 1 outcome favorable to the event of getting a head. Pulling an Ace from a deck of cards on the second try if a King was removed on the first, $P(\text{Ace on second try when king on first}) = \frac{4}{51}$, Some of these questions could have been solved using other methods. The world's most comprehensivedata science & artificial intelligenceglossary, Get the week's mostpopular data scienceresearch in your inbox -every Saturday, Join one of the world's largest A.I. Example: removing colored marbles from a bag. Let’s think about what would happen if we had a bag of 2 blue, 1 red, 3 white, 2 green, and 4 yellow marbles. Video Examples: Finite Mathematics - Probabilities, Events and equally likely outcomes 1.Getting an odd number when you toss a die? Where: 1. There is a red 6-sided fair die and a blue 6-sided fair die. Here’s a final example. Once we have gone through the concepts and tried some examples, you will be better able to try the questions at the end. Conditional probability is the probability of an event occurring given that another event has already occurred. Probability is both theoretical and practical in terms of its applications. In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. For Example, in an experiment you roll two dice simultaneously. 2. Event Definition in Probability An event is a specific outcome, or a set of specific outcomes, of a random experiment. Thus, the probability of getting a blue marble is: There are 4 outcomes favorable to the event since there are four 3’s in the deck. When the chances of the an event depend on the result of another, they are considered to be dependent events. If there are ‘n’ exhaustive, mutually exclusive and equally likely outcomes of a random experiment. For each of the types of events we have discussed, there will be different strategies for finding the probability of an event. Probability definition is - the quality or state of being probable. The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur … There are very simple applications of probability, such as rolling a dice or tossing a coin. more ... An event that is affected by previous events. Mutually Exclusive (events can't happen at the same time) Let's look at each of those types. 4. 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# Potential Well

## Homework Statement

An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value $$\xi = 3.2$$.

a. How many bound states does this system have?
b. Estimate the energy of the ground state with respect to the zero energy line at the bottom of the well. Express answer in eV.

## Homework Equations

$$\xi = ka$$ where a is half the width
$$\eta = \kappa a$$

as far as I know k corresponds to the bound state while kappa corresponds to the unbound states

$$\xi tan(\xi) = \kappa$$ for even eigenstates
$$\xi cot(\xi) = -\kappa$$ for odd eigenstates

## The Attempt at a Solution

a. Not exactly sure here.

I figured I'm looking for k but when I solve for it I get a huge number (64 million)
k = xi/a = (3.2 * 2) * 10^9

b. E = 0 at the bottom of the well so then
$$E = \frac{\hbar^2 \xi^2}{2ma^2}$$

correct?


text:
Are you happy with your job / career?

Help Support The Rocketry Forum:

dr wogz

Fly caster
Exactly that. Are you happy with what you do.

Was it a life long dream to do what you do?
Did you jsut 'sort of' fall into it?
Do you secretly hate it, but fear changing?
Are you making the best of a bad situation?

I've been saying I'm going to return to school for a few years now, and I think I am finally fed up with (getting tired of) working as an Engineering tech / CAD technologist, and feel it is time to change. To do somethign different, but interesting. I beleive I'll have some support to make teh change..

My 'challenges' here are becomming less and less frequent, and being replaced by 'frustrations'.. Or, teh challenges are becomming routine, that I'm looking for something. But faults are easiest to find and bicker about..

Anyone else get this?
Anyone else do something about it?
Has it worked out to be better?

sandman

Well-Known Member
I was an auto mechanic for 18 years and after doing it for 5 years I hated it!

The old joke about the questions asked a doctor at a party really do apply to a mechanic..."come out to the driveway I want you to take a look at my car.":kill:

A customer had been coming into the shop for about 3 years and asked me if I wanted to go to work for him.

I did! A few years later I bought the business and never looked back.

Now I work 3 or 4 days a week, make a good living and have time to play with rockets and make nose cones.

No...I never thought that one day I would be working in theater but I do.

r1dermon

Well-Known Member
man, i've been working at my job for about 2 months, and im already fed up with it. lol. but i need it. im in college. i'd like to be a cop when i get out. but my dream job is being on the state SWAT task force. or as an ATF agent. i've always liked the excitement of solving hostage situations, but, this is why i go to school. once i get my degree in criminal justice, i'll probably join the coast guard reserves if i dont get picked by the state police right away. the test is once every 2 years, so its not like i can fail and take it again next week. lol.

wwattles

Well-Known Member
That's one of the reasons I got out of the Navy. I enjoyed certain aspects of the work, but others became more and more difficult to endure. For example, I loved visiting foreign countries, but I hated that to do it I had to be away from my wife for 6 months (or more) at a time. I loved helping ships become self-sustaining in their training, but I hated having to drag them, kicking and screaming, up to that point, and not getting any appreciation for it.

In the end, when they gave me a choice of "A) Sign here for another 5 years (to include at least 2 10-month trips to the war zone); or B) Don't sign and get sent to the war zone for a year with no hope of seeing your wife..." I chose option C) Get out, find a different job, and enjoy the change!

My new job? I love it. Truly, I do. I love the people (top notch engineers, machinists, programmers, etc), I love the atmosphere (very professional, yet also very friendly), I love the company reputation (one of the best gas turbine component manufacturers in the world), and I love the work I do (program management and product development). I never said that during my 11 years in uniform.

If you'd like some tips about career switching from someone who just waded through that quagmire, PM me.

WW

illini

Well-Known Member
Wouldn't trade it for anything. Only thing that could make it better would be to be self-employed, but being in a small company of < 20 people is almost as good as that. Didn't start out that way. Got the Ph.D. in aerospace engineering, rising from a lower-middle class household and stoked by a youth filled with model rocketry, a successful NASA, and anything else that flew. Had a NASA fellowship, but suffered from bad timing. Coming out of school in '91 when communism was collapsing and defense was drawing down made it hard to find a job. Found one at a solid rocket motor manufacturer out west, and quickly learned to hate the aerospace industry and NASA. Bugged out 3 years later for a new job and new career in the DC area. Have bounced amongst employers a bit, but the work has been similar. Difficult to explain what I do...wouldn't bore you with the details. Suffice to say the education is NOT wasted. No more fluid dynamics. No more combustion. [And no, I don't miss them either. Sport rocketry is sufficient to scratch that itch.] What I get to do now is actually far more fun and interesting. Would never go back.

Bottom line: education was worth it for me...made it all possible.

mike_bar

Well-Known Member
Originally posted by Dr Wogz
Anyone else get this?
Anyone else do something about it?
Has it worked out to be better?
TRF is the last place I expected to find career information nonetheless I am pleased. I enjoyed reading all the positive comments.

I have been job-hunting for over a year now. I am back in New England after living in Florida for about eight years. I suppose that I moved back home, as family is in this area.

I did not expect finding a job to be so difficult. I am trying to keep my attitude positive, but I am wondering why I ever quit a good paying job, no matter how much I disliked it. Maybe I should have stayed in Florida, visited family in August, and taken vacations to the Kennedy Space Center in central Florida.

I have eighteen years experience as an investment advisor for wealthy individuals. (Note to reader, an investment advisor is not a stockbroker, an investment advisor is similar to a financial planner.) My current résumé is located here

I have thought of a career change, but I do not know what I am qualified to do. I have thought of going back to school, but few industries prefer 45-year old newbies.

Unemployment has some advantages; I have lots of time to build model rockets, hone my skills, and read many technical reports. There is always a silver lining, if one takes the time to look.

I will keep my chin up, and thank you all for your positive comments. I have read them all.

Respectfully,
Michael OMalley

RocketboyG80

Well-Known Member
My current job is at a grocery store. The sole purpose I work there is for the money. It's hard to say whether or not I enjoy it because I have the mindset that I won't be doing this for many years to come. Every once in a while there is a humorous moment or two, but overall it is pretty dull work. The best part is when paychecks are cut every Wednesday. By the way I plan on majoring in some form of engineering when I go to college.

Ozymandias

Well-Known Member
I'm glad to see that you engineers out there like your jobs. I'm currently a freshman studying aerospace engineering at Embry-Riddle Aeronautical University. After I graduate from Riddle I plan to earn my master's degree in AE and eventually my PhD. Ultimately, I'd like to work at JPL or some place like that. The prospect working on advanced projects and creating new technology is very exciting to me. In a few years, I hope I can say I love my job too.

hokkyokusei

Well-Known Member
I've periodically loved and hated the jobs I've had. I fell into engineering, and have drifted from job to job over the years. I started out an Electrician, went back to school, moved into Electrical Engineering, more school, and from there into electronics and eventually Software Engineering. I can still get excited about it but it's not as easy as it was. These days I work in a small startup company on a project I really believe in, and so it's easier to be excited!

But even now, I sometimes wish I had chosen a different career. I wish I done someting more artistic. Maybe graphoc design I would also like to write, maybe journalism. One of the most unexpectedly satisfying things I have done, was to edit UKRA's newsletter. Editing a rocketry magazine could be my ideal full-time job!

jflis

Well-Known Member
oh man, is *this* the forum for *me* to answer this sort of question, or what???

Yea, I love my job, what can I say...???

I worked 25 years in the high tech field rising from test-technician to Principle engineer (software) and Sr. Eng (hardware) making a darned good salary. I got laid off 3 years ago and decided to change my focus. Now I'm working harder than i EVER have, making less money then I EVER did and enjoying it more than i could have EVER hoped.

hey kid, wanna buy a rocket?

jim

mike_bar

Well-Known Member
Originally posted by hokkyokusei
But even now, I sometimes wish I had chosen a different career. I wish I done someting more artistic. {snip}
Hokkyokusei,
I agree with your thinking above, yet this seems so cliché, as do the ideals of the younger TRF members.
• Do we loose our idealism after a few years?
• Are we more realistic?
• Are we more experienced in how the world works?
Oh no, I am becoming an elder. Yikes

mike_bar

Well-Known Member
Originally posted by jflis
Yea, I love my job, what can I say...??? {snip}
Jim,
You are the poster child for career change advice on the TRF!
Best wishes in your new, successful enterprise.
Regards,
Michael

GL-P

Well-Known Member
Right now I work during the winter at a ski hill. I'm trying to become an instructor. The pay ain't the best but the perks are sweet! (3rd year, FREE season's pass!)

Don't know what I want to do. I'm interested in aerospace and would gladly work with any aerospace company. I'm interested in SPACE camp and the various CSA internship programs. I've talked with a few at the local Carleton U aerospace faculty. I've impressed them with some of what I asked them!

I also am interested in Civil engineering like bridges and dams.

tnrocketman

Well-Known Member
Overall, I loved my job until about 4 years ago. I have worked at the same company for 18 years in several different roles in IT. Not the place to be now, with most of it being outsourced to Asia/Eastern Europe, and less and less interesting work. Well paid now, but how much longer will it last? I'm 40, first kid starts college next year, and I know I will likely have to take about a 40% pay cut when this runs out, while the cost of everything goes up relentlessly.

Some free advice: when analyzing a job field, do your best to pick one that can't be done on the other side of the world overnight for a tenth the labor cost.

Sorry, it has been a depressing day.

hokkyokusei

Well-Known Member
Originally posted by Mike_BAR
Hokkyokusei,
I agree with your thinking above, yet this seems so cliché, as do the ideals of the younger TRF members.
• Do we loose our idealism after a few years?
• Are we more realistic?
• Are we more experienced in how the world works?
Oh no, I am becoming an elder. Yikes
I'm not sure which part you think is clichéd, but in answer to your questions above:
• To an extent, but I think our ideals change, mellow maybe.
• I think so.
• Definately!

So to sum up, I know I'm not as wildly idealistic as I used to be, probably because I'm realistic enough to see that there's a limit to what one person can do. But I'd also like to think that I have the experience to recognise when one person can make a difference.

Hospital_Rocket

Well-Known Member
Originally posted by Mike_BAR
I have thought of a career change, but I do not know what I am qualified to do. I have thought of going back to school, but few industries prefer 45-year old newbies.
Teach!

I can think of no more rewarding career change. Many many schools now offer programs where experienced professionals bring their real world viewpoint into the classroom. Many many young people would benefit from knowing how to manage money.

A

Rocketmaniac

Well-Known Member
As of the beginning of 2004, I really disliked my job. I worked in a factory that made test tubes. I hated the hours (nightshift) and disliked management (at least their decisions and policies). Actually, I disliked just about everything about the job. The amount of money I made was the only positive thing about the job.

This is why when my grandmother left me money to go back to school, I jumped at the chance. I am hoping to get into Radiologic Technology. I will be applying for admission into the program in January. Meanwhile, I am taking a full load of coursework to reduce the number of classes I have to take once in the actual program (I am allowed to anything except the "Core" courses). I am working pretty hard right now, trying to get the best GPA I can. GPA is one of the factors that the review board looks at when selecting people for the program. If I can maintain my current grades for another 10 days I will have a 3.7 average.

I should know in February or March if I am accepted!!!!!

astrowolf67

Well-Known Member
I currently enjoy my job. Ask me in a couple of days, and I may hate it

When I graduated High School, I took the easy path. A local tech school, offering a degree after two years, and job placement promised. It wasn't till 3/4 of the way through, and after having fully paid, that we were told the jobs were in either Kansas, or Texas. Nothing against those states, but they weren't home. So, after school, I started job searching on my own. In my area, there's very little available in the electronics field. I ended up working nights at a wholesale warehouse. Eventually I worked my way up to the night manager, which lasted all of about a year. As soon as the opportunity came up, I got out of that, and moved into the transportation dept (driving). A bit later, we moved up to tractor trailers, and I got to train for and obtain my CDL for free. Now, I work for the local Coca Cola company, running a regular route. Sure it's hard work, but it pays much better that most would think. I toss soft drinks all day, with no worries about who's watching, no bosses looking over my shoulder all the time, meeting new people every day, and make more than I ever was promised from the tech school.

Omega_D

Well-Known Member
I didn't graduate high school. Technically I'm a 12th year drop-out (long story).

After high school I fell into a job working at an autobody repair shop. I liked working on cars, I had a few muscle cars. I worked for ~7 years in several different body shops, and I was very good. I was restoring classic cars at a high-end shop for the better part of 4 years. Unfortunately, I hated it after the first couple of years and thought I could do nothing else.

I've been a ham radio operator since I was 13, I always liked electronics and technology. My dad was an engineer at Westinghouse. I didn't think I was smart enough to be an engineer but, it's what I really wanted to be.

Finally I said screw it, and I went to electronic tech school while working at the body shop. Breezed through it, got a job at a small company as an electronic technician. I loved it! I sold all of my tools and swore I would never work on cars again. Worked for ~10 years as a tech and finally decided to return to school to get my engineering degree.

I started college in 1996 and I struggled through it but I stuck with it. I graduated in 2002 at the ripe old age of 40 with an EE degree. I am now in an engineering position in a top rated medical equipment company and loving it. I won't kid you, it was hard, real hard (hardships in my personal life not withstanding).

I am now thinking about going for that Masters. It won't be easy but, I can't say enough about going back. Going to work everyday is a whole lot easier now than it was 20 years ago.

My advise, DO IT. If you try and fail, at least you can say you tried. Otherwise there will always be that little bit of regret lingering in the back of your mind.

mike_bar

Well-Known Member
Originally posted by Omega_D
My advise, DO IT. If you try and fail, at least you can say you tried. Otherwise there will always be that little bit of regret lingering in the back of your mind. {snip}
Omega_D,
That is one inspirational story. Thank you for sharing it.

mike_bar

Well-Known Member
Originally posted by hokkyokusei
{snip}
So to sum up, I know I'm not as wildly idealistic as I used to be, probably because I'm realistic enough to see that there's a limit to what one person can do. But I'd also like to think that I have the experience to recognise when one person can make a difference.
Hokkyokusei,

OK, cliché is the wrong word. I am not sure how to describe my feelings, but your comments hit home for me. I too have wondered if I should have choosen a different career. I too wish I had done something more artistic. This sort of reflection must be common, while not cliché. Maybe we should incorporate some of the idealism of the younger group, while maintaining our realistic perspective from our many life experiences.

I try to keep my spirits up and maintain a positive outlook. Sometimes I get negative and appear grumpy. I am sorry if my comments were out of turn.

Respectfully,
Mike

DynaSoar

Well-Known Member
I sort of fell into what I do, but each little fall was suited to me more and more, until I ended up with something I'm more suited for than anything else I can think of.

It took quitting my previous path and risking everything.
I did not know what my end point would be.
It took accepting the advice "do not think of what you want to be or where you want to go study, rather find someone you want to learn from and do that".
It took 10 years, 4 degrees (one of which having nothing to do with the others, except to make more more employable than someone else with the same primary training), and >$100,000. I'm a neuroscientist specializing in nonlinear signal analysis, something very few of my colleagues even understand. I invent new ways to look at the brain/mind. It's such a cutting edge job (way too small to call it a field) that my two post-docs, at National Institutes of Health and at the Department of Psychiatry at Yale Medical School, were by invitation. I did not have to compete for them. I learned science from some of the finest minds in any field learning to think together (Santa Fe Institute), and was mentored in my field by one of the greatest biological psychologists (and neurologists and philosophers and and and) Karl Pribram. This happened because I trusted the process and went with the flow, and most of all looked for what I thought would be fun. If the only way I could do what I do was to have a job doing something else for money to live on, so I could do this for free in my spare time, I would do that. Yes, I like it that much. I "started" at age 38. jerryb Well-Known Member I worked 18 years as a production foreman/ engineer for a local oilfield service company...hating EVERY waking moment of it... hated the work... hated the people...hated the customers... hated the feast or famine attitude of the owners.... I have since grade school been obcessed with computers and technology... 4 years ago, i quit.... went back to college and got certified as a network engineer... and went to work for myself as a consultant... After a few months, the local school district had an opening as a field tech for pc's, which i took. (who could pass up a big fat gov't job eh??) In July, i took over as the district's network administrator and LOVE every aspect of it. I'm in charge of everything to do with technology for the school district, purchasing, planning, and implementation of it. In my 4 years of employment here, my WORST day... is still LEAGUES better than my best day working in the oilfield ever was. It was a daunting and very difficult decision to leave the security of my previous employment... but everything has worked out beyond my greatest expectations so far. I get to do what I love... work with great people, get to work with the folks that are responsible for my children's education, and even get to influence how that education will come about in some regards. hey... I even get to share neato stuff about my hobby with the teachers and district staff.... how cool is that...lol A career change is never easy, but in my case it was the right thing to do. later Jerryb Hospital_Rocket Well-Known Member Do I like my job, yes. So I'll also share the backstory. I was one of those driven kids in HS, who had parents that meant the best yet pushed way too hard. I spent my formative years bucking what my parents tried to make me becuse somewhere down inside I knew it was not right. I completed my entire BS in Metallurgical Engineering coursework except, English composition and a couple of humanities electives when I graduated HS. I did this in 30 months of 21 hour courseloads during the Fall/Winter and overclocking myself during the Summer. The missed courses were in the category I referred to as "underwater bb stacking". I mean, I can always take that fluff later, right? Well one morning I woke up in an alcohol induced fog and none of it made any sense. I was totally, completely, flatline, burned out. I took a 3.7 GPA and shot it in one 19 hour semester. I then realized I needed I was 20 years old and needed to figure out what I was. I chose an enlistment in the USCG (WWattles keep yer comments to yerself, remember I could walk back if my ship got in trouble) After two hitches as an electronics technician, I got out and took a position as an engineeering tech with a large manufacturer of NC equipment. I went to night school, completed my BSEE and worked in engineering. As the company imploded, I took a risk, and tried a stint in procurement. They say without risk, there is no growth. Well I also found that I was spectactulary unsuited for the job. I got bagged and became a consultant (temp for about a year). I took a position as a contract PC technician as engineering jobs were scarce at the time and, well, I needed a job. From there, over a one year period I moved from contract technician, thru systems analyst, to Manager of Desktop Support. Ok, why Al loves his job: I work in one of the larger teaching hospitals. (Yale-New Haven). I see wonderful things everyday. I see babies that weigh a pound at birth go home happy and healthy. I see people horribly injured go home restored. The miracles never cease. I guess what I'm saying is that what I do means something. I help make sick people better. No, I don't treat them, but I help make that treatment possible. What more can I ask? Yeah, some days I get the bejeesus slapped out of me, yet I would not trade it for the world. Al Stymye Well-Known Member I got layed off after 16 yrs with the same company(along with over 100 others). so I have been self imployed for 3 yrs now and I'm doing what I love to do .. design/build industrial machinery.I've been doing it for 23 yrs so I don't have much choice. I still enjoy my job except for the fact that I work alot of hours right now busines is booming ..and leaves little time for personell stuff,but I consider myself very lucky.. and thankfull to have the work.I'm getting too old to do anything else . Susi and I have seriously tossed around the idea of starting a small business to retire with , either a Hotwings shack or a used CD shop. Hospital_Rocket Well-Known Member Originally posted by stymye ...and I have seriously tossed around the idea of starting a small business to retire with , either a Hotwings shack or a used CD shop. What You are not going to open a hobby shop dedicated solely to rocketry with a standing 50% discount off your cost to TRF members?! Well, I never.... sandman Well-Known Member I'd like a double order of hot wings please...no I'll eat 'em here...and a diet coke. Gotta watch the figure. ResearchWorm Well-Known Member Sounds as if I'm a bit of a youngster here at 34. I survived high school in '88, stumbled my way away from Computer Science to Cultural Anthropology because I couldn't hack my way through the Calculus filter classes. Weird thing was that the CS majors had to take more mathematics than the math majors. Departmental jealousy I think. Odd jobs until I was an organically based assembly robot at Boeing Commercial Aircraft Group in Everret. Got laid off in '99 (who at Boeing didn't?), went back to school for 2 years, and got almost 2 ATA's in Electronics and Telecommunications. Picked up the FCC General Radiotelephone Operators License (Elements 1,3,7,8,9) to be a 5 percenter, and am now in a rather quiet field of work. I like the job. The pay is pretty good, with more overtime then I know what to do with (I have seen 100+ hrs of OT in a 2 week period, not often though.), but I really miss being able to go home at night. It's not as bad as being in active duty, as are some of the folks I work with, but I've been home 4 times in the last 2 years. If I could find a job that pays as well or better, closer to home or inexpensive to relocate to, I'd be there instead of here. But until then.. Guess I'll have to see if I can get the elements of the GROL that I don't have so I can be a 1 percenter. Maybe I'll pick up an amateur-radio license or two while I'm at it just so I can really confuse people. I'd love to work in the Info-Resources/IT field for an aerospace company, but they're all either so large that I'd have no chance of getting hired (Boeing [Only job I'd accept there anyway is an HR position specifically created to fire Stonecipher & half of middle management], Lockheed, etc), in Employer/Employee unfriendly [Taxes, housing cost] places (California, Oregon, etc), or so small and highly educated that they don't need a dedicated department of people with my skills (Scaled, SpaceDev, etc). So for the near term, I'm stuck doing what I am doing. Promotions are coming up though, so I might luck out and get a$7K/year raise.

Who knows, with my luck I'll end up managing the IT/Communications department of a cruise-ship and telling some centigenarian retiree for the twelvth time why he can't plug his RJ-11 deskphone into an RJ-45 jack.

Harm none,

ResearchWorm

mike_bar

Well-Known Member
This is such a great message thread.


text:
## Validation of linear regression models.(English)Zbl 0930.62041

Summary: A new test is proposed in order to verify that a regression function, say $$g$$ has a prescribed (linear) parametric form. This procedure is based on the large sample behavior of an empirical $$L^2$$-distance between $$g$$ and the subspace $$U$$ spanned by the regression functions to be verified. The asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the $$L^2$$-distance between the regression function $$g$$ and the model space $$U$$.
Based on this result, a test is proposed for the hypothesis that “$$g$$ is not in a preassigned $$L^2$$-neighborhood of $$U$$,” which allows the “verification” of the model $$U$$ at a controlled type I error rate. The suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic. In particular, it does not require nonparametric estimators of the regression function and hence, the test does not depend on the subjective choice of smoothing parameters.

### MSC:

 62G08 Nonparametric regression and quantile regression 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics
Full Text:

### References:

 [1] Achieser, N. J. (1956). Theory of Approximation. Dover, New York. · Zbl 0072.28403 [2] Barry, D. and Hartigan, J. A. (1990). An omnibus test for departure from constant mean. Ann. Statist. 18 1340-1357. · Zbl 0706.62046 [3] Berger, J. O. and Delampady, M. (1987). Testing precise hy potheses. Statist. Sci. 2 317-352. · Zbl 0955.62545 [4] Bordeau, F. (1993). Tests for the choice of approximative models in nonlinear regression when the variance is unknown. Statistics 24 95-106. · Zbl 0808.62059 [5] Breiman, L. and Meisel, W. S. (1976). General estimates of the intrinsic variablity of data in nonlinear regression models. J. Amer. Statist. Assoc. 71 301-307. · Zbl 0336.62069 [6] Chow, S. C. and Liu, J. P. (1992). Design and Analy sis of Bioavailability and Bioequivalence Studies. Dekker, New York. · Zbl 0823.62086 [7] Cox, D., Koh, E., Wahba, G. and Yandell, B. S. (1988). Testing the (parametric) null model hy pothesis in (semiparametric) partial and generalized spline models. Ann. Statist. 16 113-119. · Zbl 0673.62017 [8] Davison, A. C. and Tsai, C. L. (1992). Regression model diagnostics. Internat. Statist. Rev. 60 337-353. · Zbl 0775.62201 [9] Delgado, M. A. (1993). Testing the equality of nonparametric regression curves. Statist. Probab. Lett. 17 199-204. · Zbl 0771.62034 [10] Dette, H. and Munk, A. (1997). A simple goodness-of-fit test for linear models under a random design assumption. Ann. Inst. Statist. Math. · Zbl 0903.62039 [11] Dette, H., Munk, A. and Wagner, T. (1998). Estimating the variance in nonparametric regression by quadratic forms-what is a reasonable choice? J. Roy. Statist. Soc. Ser. B. To appear. JSTOR: · Zbl 0944.62041 [12] Dieboldt, J. (1995). A nonparametric test for the regression function: asy mptotic theory. J. Statist. Plann. Inference 44 1-17. · Zbl 0812.62051 [13] Eubank, R. L. and Hart, J. D. (1992). Testing goodness of fit in regression via order selection criteria. Ann. Statist. 20 1412-1425. · Zbl 0776.62045 [14] Eubank, R. L. and Spiegelmann, C. H. (1990). Testing the goodness of fit of a linear model via regression techniques. J. Amer. Statist. Assoc. 85 387-392. JSTOR: · Zbl 0702.62037 [15] Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika 73 625-633. JSTOR: · Zbl 0649.62035 [16] Hall, P. and Hart, J. D. (1990). Bootstrap test for difference between means in nonparametric regression. J. Amer. Statist. Assoc. 85 1039-1049. JSTOR: · Zbl 0717.62037 [17] Hall, P. and Marron, J. S. (1990). On variance estimation in nonparametric regression. Biometrika 77 415-419. JSTOR: · Zbl 0711.62035 [18] Härdle, W. and Marron, J. S. (1990). Semiparametric comparison of regression curves. Ann. Statist. 18 83-89. · Zbl 0703.62053 [19] Härdle, W. and Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 1926-1947. · Zbl 0795.62036 [20] King, E. C., Hart, J. D. and Wehrly, T. E. (1991). Testing the equality of regression curves using linear smoothers. Statist. Probab. Lett. 12 239-247. [21] MacKinnon, J. G. (1992). Model specification tests and artificial regressions. J. Economic Lit. 30 102-146. [22] Mandallaz, D. and Mau, J. (1981). Comparison of different methods for decision-making in bioequivalence assessment. Biometrics 37 213-222. JSTOR: · Zbl 0468.62094 [23] Metzler, C. M. (1974). Bioavailiability: a problem in equivalence. Biometrics 30 309-317. [24] M üller, H. G. (1992). Goodness of fit diagnostics for regression models. Scand. J. Statist. 19 157-172. · Zbl 0760.62037 [25] Neil, J. W. and Johnson, D. E. (1985). Testing linear regression function adequacy without replication. Ann. Statist. 13 1482-1489. · Zbl 0582.62056 [26] Orey, S. (1958). A central limit theorem for m-dependent random variables. Duke Math. J. 52 543-546. · Zbl 0107.13403 [27] Rice, J. (1984). Bandwidth choice for nonparametric regression. Ann. Statist. 12 1215-1230. · Zbl 0554.62035 [28] Sacks, J. and Ylvisaker, D. (1970). Designs for regression problems with correlated errors III. Ann. Math. Statist. 41 2057-2074. · Zbl 0234.62025 [29] Schuirmann, D. L. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J. Pharmacocinetics and Biopharmaceutics 15 657-680. [30] Shillington, E. R. (1979). Testing lack of fit in regression without replication. Canad. J. Statist. 7 137-146. · Zbl 0445.62075 [31] Silverman, B. W. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Roy. Statist. Soc. Ser. B 47 1-52. JSTOR: · Zbl 0606.62038 [32] Staudte, R. G. and Sheather, S. J. (1990). Robust Estimation and Testing. Wiley, New York. · Zbl 0706.62037 [33] Staniswalis, J. G. and Severini, T. A. (1991). Diagnostics for assessing regression models. J. Amer. Statist. Assoc. 86 684-692. JSTOR: · Zbl 0736.62063 [34] Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist. 25 613-641. · Zbl 0926.62035 [35] Whaba, G. (1978). Improper priors, spline smoothing, and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B 40 364-372. JSTOR: · Zbl 0407.62048 [36] Whittle, P. (1964). On the convergence to normality of quadratic forms in independent variables. Theory. Probab. Appl. 9 103-108. · Zbl 0146.40905 [37] Yanagimoto, T. and Yanagimoto, M. (1987). The use of marginal likelihood for a diagnostic test for the goodness of fit of the simple linear regression model. Technometrics 29 95-107. JSTOR: · Zbl 0608.62055 [38] Zielke, R. (1979). Discontinous Ceby sev-Sy stems. Lecture Notes in Math. 707. Springer, Berlin. [39] Zwanzig, S. (1980). The choice of approximate models in nonlinear regression. Statistics 11 23-47. · Zbl 0446.62064
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text:
3 Jun 13:00 2015

### Re: [felix] Active programming revolution

On 03/06/2015, at 6:41 PM, srean wrote:

> This ought to be a blog post.

Blogs are too much work. No one reads mine anyhow.
No one reads the email either but its easier to do them.

> And if you are still in touch with Stepanov, I think he would be quite excited to read this.

I'm not in touch with anyone.

--
john skaller
skaller@...
http://felix-lang.org

------------------------------------------------------------------------------

3 Jun 02:10 2015

### Active programming revolution

There is about to be a major paradigm shift in the world of
programming: Active Programming.

I have spent over 15 years developing a strong enough core to
actually implement what the original commercial job required,
and it leads to complete paradigm shift: Active Programming.

Here's what happens. in the old world we have imperative
stateful programming languages with expressions thrown in.
Control flow was king. The pairing of data flow and control
flow was broken by C and similar languages with the notion
of functions using the machine stack (data and control passed
together on the stack).

On the other side, functional programming touted declarative
specifications based on mathematics, and because of the mathematical
basis this style is ostensibly easier to analyse because of the wealth
of mathematical skills and knowledge available. But purely functional
languages just don't cut it in practice: performance is one issue but
the simple reality is recursion is too hard to understand and doesn't
match reality.

Active programming MERGES stateful imperative programming
and functional programming into a single paradigm. The paradigm
is fully declarative and so amenable to analysis.

At present I am just doing the basics. The simplest form is a pipeline:

#((1,2,3,4,5).iterator |-> (fun (x:int) => x + 1) |-> (fun (x:int) => x * x) |-> println[int]);

28 Apr 03:26 2015

### function product

This works:

fun \times[u1,u2,r1,r2] (f1:u1->r1,f2:u2->r2) : u1 * u2 -> r1 * r2 =>
fun (x1:u1,x2:u2) => f1 x1, f2 x2;

fun \otimes[D1,C1,D,C] (f1:(D1->C1), f:(D->C)) : (D1 ** D) -> (C1 ** C) =>
fun (a:D1 ** D) : C1 ** C => match a with
| (x1,,x) => f1 x1,,f x
endmatch
;

fun i2s (x:int)=>x.str+"!";
fun i2i (x:int)=>x+1;

var fs = i2s,i2i,i2s,i2s;
var r = fs.0 \otimes fs.1 \otimes (fs.2 \times fs.3);

println$r (1,2,3,4); But it isn't pretty. The final \times is requires as the ground case (and need parens because of grammar issues, \otimes is right assoc). However \prod (f,g,h) still can't be defined, i have ravel (f,g,h) in the library for up to 5 cases. -- john skaller skaller@... http://felix-lang.org  (Continue reading) 26 Apr 01:16 2015 ### mathmode I'm changing the display rules for mathmode. First, { } will not be displayed in mathmode. Use \{ \} if you want to see something. Second, a Felix identifier will usually emit \mathtt{identifier} which will cause it to be typeset in teletype font, similar to the usual program text font I hope. Next, I am thinking instead of the above, if you specify a font operator: \mathcal { ... } that overrides \mathtt. In fact I think a stack of fonts will be maintained. Fourth, i think I will make a single character identifier an exception and typeset that using \mathit. This means \mathit and \mathtt probably should NOT be used as operators! In general formulae like \mathcal X \mathcal {x + y} \mathcal (x + y) etc affect typesetting and are ALSO Felix functions. So take care  (Continue reading) 25 Apr 01:20 2015 ### Re: [felix] stumped  On 25/04/2015, at 3:44 AM, Shayne Fletcher wrote: > > On Fri, Apr 24, 2015 at 1:07 PM, john skaller <skaller <at> users.sourceforge.net> wrote: > fun ravel[u1,u2,r1,r2] (f1:u1->r1,f2:u2->r2) : u1 * u2 -> r1 * r2 > > Neat function. But I want ravel[D1,C1,D2,C2,D3,C3,....D9,C9] (f1:D1->D2, f2:D2->C2 ... f9:D9->C9): D1 * D2 *..D9 -> C1 *C2 .. C9; I can do str[D1,D2, ... D9] (p1:D1, p2:D2,.. p9:D9):string given str:T->string which should be harder, since it involves polymorphic recursion. However the latter is just a string fold of the individual components. However I don't think Ocaml can do this using any method, and I'm not sure Haskell can either (in fact Haskell doesn't even HAVE tuples AFAIK) Felix and C++ can do it. However I can't generalise it, even if you want a bool fold of some property, i.e. fix the return type. The ravel doesn't need any typeclass, it can be done with a purely  (Continue reading) 24 Apr 19:07 2015 ### stumped I am stumped at the moment defining certain operators on tuples. If you look at src/lib/std/datatype/tuple.flx you will see there is general way to apply a function T -> K T * T -> K to a tuple, where K is a constant type. For example T -> string // Str T * T -> bool // Eq are defined. See also that we can do F T0, F T1 ... F TN -> F (T0, T1 .. TN) in some cases, such as in src/lib/std/algebra/set.flx we can "almost" define \otimes (set_form[T0], set_form[T1],.. set_form[TN] ) I say almost because actually we can do var x = { x: int | x > 0} \otimes { x: double | x > 0.0} \otimes { x:string | x > "H" }; println$ (24,3.2,"Hello") \in x;

but this is right associative. What I REALLY want to define is:

\otimes (s1,s2,s3);

24 Apr 09:56 2015

### Maths DSSL

The below will give cute display in Felix code, if displayed by flx_web.
The "font" operators are just ordinary functions .. so you have to actually
define them if you want stuff to work!

////////////////////////////////////////////////////////////////////////////////
// ordinary and mathmode
var x = X; // ordinary
var x = $$X$$; // mathmode

// these are all TeX commands so x ^ \font y
// typesets correctly: note \sin is an OP symbol
// so x ^ \sin y fails, and x ^ \Gamma y works
// since \Gamma is an ORD, but the y is not raised.

// font operators
var x = $$\mathrm X$$; // mathrm
var x = $$\mathit X$$; // mathit
var x = $$\mathfrak X$$; // mathfrak
var x = $$\mathbb X$$; // mathbb
var x = $$\mathbf X$$; // mathbf
var x = $$\mathcal X$$; // mathcal
var x = $$\mathscr X$$; // mathscr
var x = $$\mathsf X$$; // mathscr
var x = $$\mathtt X$$; // mathtt

// modifiers
var x = $$\acute X$$; // acute
var x = $$\check X$$; // check

var x = $$x ^ \binom {\mathtt x} {\mathtt y}$$;

3 Apr 20:18 2015

### negated comparisons

Next commit, you can write:

x not < y

and

$$x \not\less y$$

Both not and \not mean the same, however not is printed "not" as written,
whereas \not IN MATH MODE ONLY will cause the following TeX operator
to be negated by strikeout.

We need this because whilst TeX defines

\nsubseteq

it does not define \nsubset. You have to write \not\subset.
Note \not\subseteq will work as well, however, the special
form \nsubseteq is provided to make the struck out symbol
more beautiful.

Do not confuse \not with \lnot. The latter is boolean negation operator,
it applies to expressions, and it has looks like logic not symbol,
this has a different precedence than "not" applied to an expression.

Do not write \not expr, it will neither work, nor typeset correctly.
use \not to cancel comparison operators.

--
john skaller

30 Mar 13:01 2015

### Re: [felix] fix patterns

On 30/03/2015, at 7:18 PM, Martin DeMello wrote:
>>
>> This won't work as you might expect because in that pattern NIL is a variable.
>> Easy to miss. You have to write
>>
>>        | A (_, #NIL) => ..
>>
>> to tell the parser the NIL is a type constructor.
>
> Would it be hard to make this an actual warning, viz
>
> warning: variable NIL has same name as constructor. did you mean #NIL?

I don't know, it could be quite hard. It would mean at least doing a lookup
on EVERY variable name used. The problem is that the "desugaring"
of pattern matching is done long before it is possible to do any lookup.
So by the time the compiler comes to bind the code, it has no idea
it's dealing with a pattern match variable.

Pattern matches are basically macros. You can, in fact, invent your own.
It basically goes:

if  (!_match_ctor_CTOR (arg)) goto next_case;
var arg1, arg2 = _ctor_arg_CTOR (arg);

// do handler

goto endmatch;
next_case:

30 Mar 04:14 2015

### fix patterns

Using a nice tool, flx_batch_replace:

/usr/local/lib/felix/felix-latest/host/bin/flx_batch_replace -v src '.*\.(flx|fdoc)'
'fixup/src/${0}' '\?([A-Za-z][A-Za-z0-9_]*)' '\1' cp -r fixup/src/* src Be interested how to do that with standard unix tools. I do note the inconsistent replacement notation${group} for files,
but \group for strings. Internally these search and replace operations
are in fact similar. I put the ${group} in because its so hard to type \1 inside a string and get the quoting right. OTOH in bash${1} is the first
command line argument so that needs to be quoted right too.

--
john skaller
skaller@...
http://felix-lang.org

------------------------------------------------------------------------------
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by Intel and developed in partnership with Slashdot Media, is your hub for all
things parallel software development, from weekly thought leadership blogs to
news, videos, case studies, tutorials and more. Take a look and join the
conversation now. http://goparallel.sourceforge.net/

29 Mar 20:42 2015

### review of brackets

Apart from in structs, unions, and function/procedure definitions,
here is a possibly incomplete catalogue:

{ expr } --> function returning expr
{ stmt; stmt; expr } -> function returning expr
{ stmt; stmt; return expr; } -> function returning expr
{ stmt; stmt; } --> procedure
{ pattern : type | expr } --> set form

( expr ) --> expr
( expr, expr ) --> tuple
(x=expr, y=expr) -> record
struct {x = expr; y=expr; } -> record (deprecated)
( stmt; stmt; expr ) --> expr // means #{ stmt; stmt; expr }
() --> unit tuple
( var expr ) --> expr (eagerly evaluated, same as (let x = expr in x))

I am looking at some more short forms, such as

if(x)stmt;
while(x)stmt;

like C. It's not clear these will work, since they're ambiguous.
An alternative (from COBOL):

if x perform stmt;
while x perform stmt;

Note these are already allowed:


text:
# Tag Info

4

Write $\omega = \alpha_1 + \dots + \alpha_n$ where $\alpha_i = dx_{2i - 1} \wedge dx_{2i}$. The important observation is that if you expand $$\omega^n = (\alpha_1 + \dots + \alpha_n) \wedge \dots \wedge (\alpha_1 + \dots + \alpha_n) = \sum_{i_1, \dots, i_n} \alpha_{i_1} \wedge \dots \wedge \alpha_{i_n} = \sum_{I} \alpha_I$$ then if $I$ contains a repeated ...

4

For $R=\mathbb Z/4\mathbb Z$ the permanent has all the properties you list, and it differs from the determinant when $n\ge 2$. (For any matrix, the difference between its permanent and its determinant is a multiple of $2$, so in $\mathbb Z/4\mathbb Z$ the permanent is a unit iff the determinant is). In general, we can set $R=\mathbb Z/m\mathbb Z$ ...

2

So your bilinear form is non-degenerate if there does not exist a vector $v \neq 0$ such that $B(v,w) = 0$ for any vector $w \in V$. In other words, there doesn't exist a vector that sends all $V$ to zero. Consider a bilinear form $B$ and matrix $A$. If $A$ is non-invertible, then the kernel of $A$ is non-trivial. Suppose $k$ is a vector in the kernel of $... 1 I'll try to give an answer to this question that doesn't require knowing what a tensor is. Of course it will require some comfort with linear algebra, but I'll even try to keep the multilinear algebra to a minimum. Bye_World's answer in the comments is a good one, although there is slightly more that you can say: a matrix is naturally identified with a rank-... 1 Your list includes some subjects, some algebraic structures, and some objects within algebraic structures. I'll separate them to organize the list a little better. Anyone can feel free to contribute to/ edit this list as I'm certainly not an expert in all of this. Subjects: Linear Algebra: the study of vector spaces and the linear transformations ... 1 According to Wikipedia and some papers: Exterior algebra = Grassmann algebra (= differential forms, since they are a construction of the exterior algebra) (=derivations, since derivations are just one possible construction of the dual object to differential forms). EDIT: To make the claim that "exterior algebra=differential forms" precise, since as it ... 1$\Rightarrow)$To see that$rank(A)=n$, we have to proof that the columns of$A$are linearly independant. So we notice that the$j$-th column is$(\alpha_{ij})_i$. If we have$\lambda_1,\dots,\lambda_n\in F$such that$\sum_{j=1}^n\lambda_j(\alpha_{ij})_i=0$, then$(\sum_{j=1}^n\lambda_j\alpha_{ij})_i=0$, which means that for each$i=1,\dots,n$,$\sum_{j=...

1

Suppose $U$ is a vector space over a field of characteristic different from $2$. If you have any linear map $\alpha$ on $U$ such that $\alpha^{2} = I$, then either $\alpha = \pm I$, or $x^{2} - 1$ is the minimal polynomial of $\alpha$. In the latter case the minimal polynomial has two distinct roots $1$ and $-1$, thus $U$ decomposes as the direct sum of ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Proof that Sorgenfrey plane is not normal using points x × (-x)

I'm making Exercise 9 of paragraph 31 in Munkres, which is a proof that the Sorgenfrey Plane $\mathbb{R}_l^2$ is not normal. I'm having trouble on part c of the question. The full question is:

Let $A$ be the set of all points of $\mathbb{R}_l^2$ of the form $x \times (-x)$, for $x$ rational; let $B$ be the set of all points of this form for $x$ irrational. If $V$ is an open set of $\mathbb{R}_l^2$ containing $B$, show there exists no open set $U$ containing $A$ that is disjoint from $V$, as follows:

(a) Let $K_n$ consist of all irrational numbers $x$ in $[0,1]$ such that $[x,x+1/n) \times [-x,-x+1/n)$ is contained in $V$. Show $[0,1]$ is the union of the sets $K_n$ and countably many one point sets.

(b) User exercise $5$ of paragraph 27 to show that some set $\bar{K}_n$ contains an open interval $(a,b)$ of $\mathbb{R}$.

(c) Show that $V$ contains the open parallelogram consisting of all points of the form $x \times (-x+\epsilon)$ for which $a<x<b$ and $0<\epsilon<1/n$.

(d) Conclude that if $q$ is a rational number with $a < q < b$, then the point $q \times (-q)$ of $\mathbb{R}_l^2$ is a limit point of $V$.

I've done (a) relatively easy I think, simply by proving that for every irrational $x$there must be an $n$ so that $x$ lies in $K_n$, and then adding all rational one-point sets. (b) was something I did in the exercise mentioned before. My problem (at the moment) lies in (c).

First of all, I don't know if they mean only the irrational $x$'s or the rationals too. Second, in (b) we worked with the closure of $K_n$ and not $K_n$ itself. Does the closure of $K_n$ automatically lie in $V$ too? If yes, any hints how to prove this; if no, how do I actually start (c)?

-

They mean all $\langle x,-x+\epsilon\rangle$ such that $x\in(a,b)$ and $0<\epsilon<1/n$; that includes both rational and irrational $x$.

You have a particular $n$ and a non-empty open interval $(a,b)$ such that $(a,b)\subseteq\operatorname{cl}K_n$, where for each $x\in K_n$ we know that $$\left[x,x+\frac1n\right)\times\left[-x,-x+\frac1n\right)\subseteq V\;.$$

Suppose that $x\in(a,b)$ and $0<\epsilon<1/n$. In order to show that $\langle x,-x+\epsilon\rangle\in V$, it suffices to show that there is a $y\in K_n$ such that

$$\langle x,-x+\epsilon\rangle\in\left[y,y+\frac1n\right)\times\left[-y,-y+\frac1n\right)\;.\tag{1}$$

Now $(1)$ holds iff $y\le x<y+\frac1n$ and $-y\le-x+\epsilon<-y+\frac1n$. These can be boiled down to the requirements that $y>x-\frac1n$, $y\ge x-\epsilon$, $y\le x$, and $y<x-\epsilon+\frac1n$. Can you continue from here to show that such a $y$ can always be found? I’ve finished the argument in the spoiler-protected bit below.

Since $\epsilon<\frac1n$, these four inequalities further reduce to $y\ge x-\epsilon$ and $y\le x$, i.e., $x-\epsilon\le y\le x$. Since $\epsilon>0$, the open interval $(x-\epsilon,x)$ is non-empty, and it follows that $(x-\epsilon,x)\cap(a,b)\ne\varnothing$. Finally, $K_n$ is dense in $(a,b)$, and $(x-\epsilon,x)\cap(a,b)$ is a non-empty open subset of $(a,b)$, so $(x-\epsilon,x)\cap(a,b)\cap K_n\ne\varnothing$. Now just choose $y$ in this intersection, and you’re done.

It’s not true that all points of $\operatorname{cl}K_n$ lie in $V$, but the points of $K_n$ are so thickly scattered throughout the interval $(a,b)$ that

$$\{x\}\times\left(-x,-x+\frac1n\right)\subseteq V$$

for each $x\in(a,b)$, even when $x$ itself isn’t in $K_n$. For each $y\in\left(-x,-x+\frac1n\right)$ there is a point $z\in K_n$ to the left of $x$ that is close enough to $x$ that $$\langle x,y\rangle\in\left[x,x+\frac1n\right)\times\left[-x,-x+\frac1n\right)\;,$$ which of course is a subset of $V$.

-


text:
# Hypothetical syllogism

In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises.[1][2]

If I do not wake up, then I cannot go to work.
If I cannot go to work, then I will not get paid.
Therefore, if I do not wake up, then I will not get paid.

In propositional logic, hypothetical syllogism is the name of a valid rule of inference[3][4] (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). Hypothetical syllogism is one of the rules in classical logic that is not always accepted in certain systems of non-classical logic. The rule may be stated:

$\frac{P \to Q, Q \to R}{\therefore P \to R}$

where the rule is that whenever instances of "$P \to Q$", and "$Q \to R$" appear on lines of a proof, "$P \to R$" can be placed on a subsequent line.

Hypothetical syllogism is closely related and similar to disjunctive syllogism, in that it is also type of syllogism, and also the name of a rule of inference.

## Formal notation

The hypothetical syllogism rule may be written in sequent notation:

$(P \to Q), (Q \to R) \vdash (P \to R)$

where $\vdash$ is a metalogical symbol meaning that $P \to R$ is a syntactic consequence of $P \to Q$, and $Q \to R$ in some logical system;

and expressed as a truth-functional tautology or theorem of propositional logic:

$((P \to Q) \and (Q \to R)) \to (P \to R)$

where $P$, $Q$, and $R$ are propositions expressed in some formal system.


text:
# Multiplication of Cross-Relation Equivalence Classes on Natural Numbers is Well-Defined

## Theorem

Let $\left({\N, +}\right)$ be the semigroup of natural numbers under addition.

Let $\left({\N \times \N, \oplus}\right)$ be the (external) direct product of $\left({\N, +}\right)$ with itself, where $\oplus$ is the operation on $\N \times \N$ induced by $+$ on $\N$.

Let $\boxtimes$ be the cross-relation defined on $\N \times \N$ by:

$\left({x_1, y_1}\right) \boxtimes \left({x_2, y_2}\right) \iff x_1 + y_2 = x_2 + y_1$

Let $\left[\!\left[{x, y}\right]\!\right]$ denote the equivalence class of $\left({x, y}\right)$ under $\boxtimes$.

Let $\otimes$ be the binary operation defined on these equivalence classes as:

$\forall \left[\!\left[{a, b}\right]\!\right], \left[\!\left[{c, d}\right]\!\right] \in \N \times \N: \left[\!\left[{a, b}\right]\!\right] \otimes \left[\!\left[{c, d}\right]\!\right] = \left[\!\left[{\left({a \cdot c}\right) + \left({b \cdot d}\right), \left({a \cdot d}\right) + \left({b \cdot c}\right)}\right]\!\right]$

where $a \cdot c$ denotes natural number multiplication between $a$ and $c$.

The operation $\otimes$ on these equivalence classes is well-defined, in the sense that:

 $\displaystyle \left[\!\left[{a_1, b_1}\right]\!\right]$ $=$ $\displaystyle \left[\!\left[{a_2, b_2}\right]\!\right]$ $\displaystyle \left[\!\left[{c_1, d_1}\right]\!\right]$ $=$ $\displaystyle \left[\!\left[{c_2, d_2}\right]\!\right]$ $\displaystyle \implies \ \$ $\displaystyle \left[\!\left[{a_1, b_1}\right]\!\right] \otimes \left[\!\left[{c_1, d_1}\right]\!\right]$ $=$ $\displaystyle \left[\!\left[{a_2, b_2}\right]\!\right] \otimes \left[\!\left[{c_2, d_2}\right]\!\right]$

## Proof

Let $\left[\!\left[{a_1, b_1}\right]\!\right], \left[\!\left[{a_2, b_2}\right]\!\right], \left[\!\left[{c_1, d_1}\right]\!\right], \left[\!\left[{c_2, d_2}\right]\!\right]$ be $\boxtimes$-equivalence classes such that $\left[\!\left[{a_1, b_1}\right]\!\right] = \left[\!\left[{a_2, b_2}\right]\!\right]$ and $\left[\!\left[{c_1, d_1}\right]\!\right] = \left[\!\left[{c_2, d_2}\right]\!\right]$.

Then:

 $\displaystyle \left[\!\left[{a_1, b_1}\right]\!\right]$ $=$ $\displaystyle \left[\!\left[{a_2, b_2}\right]\!\right]$ Definition of Operation Induced by Direct Product $\, \displaystyle \land \,$ $\displaystyle \left[\!\left[{c_1, d_1}\right]\!\right]$ $=$ $\displaystyle \left[\!\left[{c_2, d_2}\right]\!\right]$ Definition of Operation Induced by Direct Product $\displaystyle \iff \ \$ $\displaystyle a_1 + b_2$ $=$ $\displaystyle a_2 + b_1$ Definition of Cross-Relation $\, \displaystyle \land \,$ $\displaystyle c_1 + d_2$ $=$ $\displaystyle c_2 + d_1$ Definition of Cross-Relation

Both $+$ and $\times$ are commutative and associative on $\N$. Thus:

 $\displaystyle \left({a_1 \cdot c_1 + b_1 \cdot d_1 + a_2 \cdot d_2 + b_2 \cdot c_2}\right)$ $+$ $\displaystyle \left({a_2 \cdot c_1 + b_2 \cdot c_1 + a_2 \cdot d_1 + b_2 \cdot d_1}\right)$ $\, \displaystyle = \,$ $\displaystyle \left({a_1 + b_2}\right) \cdot c_1 + \left({b_1 + a_2}\right) \cdot d_1$ $+$ $\displaystyle a_2 \cdot \left({c_1 + d_2}\right) + b_2 \cdot \left({d_1 + c_2}\right)$ $\, \displaystyle = \,$ $\displaystyle \left({b_1 + a_2}\right) \cdot c_1 + \left({a_1 + b_2}\right) \cdot d_1$ $+$ $\displaystyle a_2 \cdot \left({d_1 + c_2}\right) + b_2 \cdot \left({c_1 + d_2}\right)$ as $a_1 + b_2 = b_1 + a_2, c_1 + d_2 = d_1 + c_2$ $\, \displaystyle = \,$ $\displaystyle b_1 \cdot c_1 + a_2 \cdot c_1 + a_1 \cdot b_2 + a_1 \cdot d_1$ $+$ $\displaystyle a_2 \cdot d_1 + a_2 \cdot c_2 + b_2 \cdot c_1 + b_2 \cdot d_2$ $\, \displaystyle = \,$ $\displaystyle \left({a_1 \cdot d_1 + b_1 \cdot c_1 + a_2 \cdot c_2 + b_2 \cdot d_2}\right)$ $+$ $\displaystyle \left({a_2 \cdot c_1 + b_2 \cdot c_1 + a_2 \cdot d_1 + b_2 \cdot d_1}\right)$

So we have $a_1 \cdot c_1 + b_1 \cdot d_1 + a_2 \cdot d_2 + b_2 \cdot c_2 = a_1 \cdot d_1 + b_1 \cdot c_1 + a_2 \cdot c_2 + b_2 \cdot d_2$ and so, by the definition of $\boxtimes$, we have:

$\left[\!\left[{a_1 \cdot c_1 + b_1 \cdot d_1, a_1 \cdot d_1 + b_1 \cdot c_1}\right]\!\right] = \left[\!\left[{a_2 \cdot c_2 + b_2 \cdot d_2, a_2 \cdot d_2 + b_2 \cdot c_2}\right]\!\right]$

So, by the definition of integer multiplication, this leads to:

$\left[\!\left[{a_1, b_1}\right]\!\right] \otimes \left[\!\left[{c_1, d_1}\right]\!\right] = \left[\!\left[{a_2, b_2}\right]\!\right] \otimes \left[\!\left[{c_2, d_2}\right]\!\right]$

Thus integer multiplication has been shown to be well-defined.

$\blacksquare$