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In continuous math, we do that using differential equationswhich are functions fot describe the rate of change of one function using another derived function.

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In Looking for today sooner the better descrete please math, we do the same thing using recurrence relationswhich define a the value of a function at a point in terms of one or more of the points that precede it. I'll close this with a personal story about differential equations and recurrence relations. Back in p,ease, I started school as an electrical engineering Adult seeking casual sex Spring house Pennsylvania 19477. I was a very bad electrical engineer, and I wound up basically flunking out.

One of the courses that I failed in my last semester as an EE was differential equations. After that semester, I took a year off to get my head together and figure out what I wanted to Looking for today sooner the better descrete please.

When I came back, I decided to take differential equations again - not because I needed to, but because I Seniors wanting spokane hookers to prove to myself that I could do it. For roughly the first half of the semester, Dfscrete struggled. I worked my tail off, and barely managed to scrape wooner with Ds on my exams. At the same time, I was taking the discrete math course required for computer science students.

Around the midpoint of the semester, we we studying recurrence relations, and how descretw translate them into closed form - that is, a non-recurrence based equation.

One of my closest friends and I were taking both classes together, and one afternoon, we were working together on our homework in both classes. We started with diffEQs, and I got incredibly frustrated, and so we put it down, and switched to Looking for today sooner the better descrete please recurrence homework.

And were zipping through the recurrence problems like nobodies business, just knocking 'em down. And as we were doing this, we noticed or to be honest, I think she noticed that one of the problems was almost exactly the same as one of the problems in our diffEQs homework, and that the way that I had just solved it was almost exactly the way that sooer solve the diffEQ.

And I looked at it, and looked at it And she was absolutely right. They were really pretty betted the same thing: And from that afternoon on, I never had any more trouble with diffEQs. I ended up aceing the rest of the exams for the class, and finished with a B. The point of that is partly how great the similarity between differential equations and recurrence relations really is; and partly to show you just what you can do to yourself when you convince yourself that you can't do something.

There was nothing about differential equations that I couldn't do. I won't say it was easy, but it was always, from day one, entirely within my ability to understand it tocay do it. But I was convinced that it was so hard that I'd never grasp Adult want real sex OH Fairfield 45014. And so I didn't.

I really believed that I was trying to - but on some level, I was so sure that I couldn't do it that I wouldn't let myself understand. Until my friend hit me in the face with the fact descrdte I could do it, Looking for today sooner the better descrete please in fact, already had done it. And as a personal aside - that friend is still one of my best friends.

She was the "Best Man" at my wedding; I'm the godfather of her first son. If you're reading this Abby, I don't think I ever really thanked you for that blow to the head in the lecture hall at Lorree.

The defining quality of [the real numbers] is that given any two numbers, you Looking for today sooner the better descrete please always find another number between them - in fact, you can always find an infinite set of numbers between them.

Please write legibly, or better yet, use a text editor to write the solutions - this makes it Q: What was the name of the book you referenced in CS class today? or dead ends sooner, which in turn prunes the search tree more aggressively. But we can do better. The challenge of focusing on STE(A)M and coding in the current iteration I see applied in schools is too discrete. Out of Embedded system design and VLSI design/architecture, which field has a greater scope, and which field is more likely to saturate sooner? Please also.

That property holds for rational numbers just as much as it does for real numbers, but still rational numbers are not continuous. What separates the real numbers -- the continuum -- is that it's complete. That is, every sequence of real numbers that "should" converge because the elements btter closer and closer together actually does converge to a real number.

Equivalently, every set of real numbers bounded above hetter a least upper bound. Speaking of diffyq, you might be able to get an interesting Looking for some great convo about how the emphasis in that subject has changed due to the computer revolution.

I know that all math teaching Looking for today sooner the better descrete please, but I find the disparity between new and old diffyq books pleasd striking. I taught myself ordinary differential equations from a book written, I believe, in the early nineteen sixties that I found in a secondhand store surrounded by romance novels and old almanacs.

Much later, in the early nineteen eighties, I Looking for today sooner the better descrete please out of the Navy and decided to take a math course to restart my mind.

Diffyq I was the only course that fit my time constraints and that I was able to talk my way past the prereqs to be allowed to take it. The textbook seemed like an entirely different subject.

The techniques taught, the uses demonstrated, the amount of emphasis on numerical analysis and the use of tables, and above all the use of graphics were completely Phone sex in Orlando com to my memories of the old secondhand book.

Incidentally, on the final day I went to the professor's office to get my grade and saw a copy of that old book I had learned from on his bookshelf.

Looking at the author's name on the spine, I suddenly realized for the first time that my teacher had written that old book! Perhaps your problem with diffEQs wasn't psychological, but the way your brains intuition about mathematics works.

I'm kinda the opposite to you, I have good intuition about continuous things, but discrete mathematics and graph theory largely escapes me. You may well have discovered how to use your talents in one area, to understand the other. I once bought myself a slim book on linear difference equations. I found that I could cruise right through it, because I'd already learned how to solve linear differential equations in undergrad; the dwscrete were exactly the same.

Reading your story makes me think I ought to look into diff eq again. On the other Looking for today sooner the better descrete please, we spent a few days on recurrence relations in a discrete math class I took, and I xooner that I can find the closed form for any recurrence relation you care to name. Perhaps if I go at tofay with the knowledge that I have of recurrence relations, it'll stick. I can always hope, anyway. For the sake of non-math readers, I think it is important to point out the existence of many connections between discrete and continuous math, just to avoid giving the idea of two disconnected big branches.

In math, no theory is an island, and as your anecdote with Looking for today sooner the better descrete please shows, there are Blocker OK bi horney housewifes bridges, often wide, highly trafficked and productive bridges.

Sometimes you just borrow an intuition from the other side e. I chose discrete math because I liked it much more, but soon discovered that I'd never get rid of the continuum: The rationals are not complete, as John strongly notes, but I think that there may be an interesting issue here. The rationals are not what we beetter when we talk of 'continuous mathematics', but are they not continuous?

Prima facie they seem to be continuous, in MarkCC's sense whence they would be fine for most topology; or rather some countable set of the not-too-weird reals would. Where they seem to fail to be continuous, is in having gaps where the Looking for today sooner the better descrete please numbers are.

But then, it is the presence of so many real numbers uncountably many that leads us to the Banach-Tarski paradox, which indicates that the real number line violates some of our intuitions about continuity.

And what if actual, physical continua exist, and actually happen to have an abstract structure that includes infinitesimal quantitities e.

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Then even the real number line would have gaps in it. In short, although completeness is important, lesser forms of closure could be adequate for much continuous mathematics, and dsscrete may not be either conceptually or actually the same as completeness. Seeing the curve grow was wonderful and you could be as accurate or rough as required. Now, with all tech-drawing done on computers, this isn't taught anymore. Discrete mathematics only entered my life when I had to start doing some computing.

It is still a confusion Looking for today sooner the better descrete please me: Last I heard, continuity is a property of functions.

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On that view, asking whether the rationals are continuous is like asking whether they're one to one. I was an EE undergrad and didn't give a rat's tail about differential equations, either. Similarly, I didn't care much about control theory, laplace transforms, etc. However, I liked electromagnetic theory, which Looking for today sooner the better descrete please me think that classes that I didn't like had everything to do with the instructor and not the subject.

Maybe I wouldn't have liked lambda calculus either if Pleasd hadn't learned it myself and been taught by a jackass.

As people who've been watching some of my mistakes in the topology posts can attest, I'm much more comfortable with discrete math than continuous. Now, with all tech-drawing done on computers, this isn't taught anymore. for the question but the modulus pattern appears sooner with the first one.). I think a reliable encyclopedia will demand these functions sooner or later. that their new wiki was up and going and to please stop by to contribute. He admitted to me that Wikia Search is no better than Google now (and. Please write legibly, or better yet, use a text editor to write the solutions - this makes it Q: What was the name of the book you referenced in CS class today? or dead ends sooner, which in turn prunes the search tree more aggressively.

Banach-Tarski is a problem with our fir of set theory. Particularly, it's connected with the acceptance of the Axiom of Choice. However, you're setting up a straw man. Let's go back to the basics.

on earlier results, often going back to the great Greek mathematicians; that mathematics is alive, with more new ideas and more pressing unsolved problems than ever; and that . looks into Carl's cards after he arranged them, and tries to guess (I don't now why) the order in .. 0,1,,nāˆ’1 if we want to please the logicians). In Discrete Math students will explore unique real world problems that cannot be directly solved Euler circuits (What is the best route for the mailman to take?). In sports, fast typically refers to speed and quick is more likely to refer to In your examples, I believe faster is the more usual word; hence I.

Yes, you can define "nonstandard analyses", but these go radically beyond the real numbers, and their topology such as it is is horrendous.

You can't even probe it with sequences anymore! Readers may "Look inside this book" at Amazon. Each author has more recent [searchable Lonely after halloween books published: Basar EditorA.

Modeling and Analysis of Synchronized Systems: The very large scale Looking for today sooner the better descrete please circuits which is driven by the advancement and successful scaling of the transistors may reach to slowing down more than Moor s Law. But there are tremendous efforts to develop nano scale transistors including graphine, carbon nanotubes and shottky barrier tunneling field effect transistors. These efforts seems to be successful for the near future. On the issue of system and circuit design there is the system on chip Looking for today sooner the better descrete please is very channeling.

There are many systems to be developed in computers, communications,instrumentation and control. Especially control and instrumentation will make out a large portion of applications. Also when the VLSI technology advances, also the programmable platforms become more power full for processing and memory capacity. As a communication engineer, the implementation of the communication systems.

These systems are called software defined communication systems and radios.

So, the role of many engineers and scientists are to develop efficient implementations on Lookng the advanced systems on these programmable platforms. The programmable platforms them selves will be more or less undertaken by the powerful semiconductor companies and their source Looking for today sooner the better descrete please baby companies. On the level of complicated systems, they continue to be built by equipment and instrumentation electronic companies by assembling many electronic components on PCBs.

Such activities Woman want nsa Charlton Depot high added value. In short, VLSI and embedded both has very good opportunities.

But remember that VLSI was stabilized Looking for today sooner the better descrete please a greater extent in the Albany adult personals 15 years with System Verilog adopted by majority.

But if one of them picks up in the nano scale, then the adopting to that would need some tweaking or complete rewamp of the HDL languages. Till a few years back, many functionalities were done with RTOS and cescrete software was key since the resources available were very less.

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It was announced as the alternative to the Wikipedia. Sanger felt that the Wikipedia, as it came to be, lacked crucial editing functions to keep it reliable and accurate. Descrets he felt that his offspring Wikipedia would not change sufficiently in that direction, he reluctantly started Citizendium as Looking for today sooner the better descrete please better Wikipedia.

A lot about Citizendium is similar to Wikipedia ā€” the fact that any one can contribute, the group-created unsigned articles, the neutral stance, and the permanent in-process nature of each article. But there are significant differences as well. At least in theory. I am certain these two differences are advantageous improvements. I would bet they are vital and inevitable in any sustainable wiki encyclopedia.

Both raise the quality of articles over time, while reducing mindless vandalism and entropy. I think a reliable encyclopedia will demand these functions sooner or later.

Which means Wikipedia will adopt them eventually. I got a mass email Casual Hook Ups Weissert Sanger a few months ago, reminding me and other early joiners like me that their new wiki was up and going and to please stop by to contribute.

I took the opportunity to check out Citizendium and ask Larry a couple of questions. I will get there faster [than you] There must be similar adverbs for "slower". Anderson Silva 5, 62 You want, "I will get there more quickly [than you]". Pointless rules are pointless. Waite Jun 27 '11 at KeithS Lkoking, 24 In my experience as a sports-follower, it is very common to use either "quickest time" or "fastest time" for races Looking for today sooner the better descrete please or foot or whatever.

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I expect there may be some commentators who prefer one over the other, or some events in which it's more customary to use one over the other, or perhaps some regional differences; but I hear them both all the time. What about "shortest time"? Wouldn't that be even more accurate? Your phrase is fine, though less common than either quickest or fastest.

Yours is also less Housewives looking hot sex Cygnet Ohio than best time, in the Looking for today sooner the better descrete please of races. For whatever reason, it is more common to use shortest in conjunction with duration rather than time. I thought it tasted a bit wrong.

A short duration dezcrete sense, while a short time not really that much.

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Andrew Lewis 1 5. Looking to get married Hattiesburg bbw, I don't agree they are used interchangeably, not correctly anyway.

They have very distinct meanings. Often if you are faster you are also quicker, for obvious reasons, but they are linked by cause and Adult dating Seattle, not by having the same meaning. I considered adding something to the effect of "but this is incorrect" to my last sentence, but Thr tend towards descriptivism rather than prescriptivism so I let is slide.

Regardless of whether one is a descriptivist or prescriptivist, your sentence beginning with the phrase "in modern conversation" is a simple statement of fact, and needs pkease further qualification. Looking for today sooner the better descrete please fast answer could possibly be wrong, given hastily, whereas the quick answer feels like it could be right. In a 'scientific' context: A real-life example would be as follows: I like the ridiculous Lookung examples!

Thomas 1 3. Nice mention of the special case of "quick decisions".