Is There Anything That the Whole World Is Collectively Doing Wrong?
. There is always something that needs to be taken care of. . More wants.. More desires.. Children.. It's a never ending list.True fulfilment comes from having good health.. Friends who are always available when you need them. Being able to spend time with naturecherishing every moment.. Being at peace with what you have.. And not from fancy cars.. Houses.. Gucci bags and watches. .. We do learn this lesson.. But sometimes a little too late in life..What is this life.. If full of careWe have no time to stand and stare.. No time to stand beneath the boughs.. And stand as long as sheep or cowsLeisure.
. W H DaviesOf time gone by.
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What important topics of number theory should every programmer know?
I assume you are asking for "must-know" knowledge for algorithm programming contests (e.g., the ACM-ICPC, Topcoder SRMs, ...). I'm not so sure if every programmer should know some number theory knowledge.I participated in the ACM-ICPC for 4 years, entering the World Finals twice. I am not really very strong at Number Theory problems, but I wish to answer as far as I could. The following items are categorized based on subjective judgement.Basics:nLCM and GCD(Extended) Euclidean algorithmModular arithmetic (addition, subtraction, multiplication)Modular multiplicative inverse ("division") - Existence and computation(Fast) Prime list generationFast prime factorization (with/without pre-process)Exponentiation by squaring (e.
g.
, computation of x^n, A^n for square matrix A, and so on)nIntermediate:nSolving systems of linear modular congruences - Chinese Remainder TheoremnSolving linear recurrences by fast exponentiation of matrices (e.g., Fibonacci Sequence)nEuler's phi function and fast computationsnMiller-Rabin primality testnAdvanced:nPrimitive root modulo NnDiscrete logarithm Discrete square rootMultiplicative function and Möbius inversion FormulaFarey sequence and applicationsn(And there should be a lot more)nQuite often, a single problem will require some of the following items together with Number Theory knowledge, so that you can solve it:nDynamic Programming(Basic) Enumerative Combinatorics: _nC_r and _nP_rLucas' TheoremInclusion-exclusion principleProbabilitynFinally, feel free to correct errors and add any missing important items. Any suggestion is welcome. :D(Oh, this is my first answer ever at Quora.
)This is entirely based on my personal understanding of how recruiting/interviewing works. I am not referencing any internal materials when writing this answer.Important Topics of Number Theory that every programmer should know?.
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How big is your video game collection?Currently my collection in my Steam library is at 67 games.No, I have not yet played all of them and I also didn't really pay full price for all of them. Some were free, back when HumbleBundle would give away a free game, or package of games, for free at least once each month (apparently they've begun doing this again since the 14th of march of this year). Fanatical also offered some free game downloads that I've taken advantage of. Most of the games in my Steam library were purchased at a discount, if not all (I never buy a game at release to give time for the developers to fix bugs and to allow time for a price drop).My PS4 game collection is hovering at around 15 games (I've let friends borrow some so my count could be one or two off), including two digital purchases where the digital version of the game was cheaper than the physical copy (Final Fantasy XV and MGS V: The Phantom Pain).
My PS3 game collection is around 7 or 8 titles now since I've tried to sell them off because my console was stolen during a break-in.My PS2 game collection is between 15 and 20 games; if I include PS1 titles that I own and play on the PS2 the number goes up to between 18 and 23 (Final Fantasy VII, The Legend of Dragoon & Metal Gear Solid: Tactical Espionage Action).So, considering everything I can currently account for, the total number of games that stretches over four, or five, generations of consoles and PC games, I'm counting at least 107 games.
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Why can't we sum an uncountable collection of numbers?We can, but we have to define what we mean by it.Strictly speaking summation is something you do to just two elements, or by extension (due to transitivity and symmetry) to a finite collection of elements.Summation is frequently extended to countable sequences of elements using the concept of a series, where the 'sum' of a series is defined to be the limit of the partial sums (and occasionally something more exotic when that limit doesn't exist). Note that this sum can depend on the ordering of the terms.In the case of uncountably many terms, there cannot be any order for the summation, so sequences and series aren't useful. However, we can still define a notion of sum using a generalisation of sequences called nets.
Rather than defining a sequence of partial sums, we define a partial sum for every finite subset of terms. Since the set of all finite subsets forms a directed set with set inclusion (meaning that every two finite subsets have an upper bound, namely their union), the mapping from subsets to partial sums forms a net (to the reals, or some other topological space).To define the limit of this net, we first say that the net is eventually in a subset X (of the net's codomain) if there exists a finite subset of terms such that the partial sums at all finite subsets that contain it lie in X. We then say that the limit of the net is x if the net is eventually in every neighborhood of x.This definition agrees with the one for series for all absolutely convergent series. Additionally (and perhaps disappointingly for the OC) any uncountable collection of reals with a finite sum must be zero in all but countably many terms.
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For people who have collections, what do you collect and how did it all started?I collect a few things none of which are particularly valuable to anyone but other collectors...The main one is dice, not the normal kind you use for Monopoly or Yahtzee but RPG dice that have 4, 6, 8, 10, 12, or 20 sides. I have 6 glass vases on my bookcase, one for each type and they are all filled with a hundred or more of each type (the 4 sider vase has about 400 in it) and then there are other types as well.I've got 5-siders, 7-siders, 14-siders, 16-siders, 24-siders, and 30-siders. I have dice made of obsidian, dice made of quartz, and dice made of steel, I have a 20-sider the size of a baseball, dice that light up when rolled, dice that glow in the dark, there are even a few dice with roman numerals and dice with zodiac signs (12-sided).The other thing I actively collect are called Tegata.Tegata are a special autograph made by Sumo wrestlers. They are created by having the wrestler cover his hand in ink (red or black) and then pressing it against a special board. Once the ink is dry the wrestler writes his name using calligraphy. The process is done only occasionally due to the time required and the tegata are never sold, instead they are given away to companies that sponsor matches, members of their 'support clubs' which are like fan clubs that help pay for things like the mawashi and such and sometimes put in the gift bags given to people who purchase the expensive box seats at tournaments.
Due to the restrictions and time needed to make the items they can be pretty rare although it is actually the lower ranked wrestlers who are the hardest to find. The Yokozuna (grand champions) have regular session every few of months to create tegata where they produce hundreds at a time while the lower ranks might only do it once a year unless their popularity is high.Do you collect anything? If so, when did you start collecting? How large is your collection?.
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Are there any statistics on the success of debt collection phone calls vs debt collection letters?It has always been my experience that neither letters or phone calls by themselves are the most successful solution when it comes to debt collection. I find that success comes from using both methods simultaneously as part of your overall collection process.Not all customers are alike and very often most customers will pay upon the receipt of the first reminder letter. This is usually because they have simply forgot to pay your bill on the assigned due date and as such a simple, gentle reminder in the form of a letter is usually enough.Other customers however, for a variety of reasons will ignore your letters delay payment as late as possible. In this case if you rely on just letters you are not going to be very successful in recovering the debt. This is because the control is all in the hands of the customer as the communication is going one way and they are the ones who are deciding whether or not to respond. This is where phone calls are important as it allows you to take back some control of the situation by engaging with your customers.The best results come from using both methods, usually in the format of one method immediately following the other method.
I would advise the following approachPre-due letter/email sent 5 days before the invoice due dateFollow up phone call made the following day1st reminder letter/email sent 7 days after the invoice due dateFollow up phone call made the following day2nd reminder letter/email sent 14 days after the invoice due dateFollow up phone call made the following day3rd & final reminder letter/email sent 30 days after the invoice due dateFollow up phone call made the following dayThe timing and number of reminders might vary depending on your line of business, but I wouldnt recommend going beyond 3 warnings before you take final action to recover the debt
