Boogles Money Maths. Workbook 3 (Number Crunching)

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Average Review. Write a Review. Related Searches. Are you struggling to pray while dealing with infertility? It contains a month's worth of devotions, View Product. This is a classic television comic book from the 's This is a classic television comic book from the 's. Boogles and The Self Employed Consultant. Boogles meets various characters in the 'Busy Manager' series and assists them with their bookkeeping. A simple story with illustrations on how to A simple story with illustrations on how to do the bookkeeping organising file management in a small business, and an overview of the kind of things to keep it mind when running and A simple story with illustrations on how to do the bookkeeping organising file management in A simple story with illustrations on how to do the bookkeeping organising file management in a small business, and an overview of the kind of things to keep it mind when running and growing a small business.

Ideal for entrepreneurs Avez vous Vous voulez termine votre livre rapidement? In working with hundreds of small businesses and individuals over the past decade both hands-on What you are pointing out is problems of convention and consensus. Off the top of my head I can think of a handful of strategies for coming to agree on the 0th value of the Fibonacci function in English.

I bet you do too - all those things are intuitive to humans and we take them for granted. In computer science many of those problems have already been formalised, and some have been solved. S You have been using the concepts of "communication" and "information". Shannon formalised those! S Fibonacci is an numerical formalisation of the Golden spiral. In a nutshell, what I am pointing out is succinctly expressed by Donald Knuth.

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Science is what we understand well enough to explain to a computer. Art is everything else we do. The Chomsky hierarchy covers all of that. It's linguistics for formal languages. Grammar, syntax and semantics together with reflection allows for formalisms and meta-formalisms. It all culminates in Turing Completeness. Chomsky Type 0 grammars.

If you find something more powerful than a Chomsky Type 0 grammar - you have made a ground-breaking scientific discovery. I'd say what mathematicians do is "think". We call the sort of thinking mathematicians do "mathematics". I get through quite a bit of grad stats in any given week and I'd say that what I'm not doing reading the computations of other mathematicians.

I'm reading words in english, which try to explain concepts which are then sketched formulaically. I'm also reading proofs that are usually completed by a "mathematical" intuition and are very rarely if ever constructivist. Maybe, that's just me busy thinking whilst the rest are busy computing By the way - this is rather circular and it begs questions. Is it any different to the kind of thinking computer scientists do? Once you are done thinking your thought function returns a result in the form of language, no? Or does thought fail to halt?

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A lookup table is a particular case of a space-time trade-off. Sure, if you restrict yourself to intuitionistic logic I need to go home and eat a bunch of weed edibles so I can read this comment. Update: So I got drunk instead which has basically the same effect on me. Programming is math, except in the real world you have to deal with countless technical and business constraints.

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So unsurprisingly, theory! The substance might just change in practice because a theoretical answer is completely impractical. A formal language? Mathematics is a language of hand-waving.

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When you translate math into algorithms and real programs, you begin running into problems that shape your solution. Really, you could come up with infinite different solutions to the same problem, all with different characteristics, use cases, strengths and weaknesses. There's no point in making a shared library, because it would be too fucking big and confusing.

Better to formulate a solution yourself at this point, if you know what you're looking for, and tune it as you go. I expect little to no cross-pollination because mathematicians love math and love their own work and love not having to deal with implementation issues, and have no desire to learn anything you mentioned. Unit testing, refactoring, Even many CS profs don't care, it's just the way it is -- a love of powerful ideas, not so much the dirty work of making them a reality. They theorize, and write off everything else as "applications. I do sometimes think more math might unlock more options for my software career like if I had a better grasp on calculus I could be more effective at 3D graphics and simulations, for example.

But right now, I probably use math more often in my main hobby than I do when I program, and that hobby is board game design. I'm often resorting to math to figure out how to make sure my designs are balanced, how many cards I should use at different player counts, how many cards I should include if I have different combinations of symbols on them first time I've had to break out combinatorial functions outside of school , determining and balancing probabilities of different things happening, recording the results of multiple playtests and compiling and analyzing various statistics from those playtests, etc.

Some designs for my games have even been inspired by game theory, computer science structures, fractals, etc.

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One of the most prolific game designers out there today is Reiner Knizia, who has over published games, and has a doctorate in Mathematics. I can see why. There's all sorts of neat fun things that can be found by probing different features and patterns in mathematics.

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What I've been trying to do is find corners he probably hasn't discovered himself yet, and considering I'm only aware of about 50 of his more well-known games, so probably the concepts I think are pretty new could very well be hiding in one of his lesser known other games. Several times I've come up with an idea, only to bump into one of his designs a month or two later that does something similar.

So if I can find a bunch of uses for math for game design, there's probably a ton of potential applications I could see if I directed those energies more towards software engineering. And learn more math.

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  • Proofs, abstract algebra, Denotational semantics etc. DennisP 69 days ago. Aside from probability, what math do you use in board game design? Lots of things, especially with patterns. Let's take scoring for example. Set collection is a common mechanic in games, where you try to collect sets of various things, and generally the more you collect of something, the better you score. But when you're designing the game, how much should that increase?

    First there's linear, like 1 is worth 1 point, 2 is worth 2 points, 6 is worth 6 points. For that, there's not a whole lot of incentive to encourage people to make sure they get more cards in that set. But one way in which it could work is if they can only score in certain sets, so they prioritize them because that's the only way they can score it. But if you want to encourage players to go after a set that they already have the most of, you need to have each one worth progressively more, and a really good pattern for that is the Triangular number pattern.

    So if you only have 2 of a thing it's only worth 3 points, but if you get 6 of a thing it's worth 21 points, significantly more. You'll see this scoring pattern quite often in set collection games. Offhand, I know Ponzi Scheme and St.

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    Petersburg use it, but I've probably seen it in at least 20 games. If you're not a mathematician or you haven't encountered it in a bunch of other games, you might not recognize the pattern or realize that it's a good way to score set collection. Another way that is used less often, because it's a much steeper increase, is exponential scoring, i. But if you want the person to win to almost always be the person who got the biggest single set, and make people really battle it out just to get one more card in their biggest sets, then this is the way to go. I've seen it work really well in The Rose King, which even includes an exponential chart on the back of its rules going all the way up to like 32 squared, because it's possible to get groups that big although rare.

    Apparently an old Alex Randolph game called Good Neighbors also used this. One I've been playing around with lately is multiplicative, i. It opens up an interesting dynamic where sometimes it's better to get cards in a new set than to keep going in one set, but only getting one card doesn't do you any good, and sometimes you'll score more points getting cards in a set you have very little of instead of getting more cards in a set you have a lot of.

    Then there's an old one Knizia likes to do where it's basically doing a minimum function on your sets, where you score the set you got the lowest number of points in. This scoring method forces the user to have to try to get a variety of sets and not to ignore any set, because whichever set they don't get as much of will be the one they score. Another one I haven't seen too much of, but I've designed a game using it and seen at least one other game that uses it That's Life! If you have an odd amount of a set, you score positive, and an even amount you score negative.

    Back and forth like a sine wave. It has an interesting property in that the more you get of something the better you score, but at the same time the more you try to get something and fail to make sure it stays an odd amount, the worse you score. So it's like walking a tightrope for that set, and the more you get the better it is and the more dangerous it is at the same time!

    Another scoring method Knizia used to good effect in his card game High Society, is kind of the same concept as outliers in statistics this one is a bit of a stretch, admittedly.