background preloader

Combinations and Permutations

Combinations and Permutations
What's the Difference? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words: So, in Mathematics we use more precise language: In other words: A Permutation is an ordered Combination. Permutations There are basically two types of permutation: Repetition is Allowed: such as the lock above. 1. These are the easiest to calculate. When we have n things to choose from ... we have n choices each time! When choosing r of them, the permutations are: n × n × ... (In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.) Which is easier to write down using an exponent of r: n × n × ... Example: in the lock above, there are 10 numbers to choose from (0,1,...9) and we choose 3 of them: 10 × 10 × ... (3 times) = 103 = 1,000 permutations So, the formula is simply: 2. In this case, we have to reduce the number of available choices each time. Do you see? 1. 2.

http://www.mathsisfun.com/combinatorics/combinations-permutations.html

Haskell/Category theory This article attempts to give an overview of category theory, in so far as it applies to Haskell. To this end, Haskell code will be given alongside the mathematical definitions. Absolute rigour is not followed; in its place, we seek to give the reader an intuitive feel for what the concepts of category theory are and how they relate to Haskell. Rubik's Cube theory This section introduces some basic cube theory. Understanding a little about the cube's properties will help you to realise what is possible and what is not, as well as help you to see more elegant ways to solve Rubik's Cube. Basic definitions Learn about pieces, permutations and orientations. Laws of the cube Learn what a "legal" move is and why certain positions are not reachable by legal moves.

Graph Theory YAMAGUCHI, Jun-ichi In the sprign semester 2005, I take the mathematics course named "Graph Theory(MATH6690)." This course is hard but very interesting and open my eyes to new mathematical world. Parsec This article is a stub. You can help by expanding it. 1 Introduction Binary marble adding machine Way back when I built my Marble Machine one , I incorporated a few logic-like elements in it, including several divide by two mechanisms, as well as a complicated and slightly unreliable divide by 6 mechanism. It had occurred to me that perhaps with an insane amount of perseverance, it might be possible to build a whole computer that runs on marbles. But my second marble machine was much less based on logic - it was more about just making lots of cool noises.

Making Mathematics: Mathematics Tools: Iteration Iteration is the repeated application of a function or process in which the output of each step is used as the input for the next iteration. Iteration is an important tool for solving problems (e.g., Newton's method) as well as a subject of investigation (e.g., Julia sets). Any function that has the same type of mathematical object for both its argument and result can be iterated. Helloooooo Multiplication Yup, you read it right! It's that time of year again in 3rd grade when we leave place value, addition and subtraction to begin multiplication! So last Thursday we had a review day filled with addition, subtraction and place value centers! Then we had our test Friday....which I still need to grade before tomorrow:( Tomorrow is the beginning to multiplication and I was trying to think of a new approach to introducing it. So I found this on Pinterest and was so excited about it...but the link was broken:(

Learn Haskell Fast and Hard tl;dr: A very short and dense tutorial for learning Haskell. Thanks to Oleg Taykalo you can find a Russian translation here: Part 1 & Part 2 ; Table of Content I really believe all developers should learn Haskell. I don’t think everyone needs to be super Haskell ninjas, but they should at least discover what Haskell has to offer. Learning Haskell opens your mind. Binary Game Skip to Content | Skip to Footer Cisco Binary Game The Cisco Binary Game is the best way to learn and practice the binary number system. Sequences You can read a gentle introduction to Sequences in Common Number Patterns. What is a Sequence? A Sequence is a list of things (usually numbers) that are in order. Infinite or Finite

Grants and Funding The following websites are possible sources to fund Professional Development for educators. This is not a comprehensive list. You may also check with your district and state for any local funds that may be available. The Actuarial Foundation Through its Advancing Student Achievement program, the Actuarial Foundation awards monetary grants to schools and nonprofit groups throughout the United States and Canada.

Why Do Monads Matter? « Sententia cdsmithus (A Side Note: I’ve been formulating the final thoughts on this post for about a week now. In an entirely unrelated coincidence, a good friend of mine and fellow Haskell programmer, Doug Beardsley, ended up writing two posts about monads over the weekend as well. Weird! But don’t fret; this isn’t really the same thing at all. I’m not writing to teach Haskell programmers how to use monads. Sequences and Series: Terminology and Notation Sequences and Series (page 1 of 5) Sections: Terminology and notation, Basic examples, Arithmetic and geometric sequences, Arithmetic series, Finite and infinite geometric series A "sequence" (or "progression", in British English) is an ordered list of numbers; the numbers in this ordered list are called "elements" or "terms". A "series" is the value you get when you add up all the terms of a sequence; this value is called the "sum". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.

Related:  math