Mathing Time

geometry witch

Comic day :) Have a great weekend ^_^

1) UNDERSTAND THE MATERIAL! Be able to apply the material you know to different types of problems and scenarios. Teachers like to throw students off with problems that only students who understand the material are able to solve.

2) ASK YOUR TEACHER FOR HELP! That’s why you teacher is there. If you are having trouble understanding a concept, having the lesson repeated or said in a different perspective may help.

3) DO YOUR HOMEWORK! Homework gives you a chance to practice your material. Similar problems on homework often show up on tests.

4) RE DO THE ANSWERS YOU GET WRONG ON HOMEWORK AND TESTS! This way you’ll be able to see where you went wrong and know not to make that mistake again.

A very neat visual proof for the formula of the first n square numbers.

Hi,

@rebeccastudiesmaths is probably my favourite maths studyblr.

I also follow:@studylove, @mathmewishing, @thestudyingprocess, @mathbrain, @gingerlie-math

Studyblrs studying maths/further maths at A-level:@almost-an-economist, @astro-study, @bookssweatandtears, @bucketchemistry, @code-bug, @penandanotebook, @study-at-peace, @studyanise

In math, a group is a particular collection of elements. That might be a set of integers, the face of a Rubik’s cube–which we’ll simplify to a 2x2 square for now– or anything, so long as they follow 4 specific rules, or axioms.

Axiom 1: All group operations must be closed, or restricted, to only group elements. So in our square, for any operation you do—like turn it one way or the other—you’ll still wind up with an element of the group. Or for integers, if we add 3 and 2, that gives us 1—4 and 5 aren’t members of the group, so we roll around back to 0, similar to how 2 hours past 11 is 1 o’clock.

Axiom 2: If we regroup the order of the elements in an operation, we get the same result. In other words, if we turn our square right two times, then right once, that’s the same as once, then twice. Or for numbers, 1 + 2 is the same as 2 + 1.

Axiom 3: For every operation, there’s an element of our ground called the identity. When we apply it to any other element in our group, we still get that element. So for both turning the square and adding integers, our identity here is 0. Not very exciting.

Axiom 4:  Every group element has an element called its inverse, also in the group. When the two are brought together using group’s addition operation, they result in the identity element, 0. So they can be thought of as cancelling each other out. Here 3 and 1 are each other’s inverses, while 2 and 0 are their own worst enemies.

So that’s all well and good, but what’s the point of any of it? Well, when we get beyond these basic rules, some interesting properties emerge. For example, let’s expand our square back into a full-fledged Rubik’s cube. This is still a group that satisfies all of our axioms, though now with considerably more elements, and more operations—we can turn each row and column of each face.

Each position is called a permutation, and the more elements a group has, the more possible permutations there are. A Rubik’s cube has more than 43 quintillion permutations, so trying to solve it randomly isn’t going to work so well. However, using group theory we can analyze the cube and determine a sequence of permutations that will result in a solution. And, in fact, that’s exactly what most solvers do, even using a group theory notation indicating turns.

From the TED-Ed Lesson Group theory 101: How to play a Rubik’s Cube like a piano - Michael Staff

Mathematics is everywhere and we all learned it at some point, but what is mathematics, really? A search on the internet will yield many different interpretations. According to Google, mathematics is “the abstract science of number, quantity, and space.” Here is a collection of how some of history’s greatest minds described mathematics.

An intellectual game “Mathematics is a game played according to certain simple rules with meaningless marks on paper.”—David Hilbert

“Pure mathematics is the world’s best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It’s free. It can be played anywhere—Archimedes did it in a bathtub.”—Richard J. Trudeau

“Mathematics is about making up rules and seeing what happens.”—Vi Hart

“Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.”—Plato

“Mathematics is an independent world created out of pure intelligence.”—William Woods Worth

A tool for the sciences “Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.”—Paul Dirac

“Our physical world doesn’t have just some mathematical properties, it has only mathematical properties.”—Max Tegmark

“Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects …”—H. F. Fehr

“In order to understand the universe, you must know the language in which it is written. And that language is mathematics.”—Galileo

A search for pattern, order, and structure “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”—G. H. Hardy

“Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.”—Joseph Fourier

“Go down deep enough into anything and you will find mathematics.”—Dean Schlicter

Logic and reasoning “All Mathematics is Symbolic Logic.”—Bertrand Russell

“Pure mathematics is, in its way, the poetry of logical ideas.” –Albert Einstein

“Mathematics is the supreme judge; from its decisions there is no appeal.“—Tobias Dantzig