Basis Lab

The mathematics underneath

Read any line of mathematics in this library without translating it first, by knowing what each symbol is standing for, which marks are names and which are instructions, and how to say a formula out loud as the sentence it was compressed from

Reading the Notation

Mathematics is a written language with about thirty words in it. This course teaches the reading, not the doing, so that every later course can be read rather than decoded.

8 lessons, written and corrected before you arrived. Reading them here needs no account. The first reads the whole way through; the others open and then stop, because a page nobody owns cannot tell who is reading it. Starting the course gives you your own copy, where every idea has problems standing under it and you can ask about any sentence.

Start reading

This is course 1 of 8 in a reading track: read any page here without stopping at the symbols. The track is an order, not a gate, and the rest of it is on one page.

  1. 01A Letter Is Standing In For SomethingEvery letter in a formula is doing one of three jobs. Working out which job each one has is the first move in reading any line of mathematics.
  2. 02Something In, Something Outopening onlyFunction notation is a machine with labelled inlets. Reading it is a matter of knowing which letters go in, which are held still, and what comes out.
  3. 03The Sum Sign Is a Loopopening onlyThe big sigma abbreviates an addition. Expanding one by hand, and compressing a long addition back into one, is the whole of the skill.
  4. 04Numbering Thingsopening onlyA small number beside a letter says which one. Two of them say which row and which column, and the mark above the line means three different things.
  5. 05Products, Powers and Rootsopening onlyThe product sign is a loop that multiplies. Powers count the repeats, and the negative and fractional ones are the same idea pushed somewhere it still works.
  6. 06Four Different Equals Signsopening onlyAn equals sign can define a thing, claim something always true, pose a question, or record one lucky coincidence. The four read very differently.
  7. 07The Alphabet Everyone Assumesopening onlyGreek letters, membership marks, bars and hats. None of them are explained anywhere, because everybody who writes them learned them from somebody who did not explain them either.
  8. 08Reading One Real Formula All the Way Throughopening onlyOne line from a real paper, taken apart with everything this course has covered, and then put back together as a sentence anybody could say out loud.