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M01.1 · Numbers, algebra and notation

A free, illustrated module of 4 lessons and one interactive in M01 Math Foundations: Kinds of numbers and the number line; Expressions and the rules of algebra; Equations and inequalities; Reading notation: subscripts, Greek letters and formulas.

M01.1 L0 · Foundation 4 lessons · about 100 min Live · in review

Part of M01 Math Foundations in the Mathematics track.

The language that every later course is written in. These four lessons put four kinds of number on one line, turn the rules of algebra into pictures of areas, solve equations on a balance and inequalities on a number line, and end by reading a machine-learning formula aloud, symbol by symbol, on the four data points that run through this course.

What you need first. School arithmetic: adding, subtracting, multiplying and dividing whole numbers, fractions and decimals. No Python is assumed; every line of code is explained, and P01 Python from Zero can be taken alongside.

Lessons

1. Kinds of numbers and the number line M01.1.1 25 min

   Nearly every number in machine learning is a point on one line. Meet the natural numbers, integers, fractions and real numbers, convert between fractions, decimals and percentages by hand, measure distance with absolute value, and see why Python’s 0.1 + 0.2 is not quite 0.3.

2. Expressions and the rules of algebra M01.1.2 25 min

   A letter stands for a number. Evaluate expressions such as wx + b in the agreed order, read powers and square roots, and see the commutative, associative and distributive laws as rectangles of area, ending with (a + b) squared read off a cut-up square.

3. Equations and inequalities M01.1.3 25 min

   An equation is a balance: do the same thing to both sides and it stays level. Solve 3x + 2 = 14 step by step, rearrange y = wx + b for x, and see why multiplying an inequality by a negative number flips it, using the decision rule 2x - 6 >= 0.

4. Reading notation: subscripts, Greek letters and formulas M01.1.4 25 min

   Read a formula aloud, symbol by symbol: variables, constants and parameters, subscripts that label the items of a list, hats for predictions and bars for means, the signs of comparison, and the Greek letters later courses use, all worked on this course’s four data points.

The interactive

M01.1-X1 · Equation balance. A two-pan balance holds an equation such as 3x + 2 = 14. Each button does one operation to both pans and writes the new line of algebra; switch on “Change the left pan only” and watch the beam tip when the rule is broken. It lives in Equations and inequalities.