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Math and natural sciences

Plans for adults coming back to math, physics and chemistry after school or going further — into calculus and statistics. Each article gives an order of topics, self-check problems and free textbooks.

In what order to take the subjects#

Almost everything here rests on school algebra. Fractions, powers, equations and graphs of functions are needed in physics, in chemistry and in statistics, so if that base is shaky, start with math even when your goal is another subject. Physics leans on algebra and a little geometry, chemistry on ratios and percentages, statistics on algebra and the habit of calculating carefully. Calculus requires confident handling of functions and trigonometry; otherwise limits and derivatives turn into memorising formulas without understanding.

How to check yourself in the exact sciences#

Checking yourself is easier here than in the humanities: a problem has an answer you can compare against. Work through textbooks with answers at the back, and a day or two after each topic solve a few problems with no hints — that shows what stayed in your head and what was only recognition. Write your mistakes down separately: most of them repeat in the same place, such as signs when moving a term across the equals sign or units of measurement.

  • Math and natural sciences How to learn university math on your own

    People teach themselves university math for different reasons: to understand machine learning, to catch up before an exam, to read engineering or economics literature. The path is much the same for everyone — limits and derivatives, integrals, linear algebra, then differential equations and series. Below is the order, a rough timeline and ways to check that you really understand rather than just recognise formulas.

  • Math and natural sciences How to learn statistics from scratch

    Analysts, researchers, doctors, marketers and anyone who reads the news with numbers in it need statistics. The easiest way to learn it from zero is in three layers — describe the data, understand probability, draw conclusions from a sample — and to calculate on real data at every layer. Here is the order of topics, how to practise and the traps that catch even experienced people.

  • Math and natural sciences How to learn physics from scratch

    For many people school physics stayed a pile of formulas to plug numbers into before a test. As an adult you have it easier: you can take your time and ask, every time, where a formula comes from and what it describes in the real world. The plan below goes from mechanics to electricity and optics — in the order in which each topic rests on the previous one.

  • Math and natural sciences How to learn math from scratch

    An adult coming back to math rarely needs to start with the times tables — usually the foundation breaks in one particular place: fractions, negative numbers, equations. The plan below starts by finding that place and then leads through arithmetic and algebra to functions and geometry, without school pressure or grades.

  • Math and natural sciences How to learn chemistry from scratch

    Chemistry looks frightening because of all the formulas, but it rests on a handful of ideas — what an atom is made of, why atoms bond, and how to count substances in moles. Take them in order and the rest — organic chemistry, solutions, electrochemistry — builds on a solid base. Below is a three-to-four-month plan for an adult starting from an almost blank page.