Library / What Each Major Knows

What Each Major Knows

96 pieces · 20 hours of reading

Calculus I: Slopes, Totals and the Bridge Between Them

Your car's speedometer is a derivative. Its odometer is an integral. Everything a first calculus course teaches is a way of moving between the two.

ReadInteractive10 min 02

Multivariable Calculus: Calculus on a Landscape

A raindrop on a hillside picks the steepest way down without thinking. The arrow it follows is the same one that trains every neural network and drives heat through a metal plate.

ReadInteractive10 min 03

Differential Equations: Laws Written as Rates

A cup of coffee cools, a capacitor charges, a car bounces over a bump, a fish stock collapses. Each follows a rule that says how fast things change, not where they will be. Solving it is the whole course.

ReadInteractive11 min 04

Linear Algebra: Machines That Move Space

A grid of numbers is really a machine that moves all of space at once. Learn to see it, and circuits, bridges, search engines and AI all start to look alike.

ReadInteractive13 min 05

Probability & Statistics: Reasoning with Uncertainty

Nothing you measure is exact, and no part comes out the same twice. Statistics is the discipline of knowing how much to trust a number.

ReadInteractive12 min 06

Physics I: Mechanics — Three Ways to Keep the Books

Why doubling your speed quadruples your stopping distance, why a skater spins up when she pulls her arms in, and the three questions an engineer asks before touching a calculator.

ReadInteractive10 min 07

Physics II: Electricity & Magnetism — Charge, Fields and Light

A rubbed balloon beats the whole Earth's gravity, electrons crawl through your wiring slower than a snail, and light turns out to be a field vibrating. The one course that explains your phone, your motor and your Wi-Fi.

ReadInteractive10 min 08

Discrete Mathematics: Counting, Logic and Proof

Computers cannot handle the smooth infinite; they handle countable things. This is the maths of switches, steps, networks and clocks.

ReadInteractive12 min 09

Programming Fundamentals: Instructions, State and Taking Things Apart

A computer can't guess what you meant. Everything in a first programming course is a way of saying it exactly enough, and of working out why you didn't.

ReadInteractive11 min 10

Statics: Why Things Stand Still

Every bridge, shelf and crane is a bargain between forces that cancel exactly. Learn to see the bargain and you can read a structure at a glance.

ReadInteractive11 min 11

Mechanics of Materials: Why Things Bend, Buckle and Break

A bridge cable, a bicycle frame and a paperclip are all springs with limits. Learn the few ideas that say how far they stretch, and what finally breaks them.

ReadInteractive12 min 12

Dynamics: Why a Hoop Loses the Race

Statics freezes the world to find the forces. Dynamics lets it move, and asks where it goes next: why a gyroscope turns sideways, and why the full can wins.

ReadInteractive11 min 13

Materials Science & Manufacturing: Why Things Are Made of What They Are

A paperclip bends, a mug shatters, a rubber band springs back. Same push, three different answers, and the whole course is the reason why.

ReadInteractive14 min 14

Thermodynamics: Why Every Engine Pays a Heat Tax

Energy is never lost, but it always degrades. Every engine, fridge and jet lives between those two laws, and two temperatures are enough to say how well it could ever do.

ReadInteractive13 min 15

Fluid Mechanics: Why Air and Water Push Back

Water presses, air lifts, and the equations that govern both are worth a million dollars to anyone who can prove they behave. What a graduate still sees in every flow.

ReadInteractive13 min 16

Heat Transfer: Three Roads for Heat

Conduction, convection and radiation: why a metal rail feels colder than a wooden step, why frost forms above freezing, and why a laptop has fins.

ReadInteractive12 min 17

Vibrations: Everything Is a Spring and a Mass

Why a guitar string has a pitch, a washing machine walks, and a bridge can wobble itself apart: one equation, and the number that decides how badly things shake.

ReadInteractive12 min 18

Engineering Drawing & CAD: The Contract Between Designer and Maker

A drawing is not a picture of a part. It is a promise about what will be made, how exactly, and who is to blame when it isn't.

ReadInteractive12 min 19

Machine Design: The Parts Every Machine Is Built From

A bicycle has a chain, bearings, bolts, springs, an axle and a slowly growing crack. Machine design is knowing which part does what, and how each one breaks.

ReadInteractive13 min 20

Control Systems: How Machines Hold a Setpoint

A thermostat, a cruise control and a hovering drone do the same thing: measure, compare, correct. Why that works, and why too much of it makes things oscillate.

ReadInteractive11 min 21

Propulsion: Throwing Mass Backwards

A balloon, a jet, a rocket and an ion thruster are the same machine: push mass backwards and go forwards. The rest is a fight to do it with the least fuel.

ReadInteractive13 min 22

Systems Engineering & the Capstone: Many Parts, One Product

A product is many subsystems agreeing with each other. Most famous failures happened on the lines between them.

ReadInteractive14 min 23

Data Structures: How Arrangement Decides Speed

A search that comes back in a fifth of a second across billions of records is not a faster computer. It is the same records, put in a better order.

ReadInteractive12 min 24

Algorithms: Why Growth Beats Speed

A method that is a thousand times slower per step can still win, by a mile, once the problem gets big enough. That one fact is most of the subject.

ReadInteractive10 min 25

Computer Architecture: Why Your Processor Spends Its Life Waiting

A core can start several instructions every nanosecond, then waits hundreds of ticks for one number from memory. Caches, pipelines and extra cores are all tricks for hiding that wait, and the reason clock speeds stalled is a power bill.

ReadInteractive13 min 26

Operating Systems: How One Machine Safely Pretends to Be Many

Dozens of programs share a few cores and one pool of memory, and none can read another's secrets or take the machine down. That is the operating system's whole job, done with a few hardware tricks.

ReadInteractive13 min 27

Computer Networks: Why Latency, Not Bandwidth, Rules

The network between you and a web server is unreliable on purpose, and the number that decides how fast anything feels is not on your internet bill. It is the number of round trips, multiplied by the speed of light.

ReadInteractive12 min 28

Databases: Why Your Data Survives a Power Cut

Behind every balance, booking and search box is a small set of ideas: tables, keys, an index, and a promise that a transfer either happens completely or not at all.

ReadInteractive11 min 29

Theory of Computation: What Can and Cannot Be Computed

Some questions no program can ever answer, and others it can answer only after the sun has burned out. Proving which is which is one of the strangest achievements of the twentieth century.

ReadInteractive13 min 30

Programming Languages & Compilers: How Text Becomes a Machine

You type words and symbols; a chip does arithmetic on voltages. In between is a translator, and everything it does is a small idea you can hold in your head.

ReadInteractive11 min 31

Software Engineering: How Teams Change Code for Years

Real software is written by teams, over years. That changes everything: how you design, merge, test, estimate and learn from failure.

ReadInteractive13 min 32

Machine Learning: Programs That Write Their Own Rules

Nobody wrote the rule that tells a spam message from your mother's email. A program found it by looking at examples, and everything in the field is about whether you can trust what it found.

ReadInteractive11 min 33

Computer Security: Thinking Like an Attacker

Systems fail at the cheapest door. Security is the habit of finding it first.

ReadInteractive12 min 34

Circuit Analysis: Why the Lights Dim When the Kettle Starts

Ohm, Kirchhoff and a handful of tricks turn any tangle of wires into a few numbers. Why chargers warm up, why supply wires matter, and why a radio can pick one station.

ReadInteractive12 min 35

Electronics: The Switch That Became Everything

A one-way valve, a voltage-controlled tap and a feedback trick. Three ideas, billions of copies, and the chip in your phone.

ReadInteractive13 min 36

Digital Logic Design: Gates That Decide, Flip-Flops That Remember

Every digital chip is built from two kinds of circuit: ones that decide from what they see now, and ones that remember what happened before. Learn to tell them apart and you can read a crossing light, a counter or a processor.

ReadInteractive14 min 37

Signals & Systems: Every Signal Is a Recipe of Sines

Why a room has an echo, an equaliser can fix a song, a movie wheel spins backwards, and your phone can hear a note inside a chord: one idea (a system's reply to a single click) and one trick (break everything into sines).

ReadInteractive13 min 38

Electromagnetics & Waves: Why Fast Signals Stop Acting Like Wires

Why the cable to your aerial has to be a particular kind of cable, why a pulse can bounce back from the end of a wire, why antennas are the size they are, and why your microwave door has a mesh: four equations, and a speed.

ReadInteractive13 min 39

Power Systems & Electric Machines: Supply Must Match Demand, Every Second

The biggest machine ever built is the electric grid: a continent of spinning rotors held in step. How it moves power, turns it into motion, and what happens when the balance breaks.

Deep diveInteractive15 min 40

Communication Systems: How Much Can a Noisy Channel Carry?

Why a phone can send a movie through the air at the edge of what physics allows: a message riding on a wave, noise that turns bits into guesses, a 1948 theorem that names the limit, and codes that quietly repair the damage.

ReadInteractive13 min 41

Embedded Systems: Tiny Computers With Deadlines

The computers that run the world are mostly invisible: a few kilobytes of memory, a few milliamps of power, one job, and a deadline. Embedded engineering is the craft of making them read the real world, act on it in time, and last for years on a coin.

ReadInteractive14 min 42

Microeconomics: Why Nothing Is Free and Every Price Is a Message

Everything costs what you gave up, choices happen one step at a time, and a price is the signal that makes strangers cooperate. Until it is wrong, and then you can see exactly how wrong.

ReadInteractive13 min 43

Macroeconomics: The Economy as One Machine, and Why It Stalls

Output that compounds, prices that drift, jobs that flow, banks that create money, central banks with one lever. And four schools that disagree on how hard to push it.

ReadInteractive14 min 44

Econometrics: How to Find What Caused What

Correlation is cheap. Econometrics is the craft of getting from "these move together" to "this made that happen", and of knowing how badly you could be fooled on the way.

ReadInteractive12 min 45

Game Theory: When Your Best Move Depends on Mine

Two shops pick prices, two countries pick tariffs, a hundred bidders pick bids. Game theory is the maths of choosing when everyone else is choosing too, and it explains why smart people can trap themselves.

ReadInteractive12 min 46

Behavioral Economics: How People Actually Choose

Standard economics assumes calm, consistent, self-interested calculators. Behavioral economics measures how real people depart from that, and, just as important, which of its famous findings have survived being checked.

ReadInteractive12 min 47

International Trade & Finance: Why Countries Swap, and Why Currencies Swing

Trade makes countries richer on average and leaves particular people worse off. Currencies let money cross borders, and fixing one carries a price you cannot dodge. Two ideas, one subject.

ReadInteractive14 min 48

Development Economics: Why Some Countries Are Rich, and What Has Actually Helped

In 1960 Ghana looked richer than South Korea. Sixty years on, Korea's income per person is about ten times Ghana's. The subject asks why, and which fixes have been tested rather than just believed.

ReadInteractive12 min 49

Public Economics: What Governments Can and Can't Fix

Why tax at all, who really pays it, what redistribution costs, how inequality is measured, and why the state fails in its own ways.

ReadInteractive13 min 50

Accounting: Every Transaction Has Two Sides

Accounting is the language a business uses to keep score. Learn one rule, that everything a firm owns is paid for by someone, and you can read how any company is really doing, including why a profitable one can run out of cash.

ReadInteractive13 min 51

Corporate Finance: The Price of Time and Risk

A pound today is worth more than a pound next year, and a risky pound is worth less than a safe one. Corporate finance is the craft of putting a number on both, so that a company can decide which projects are worth their money.

ReadInteractive13 min 52

Operations Management: Where Work Waits

Every business is a process, and every process has a bottleneck. A few laws explain why the line is long, why stock piles up and why a small change in demand becomes a big swing upstream.

ReadInteractive14 min 53

Organizational Behavior & Leadership: People Are the System

Why some teams speak up and others go quiet, what actually moves people to work, and which famous findings about people at work did not survive being repeated.

ReadInteractive13 min 54

Strategy & Competition: Why Some Firms Keep Their Profits

Most good ideas get copied until the profit is gone. Strategy is the study of what stops that, and competition law is the study of when it has stopped too well.

ReadInteractive12 min 55

Business Law & Ethics: Who Is Allowed to Do What, and Who Pays When It Goes Wrong

Every company is a bundle of promises, a legal person that can be sued, and a set of people with duties. The rules differ by country in ways that decide who loses when a business fails.

Deep diveInteractive15 min 56

Entrepreneurship: How to Be Wrong Cheaply

Most new ventures fail, and the survivors mostly found out what customers wanted before they ran out of money. Entrepreneurship is the craft of finding out early, and of doing the arithmetic that says how long you have to learn.

ReadInteractive13 min 57

Marketing Management: Finding the Customer, Not Shouting at Them

Most people think marketing is advertising. A marketing graduate sees something earlier and larger: who the customers are, what they would actually value, and where in their minds a product should stand.

ReadInteractive11 min 58

Consumer Behavior: How People Notice, Want, Choose and Regret

Nobody weighs every option. People notice a sliver of what is in front of them, follow each other more than they admit, and regret in predictable ways. A graduate also knows which famous "findings" have held up and which were never real.

ReadInteractive10 min 59

Marketing Research & Analytics: Asking, Testing and Not Fooling Yourself

Every survey, test and dashboard gives you a number. The skill is knowing how the question steered it, how much noise is in it, and what it quietly stopped measuring.

ReadInteractive12 min 60

Brand Management: What a Brand Is, and Why It Is Worth Money

A brand is not a logo. It is what comes to mind when a buyer meets a cue, and it is built from memory. Marketers still argue over whether it grows by being loved or by being easy to find.

ReadInteractive11 min 61

Pricing: The Number That Brings the Money In

Every other choice in marketing spends money. The price is the one that collects it. Behind a good price sit a curve, a ratio, and a few tricks, some of which turn out to be less solid than the books say.

ReadInteractive14 min 62

Digital Marketing & Advertising: Where Attention Is Bought Now

Every search, scroll and page load can trigger an auction, and every click leaves a trail. The hard part is no longer reaching people. It is knowing which of the clicks you paid for actually changed anything.

ReadInteractive13 min 63

Product Innovation & Go-to-Market: Why Good Products Still Fail

A new product has to be built, found by the right people, adopted in sequence, and sold at a cost that works. Most of what goes wrong happens after the engineering is done.

ReadInteractive11 min 64

Structural Analysis: How Forces Find Their Way to the Ground

A structure is a stack of paths from the roof to the soil. Learn to follow the load and you can see which parts are working, which are spare, and what happens when one goes.

ReadInteractive13 min 65

Structural Design: Concrete & Steel That Bend Before They Break

Design is deciding how rare a failure must be, then putting each material where it works best, so that a structure that fails does so slowly and loudly.

ReadInteractive13 min 66

Geotechnical Engineering: Everything Stands on Soil

Soil is the one structural material nobody manufactured. Learn how water, weight and shaking decide whether the ground holds.

ReadInteractive13 min 67

Hydraulics & Water Resources: Moving Water Where People Need It

Pipes, pumps, rivers, floods, dams and levees: the part of civil engineering that decides where water goes, and what happens on the day it goes somewhere else.

ReadInteractive13 min 68

Environmental Engineering: Clean Water In, Clean Water Out

The engineering behind the tap, the toilet, the stack and the bin: one accounting rule, a few microbes, and the discovery that most public health happens in pipes.

ReadInteractive14 min 69

Transportation Engineering: Why Traffic Jams Form Out of Nothing

Roads behave like a fluid, a signal like a budget of seconds, a curve like a promise to the driver. And adding a lane does not always do what you hope.

ReadInteractive14 min 70

Construction Management: Why Big Projects Run Late

A building is a network of tasks, a price with a risk range and a contract that decides who pays. Learn the critical path, the contingency and the overrun data that explain why megaprojects keep running late.

ReadInteractive14 min 71

Foundations: What Mathematics Stands On

Sets, logic and infinity: the three things every proof leans on, how they let you reach certainty about the endless, and the famous places where they run out.

ReadInteractive13 min 72

Real Analysis: Why Calculus Works

Calculus gave right answers for 150 years before anyone could say why. Analysis is the answer: the number line has no gaps, and "gets close" can be made exact.

ReadInteractive11 min 73

Abstract Algebra: Symmetry as a Structure of Its Own

Forget what the objects are. Keep only how they combine. That one move turns clock arithmetic, Rubik's cube and the unsolvable quintic into the same kind of problem.

ReadInteractive12 min 74

Complex Analysis: Calculus on a Plane Where Everything Fits Together

Take the calculus you know and let the variable wander off the number line into a plane. The rules get stricter, and in exchange the theorems become almost unreasonably strong.

ReadInteractive14 min 75

Number Theory: Primes, Clocks and the Secrets Built on Them

The whole numbers 1, 2, 3, … look like the simplest thing in mathematics, and hide the hardest questions. The same ideas that settle them also lock every web browser's connection.

ReadInteractive14 min 76

Topology: Shape Without Measurement

Forget lengths, angles and distances. Keep only what survives stretching and bending without tearing. What is left is a handful of surprisingly powerful ideas, and a coffee cup that is secretly a doughnut.

ReadInteractive14 min 77

Differential Geometry: Curvature You Can Feel From the Inside

A pizza slice droops until you fold it, an airline flight path bends toward the pole, and a pendulum in Paris slowly turns. All of them are one idea: you can measure how a space curves without ever stepping outside it.

ReadInteractive13 min 78

Numerical Analysis: Answers You Can Trust, and How Wrong They Are

Type 0.1 + 0.2 into almost any programming language and it will not say 0.3. That is not a bug. It is the first lesson in the art of getting good answers out of a machine that cannot hold a single exact number.

ReadInteractive13 min 79

Partial Differential Equations: One Law for Every Point of a Field

A guitar string, a cooling pizza, an electric field, an electron in an atom and the air over a wing all obey one kind of statement: how a quantity changes at a point depends on how it is shaped around that point. Three families of equation cover most of physics.

ReadInteractive14 min 80

Waves and Optics: When Waves Add, Light Can Make Darkness

Why noise-cancelling headphones work, why a lens can never see everything, why your sunglasses black out a phone screen, and why one photon at a time still draws a wave pattern.

ReadInteractive13 min 81

Special Relativity: Everyone Gets the Same Speed of Light

Why your phone's map needs Einstein, why cosmic-ray muons reach the ground, and how a single odd fact about light stretches clocks, shrinks rulers and turns mass into energy.

ReadInteractive13 min 82

Classical Mechanics: Let Energy Write the Equations

Why the path a ball takes is the one that makes a certain number stationary, why every symmetry hides a conserved quantity, and why a pendulum with one extra joint can never be predicted.

ReadInteractive13 min 83

Quantum Mechanics: Waves of Probability and the Limits of Knowing

Everything small is described by a wave that you can only ask questions of, one at a time. That single move explains why atoms have colours, why you cannot know everything at once, and why two particles can share a fate.

ReadInteractive12 min 84

Statistical Mechanics: Temperature Is What Counting Looks Like

Nothing in a single atom is hot. Temperature, pressure and the arrow of time appear when you count the ways trillions of atoms can arrange themselves, and the biggest count wins by a margin so large it looks like a law.

ReadInteractive11 min 85

General Relativity: Gravity Is the Shape of Spacetime

Newton said masses pull on each other. Einstein said masses bend the stage, and everything simply goes straight on a bent stage. The difference shows up in the clocks in your phone, in the light of distant galaxies, and in ripples that crossed a billion years of space.

ReadInteractive12 min 86