Balancing Chemical Equations

Count the atoms on each side and make them match, by inspection or with algebra. Two video lessons work the same five reactions both ways, then you practice on 30 reactions with a live atom count.
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Plot3D in Mathematica, a Worked Example

Turn a function of two variables into a surface, then color it by height, draw contour lines on it, and lay a contour map underneath, with the code for each step.
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The Jade Lizard, a Worked Example

Sell a put and a call spread for more than the spread is wide, and a rally cannot cost you money. A worked example finds the credit, the breakeven and where the risk lives, and compares it with a short strangle.
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Bull Call Spread, a Worked Example

Buy a call, sell a higher-strike call, and pay less for a capped gain. A worked example with real numbers finds the cost, breakeven, maximum gain and maximum loss.
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Option Payoff vs Profit

An option's payoff is what it is worth at expiration; the profit is what you keep after the premium. One chart compares the two for buying a call and selling a put, with the breakeven of each.
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The Six Building Blocks of Option Strategies

Every option strategy, from a covered call to an iron condor, snaps together from six pieces: long and short stock, calls and puts. See each one’s payoff diagram and how they combine.
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The Square-Root-of-Time Rule

Why a year of risk is not twelve months of risk added up. Volatility grows with the square root of time: how to annualize it, and what that means for option prices, expected moves and time decay.
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Straddle vs Strangle vs Guts

Three ways to profit from a big move when you cannot call its direction. One worked example compares their costs, breakevens and worst cases, and shows when traders choose each.
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Rho, the Overlooked Greek

Rho measures how an option's price responds to interest rates. It is tiny for a one-month option and large for a two-year one: why calls gain and puts lose as rates rise, and when traders should start watching it.
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The Volatility Surface

One stock's options don't share one volatility. Implied volatility changes with every strike and expiration, and the volatility surface maps it all: the skew, the term structure, and what the market fears.
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The Covered Call

Own the shares, sell the call, collect the premium. How a covered call earns income from stock you already hold, where it breaks even, and what it gives up in return.
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Information Ratio

When evaluating investments, it’s not enough to look at raw returns. Investors want to know: is this performance consistent, or is it just luck? The Information Ratio (IR) is a powerful tool for answering that question.
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What is a Hedge Fund?

Hedge funds are often surrounded by an air of mystery. You might hear about them in the news or see them portrayed in movies as high-stakes investment ventures for the ultra-wealthy. But what exactly are hedge funds, how do they work, and why are they so popular among certain investors?
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Sharpe Ratio

An in-depth explanation of one of the most widely used tools in finance for evaluating the performance of an investment by comparing its return to its risk.
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Wolfram Language

An introduction to the powerful computing language from Wolfram.
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CHNOPS: Elements of Life

CHNOPS stands for Carbon, Hydrogen, Nitrogen, Oxygen, Phosphorus, and Sulfur. These six elements make up 98% of living matter on Earth!
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4 Types of Chemical Bonds in Biology

There are 4 kinds of chemical bonds essential for life to exist.
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Ideal Gas Law

The Ideal Gas Law describes the relationship between four key variables that define the state of a gas: pressure, volume, temperature, and the number of moles of gas.
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The Kernel

Of Group Homomorphisms

In abstract algebra, the concept of a homomorphism is used to compare two structures—such as groups, rings, or fields. Homomorphisms are often not one-to-one, and one way to find how far a homomorphism is from being injective is by finding its kernel.
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Boyle's Law

Boyle’s Law is a fundamental principle in the study of gases that describes how pressure and volume are related when temperature remains constant.
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More Lessons

Spark your curiosity by browsing through our growing library of STEM lessons.
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