Finite Math—Semester B

Normal is overrated, but normal distributions aren't.

Shmoop's Finite Math course has been granted a-g certification, which means it has met the rigorous iNACOL Standards for Quality Online Courses and will now be honored as part of the requirements for admission into the University of California system.


When it comes down to it, life is all about luck. Whether you find twenty bucks sitting on the sidewalk or get struck by lighting, chance plays a bigger role in life than people admit. Even the very best Dungeon Masters and Texas Hold 'Em champions can't escape probability at work. Unless they're cheating.

In this Common Core-aligned course, we'll delve deep into the mysteries of counting theory, normal distributions, why so many people you know share the same birthday, and more. We'd tell you what else we'll cover, but we don't want to ruin the mystery.

On second thought, let's ruin the mystery. With loads of drills, examples, and projects, we'll cover

  • counting theory, Venn diagrams, and other ways to deal with large sets of numbers.
  • probability, experiments, and the famous Birthday Problem.
  • conditional probability, events, and using trees to represent them.
  • statistics, histograms, odds, and binomial events.
  • normal distributions, z-scores, and game theory.

What are the odds you'll finish this course knowing all there is to know about statistics and probability? We're betting pretty good.

P.S. Finite Math is a two-semester course. You're looking at Semester B, but you can check out Semester A here.


Unit Breakdown


  1. Finite Math—Semester B - Logic

    Logic is all about making statements. Sometimes they're fashion statements. Other times, they're mission statements. Then there's the occasional thesis statement or mathematical statement. We don't know if all the statements it makes are true, but that's where truth tables and logic circuits come into play.

  2. Finite Math—Semester B - Linear Functions

    Whether it's review or brand-new information, we'll examine straight lines in a good amount of detail in this unit. We'll learn (or recall) a thing or two about slope, what it means when lines are parallel or perpendicular, and even recognize the various forms linear equations can take—with and without the Groucho glasses.

  3. Finite Math—Semester B - Systems of Equations

    If you think you know all there is to know about systems of equations, we've got news for you: you don't. In this unit, we'll take you from refreshing your basic algebra skills all the way to solving systems of linear equations using Gauss-Jordan elimination. We'll even solve systems of more than two equations—and interpret our answers in context. Then you'll know all there is to know about these puppies.

  4. Finite Math—Semester B - Matrices

    In this unit, we'll explore the ins and outs of matrices, taking several twists and turns on our journey in order to become matrix masters. Real-world applications? Challenging math problems? We know you're dying to learn more about matrices already. So strap yourself in, and let's see how deep the rabbit hole goes.

  5. Finite Math—Semester B - Linear Programming: Geometric

    We'll start off linear programming by learning about linear inequalities. After delving into bounded and unbounded solutions to systems of linear inequalities, we'll get to the meat and potatoes of linear programming: optimization problems, the method of corners, and some really cool shading effects. Get those colored pencils ready.

  6. Finite Math—Semester B - Linear Programming: Algebraic

    Don't get us wrong: graphing is great. It's cooler than Free Cone Day at Ben & Jerry's—but like ice cream on a hot day, graphing has its limitations. Luckily, we can solve linear programming problems algebraically and get ourselves out of any sticky situation, particularly when several variables are involved. In a nutshell, algebra makes linear programming plain and simplex. (You'll get that joke after you finish this unit.)

  7. Finite Math—Semester B - Math of Finance

    Money talks—and you'll need to know a thing or two about interest, annuity, and amoritization if you're going to talk back. (Seriously, how do you expect to have a conversation if you don't speak the same language?) By the time we're through learning about loans, compounding interest, and sinking funds, you'll know exactly how to make your first million—and where to invest it.

  8. Finite Math—Semester B - Counting Theory

    You learned how to count back in preschool, so it's high-time you stepped up your counting game. We'll start out with sets, unions, and intersections, and even draw a few Venn diagrams. Then, we'll get factorials involved and talk about combinations and permutations and their many applications. By the time we're through, you'll be able to give the Count a run for his money.

  9. Finite Math—Semester B - Probability

    If probabilistic thinking is already intuitive to you, then great. You're ahead of the game. But for the rest of us, this unit is all about making probability as intuitive as how to eat the last Oreo. (Twist-and-lick, obviously.) From setting up experiments to probability properties and formulas, this unit contains more coin tosses and die rolls than you thought were possible.

  10. Finite Math—Semester B - Conditional Probability

    In this unit, we're going to learn how to tell if that third flip being heads depends on the first two being heads (spoiler alert: no). With the help of the Product Rule, trees, and Bayes' Theorem, we'll learn about a new kind of probability: one where the likelihood of an outcome can change in an instant—or at least in the blink of another event happening first.

  11. Finite Math—Semester B - Statistics

    We'll kick off the unit by discussing how to turn any kind of data into a table or graph that you trust. (Those histograms always looked a little shady to us.) After talking about probability and odds, we'll boil down our data into bite-sized summaries, like expected value, variance, and standard deviation. They're not as tasty as those mini-quiches and shrimp cocktails, but we promise they'll be more useful when it comes to data analysis.

  12. Finite Math—Semester B - Normal Distributions and Game Theory

    We won't lie to you: this unit's a biggie. Often, normal distributions can seem more abnormal than you'd think. Don't worry. We'll help you tackle with z-scores, bell curves, and binomial probabilities like a boss. After that, we'll take on game theory, talk about its different strategies, and learn how to kick your opponent's butt at Monopoly. Family game night will never be the same again.

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