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All fields Software Mathematics Physics Chemistry Biology Engineering Astronomy Environmental Other Mathematics Mathematics groups

Explore STEM Content

Search the community's STEM library — free to study, yours to make your own.

Mathematics

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Mathematics: explore STEM content (page 22 of 23) · openstem

Note~267 words · 1 min

The greatest common divisor GCD(a, b) is the largest whole number dividing evenly into both. You could list every factor of each and pick the biggest shared one, but for large numbers that's slow. The Euclidean algorithm never factors anyth

Mathematics

Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean Algorithm

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Mathematics · L3 · Number Theory: GCD, LCM & the Euclidean Algorithm

Flashcards5 cards

How many fingers do you have on one hand?1 / 5

You have 5 fingers on one hand. Count them: 1, 2, 3, 4, 5!

Mathematics

Mathematics · L1 · Counting and Numbers

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Mathematics · L1 · Counting and Numbers

Flowchart9 objects

Mathematics

Mathematics · L1 · Estimating & Benchmark Numbers · flowchart

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Mathematics · L1 · Estimating & Benchmark Numbers · flowchart

Note~292 words · 1 min

Propositions A proposition is a statement with a definite truth value: true or false, never both, never neither. The three connectives NOT (¬) just flips a single proposition's value. Building a truth table The conditional: if p, then q Con

Mathematics

Mathematics · L3 · Logic & Truth Tables

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Mathematics · L3 · Logic & Truth Tables

Note~270 words · 1 min

Distance is Pythagoras in disguise Draw a right triangle between two points: a horizontal leg |x₂ − x₁| and a vertical leg |y₂ − y₁|. The distance you want is the hypotenuse. From A(1, 2) to B(4, 6): d = √(3² + 4²) = √25 = 5. Midpoint is ju

Mathematics

Mathematics · L3 · Coordinate Geometry

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Mathematics · L3 · Coordinate Geometry

Flashcards8 cards

What is theoretical probability?1 / 8

Theoretical probability is calculated by reasoning about all the possible outcomes, without running any trials. It's the number of favorable outcomes divided by the total number of equally likely outcomes.

Mathematics

Mathematics · L2 · Probability: Experimental vs Theoretical

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Mathematics · L2 · Probability: Experimental vs Theoretical

Quiz8 questions

The Cauchy–Riemann equations for f = u + iv state:

A∂u/∂x = ∂v/∂x and ∂u/∂y = ∂v/∂yB∂u/∂x = ∂v/∂y and ∂u/∂y = −∂v/∂xCu = v everywhereD∂u/∂x = −∂v/∂y and ∂u/∂y = ∂v/∂x

Mathematics

Mathematics · L5 · Complex Analysis

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Mathematics · L5 · Complex Analysis

Quiz10 questions

What is d/dx [x⁵]?

Ax⁴B5x⁴C5x⁵D4x⁴

Mathematics

Mathematics · L4 · Derivative rules — 10 Q

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Mathematics · L4 · Derivative rules — 10 Q

Quiz3 questions

A right triangle has legs 5 and 12. What is the length of the hypotenuse?

A13B17C11D15

Mathematics

Mathematics · L3 · Triangles & the Pythagorean Theorem

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Mathematics · L3 · Triangles & the Pythagorean Theorem

Quiz5 questions

Is the number 8 odd or even?

AOddBEvenCNeitherDBoth

Mathematics

Mathematics · L1 · Odd & Even Numbers

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Mathematics · L1 · Odd & Even Numbers

Flowchart12 objects

Mathematics

Mathematics · L3 · Polar Coordinates & Graphing · flowchart

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Mathematics · L3 · Polar Coordinates & Graphing · flowchart

Flashcards7 cards

What do words like "first," "next," and "last" help us do?1 / 7

They are sequence words. They tell us the order that things happen in — what comes at the very start, what comes in the middle, and what comes at the very end.

Mathematics

Mathematics · L1 · Sequencing Events: First, Next, Last

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Mathematics · L1 · Sequencing Events: First, Next, Last

Flashcards8 cards

What is a rational expression?1 / 8

A rational expression is a fraction whose numerator and denominator are both polynomials, such as (x + 2) / (x − 5).

Mathematics

Mathematics · L3 · Rational Expressions & Equations

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Mathematics · L3 · Rational Expressions & Equations

Flashcards8 cards

What is a ratio, and name three ways to write one.1 / 8

A ratio compares two quantities. You can write it three ways: a:b, a/b, or "a to b". For 3 red marbles and 5 blue marbles, that's 3:5, 3/5, or "3 to 5".

Mathematics

Mathematics · L2 · Ratios & Unit Rates

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Mathematics · L2 · Ratios & Unit Rates

Flowchart7 objects

Mathematics

Mathematics · L2 · Graphing Inequalities on a Number Line · flowchart

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Mathematics · L2 · Graphing Inequalities on a Number Line · flowchart

Flowchart9 objects

Mathematics

Mathematics · L1 · Solving a Multiplication Word Problem

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Mathematics · L1 · Solving a Multiplication Word Problem

Flowchart15 objects

Mathematics

Mathematics · L3 · Conic Sections

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Mathematics · L3 · Conic Sections

Flashcards8 cards

What does |x| mean, geometrically, on a number line?1 / 8

|x| is the distance from x to 0 on the number line. Distance is never negative, so |x| ≥ 0 for every real number x. For example, |4| = 4 and |−4| = 4 — both points sit 4 units from zero.

Mathematics

Mathematics · L3 · Absolute Value Equations & Inequalities

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Mathematics · L3 · Absolute Value Equations & Inequalities

Flashcards9 cards

What is the difference between a recursive definition and an explicit (closed-form) definition of a sequence?1 / 9

A recursive definition builds each term from the term(s) before it, plus a starting base case. An explicit definition gives a formula that plugs n straight in to get any term directly, with no need to know earlier terms.

Mathematics

Mathematics · L3 · Recursive Sequences & Fibonacci

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Mathematics · L3 · Recursive Sequences & Fibonacci

Note~392 words · 2 min

The derivative becomes a vector In one variable, the derivative is a number. In several, there's a rate of change in every direction, so "the derivative" becomes a whole vector of partials. Geometrically: slice the surface z = f(x,y) with t

Mathematics