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Mathematics: explore STEM content (page 14 of 23) · openstem

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

Algebra, calculus, proofs and statistics on openstem — flashcards, notes, quizzes and plots shared by the community. Study free, or clone anything into your library.

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Flowchart19 objects

Mathematics

Mathematics · L3 · Solving a Series Word Problem

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Mathematics · L3 · Solving a Series Word Problem

Flowchart7 objects

Mathematics

Mathematics · L1 · Symmetry & Reflection · flowchart

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Mathematics · L1 · Symmetry & Reflection · flowchart

Note~349 words · 2 min

The problem MCMC solves You know the posterior π(θ|data) only up to a normalising constant, because the denominator is an integral you can't do. Direct sampling is out. So build a Markov chain whose stationary distribution is π, run it, and

Mathematics

Mathematics · L5 · Bayesian Computation: MCMC

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Mathematics · L5 · Bayesian Computation: MCMC

Flashcards8 cards

You have 1 quarter, 1 dime, and 1 nickel. How much money do you have in total?1 / 8

You have 40¢. A quarter is 25¢, a dime is 10¢, and a nickel is 5¢. 25 + 10 + 5 = 40¢.

Mathematics

Mathematics · L1 · Money & Making Change

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Mathematics · L1 · Money & Making Change

Flowchart21 objects

Mathematics

Mathematics · L3 · Classifying a Triangle from Its Coordinates

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Mathematics · L3 · Classifying a Triangle from Its Coordinates

Flashcards8 cards

What is a matrix?1 / 8

A rectangular arrangement of numbers in rows and columns. Each number in the matrix is called an entry (or element).

Mathematics

Mathematics · L3 · Introduction to Matrices

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Mathematics · L3 · Introduction to Matrices

Flowchart9 objects

Mathematics

Mathematics · L2 · Two-Step Equations & Inequalities · flowchart

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Mathematics · L2 · Two-Step Equations & Inequalities · flowchart

Note~342 words · 2 min

Adding and subtracting A complex number is a + bi: a real part and an imaginary part. Combine real with real, imaginary with imaginary, and never mix the two. Multiplying Expand like two binomials, then apply the one rule that makes complex

Mathematics

Mathematics · L3 · Complex Number Operations

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Mathematics · L3 · Complex Number Operations

Collection44 items

01Mathematics · L1 · Addition & Subtraction Stories

02Mathematics · L1 · Skip Counting & Patterns

03Mathematics · L1 · Measuring Length & Weight

+41 more

Mathematics

Mathematics · L1 · Arithmetic & Measurement

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Mathematics · L1 · Arithmetic & Measurement

Flowchart11 objects

Mathematics

Mathematics · L2 · Should You Use Mean or Median?

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Mathematics · L2 · Should You Use Mean or Median?

Quiz5 questions

Find the range of the data set 3, 8, 15, 4, 10.

A19B12C8D15

Mathematics

Mathematics · L2 · Range, Outliers & Data Spread

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Mathematics · L2 · Range, Outliers & Data Spread

Flowchart13 objects

Mathematics

Mathematics · L3 · Parallel Lines & Transversal Angles

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Mathematics · L3 · Parallel Lines & Transversal Angles

Flowchart7 objects

Mathematics

Mathematics · L2 · Scale Drawings & Similar Figures · flowchart

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Mathematics · L2 · Scale Drawings & Similar Figures · flowchart

Note~320 words · 2 min

Vertices, edges, degree A graph has vertices (dots) and edges (lines joining pairs of them). It's the right model whenever the relationships matter more than the things. The degree of a vertex is how many edges touch it. Degree 0 means isol

Mathematics

Mathematics · L3 · Graph Theory Basics

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Mathematics · L3 · Graph Theory Basics

Flowchart10 objects

Mathematics

Mathematics · L2 · Exponents & Square Roots · flowchart

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Mathematics · L2 · Exponents & Square Roots · flowchart

Note~219 words · 1 min

Same value, three looks Switching between the three is what lets you compare a test score, a price tag and a discount in your head. Fraction to percent Percent of a number Turn the percent into a decimal, then multiply. That's the whole met

Mathematics

Mathematics · L2 · Decimals & Percents

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Mathematics · L2 · Decimals & Percents

Flashcards7 cards

Maya has 4 apples. She picks 3 more apples from a tree. How many apples does she have now?1 / 7

She has 7 apples. 4 + 3 = 7. Put the apples together and count them all.

Mathematics

Mathematics · L1 · Addition & Subtraction Stories

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Mathematics · L1 · Addition & Subtraction Stories

Flashcards7 cards

What does a direct proof of 'If P then Q' actually do?1 / 7

It assumes P is true, then uses definitions, algebra, or known facts to derive Q in a straight chain of steps — no detour through the negation of anything.

Mathematics

Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction

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Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction

Note~376 words · 2 min

Probability is measure theory with one extra axiom A probability space is a triple (Ω, ℱ, P). Everything else is bookkeeping on top of it. That P(Ω) = 1 is the only difference from a general measure space. Everything from measure theory car

Mathematics

Mathematics · L5 · Measure-Theoretic Probability: Foundations

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Mathematics · L5 · Measure-Theoretic Probability: Foundations

Collection28 items

01Mathematics · L1 · Odd & Even Numbers

02Mathematics · L1 · Patterns: Repeating & Growing

03Mathematics · L1 · Ordinal Numbers & Ordering

+25 more

Mathematics

Mathematics · L1 · Patterns, Symmetry & Number Sense

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Mathematics · L1 · Patterns, Symmetry & Number Sense

Flowchart11 objects

Mathematics

Mathematics · L1 · Odd or Even? A Quick Test

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Mathematics · L1 · Odd or Even? A Quick Test

Flowchart11 objects

Mathematics

Mathematics · L3 · Introduction to Vectors

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Mathematics · L3 · Introduction to Vectors

Flowchart13 objects

Mathematics

Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction

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Mathematics · L3 · Proof Techniques: Direct, Contrapositive & Contradiction

Collection41 items

01Mathematics · L3 · Functions & Transformations

02Mathematics · L3 · Exponential & Logarithmic Functions

03Mathematics · L3 · Arithmetic & Geometric Series

+38 more

Mathematics

Mathematics · L3 · Precalculus

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Mathematics · L3 · Precalculus

Note~295 words · 1 min

Two things, not infinitely many Induction proves P(n) for every natural number without checking each one. It does this by proving two much smaller statements. The base case starts the chain; the inductive step passes truth along it, one lin

Mathematics

Mathematics · L3 · Mathematical Induction

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Mathematics · L3 · Mathematical Induction

Quiz6 questions

A table shows x = 1 → y = 4, x = 2 → y = 7, x = 3 → y = 10. What is the rule?

Ay = x + 3By = 3x + 1Cy = 4xDy = 2x + 2

Mathematics

Mathematics · L2 · Function Tables & Input-Output Rules

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Mathematics · L2 · Function Tables & Input-Output Rules

Flowchart7 objects

Mathematics

Mathematics · L1 · Sorting into Groups

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Mathematics · L1 · Sorting into Groups

Note~454 words · 2 min

Throwing away distance Topology asks what survives if you keep only the notion of "open" and discard distance entirely. The answer is nearly everything that matters: continuity, connectedness, compactness. The three axioms A topology τ on a

Mathematics

Mathematics · L5 · Point-Set Topology: Open Sets, Continuity, and Compactness

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Mathematics · L5 · Point-Set Topology: Open Sets, Continuity, and Compactness

Collection1 items

01Mathematics · L4 · Descriptive Statistics — Summarising Data

Mathematics

Mathematics · L4 · Descriptive Statistics

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Mathematics · L4 · Descriptive Statistics

Flowchart7 objects

Mathematics

Mathematics · L3 · Modular Arithmetic · flowchart

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Mathematics · L3 · Modular Arithmetic · flowchart

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