LEARNING WORLD

Foundations & Discrete Mathematics

Build the language of numbers, sets, theorems and counting before the formulas become dense.

Core prerequisites for computer science, data science, AI and machine learning.

CHAPTER · 8 LESSONS

Mathematical Language

Numbers, variables, sets, functions and theorems form a reusable mathematical vocabulary.

How do major theorems answer different questions, and where do their assumptions limit the answer?

17 pictures · Open → $Mathematics visual$ LESSONFunctions: Inputs, Outputs, and Graphs

How can one mathematical rule connect input values to outputs, tables, and graphs?

5 pictures · Open → $Mathematics visual$ LESSONNumber Line

What is the mathematical foundation of number line?

3 pictures · Open → $Mathematics visual$ LESSONNumbers and Number Lines

How can a number show a place?

5 pictures · Open → $Mathematics visual$ LESSONSets and Logic: From Grouping to Probability

How do grouping rules become a language for logic, counting, and probability?

5 pictures · Open → $Mathematics visual$ LESSONStarting Point Of Sigma

What is the mathematical foundation of starting point of sigma?

2 pictures · Open → $Mathematics visual$ LESSONThree Mathematical Meanings of Pi

How can the same Greek letter represent different mathematical objects?

1 pictures · Open → $Mathematics visual$ LESSONVariables, Constants, and Expressions

How do symbols turn a numerical pattern into an expression, equation, and function rule?

CHAPTER · 5 LESSONS

Count arrangements by exposing structure instead of listing every possibility.

How can counting repeated positions solve a number-wheel puzzle without guessing?

9 pictures · Open → $Mathematics visual$ LESSONCounting Using Sets

What is the mathematical foundation of counting using sets?

6 pictures · Open → $Mathematics visual$ LESSONDecode Counting Identity

What is the mathematical foundation of decode counting identity?

4 pictures · Open → $Mathematics visual$ LESSONSpecial Permutation

What is the mathematical foundation of special permutation?

12 pictures · Open → $Mathematics visual$ LESSONWhat Remains After Two Things Are Fixed?

When should both the available population and the remaining choices decrease by two?