Out of 15,290 mapped topics, these unlock the most — ranked by how much of human knowledge depends on them, at every level from preschool to the research frontier.
What a child learns before school — and how far it reaches.
1 Tens and Ones Place Value 2 Skip Counting by 10s Fluency 3 Equal Groups 4 Halves and Quarters 5 Counting to 20 6 Number Bonds to 10The grade-school ideas the rest of the map stands on.
7 Place Value for Whole Numbers 8 Multiplying Fractions 9 Area of Rectangles 10 Introduction to Fractions 11 Fractions of a Set 12 Equivalent Fractions 13 Multi-Digit Multiplication 14 Multiplication Facts Within 100 15 Multi-Digit Addition 16 Comparing and Ordering Whole NumbersWhere abstraction starts paying compound interest.
17 Ratios 18 Exponential Functions and Graphs 19 Variable Expressions 20 Multiplying Integers 21 Adding Integers 22 Exponent Rules — Product, Power, and Quotient 23 Introduction to Exponents 24 Simple Probability 25 Geometric Sequences 26 Introduction to Square RootsThe undergraduate workhorses that open the most doors.
27 Partial Derivatives: Definition and Computation 28 Function Notation Review 29 Logarithms Introduction 30 Derivative as Slope of Tangent Line 31 Introduction to Differential Equations 32 Intermolecular Forces 33 Definite Integral Definition 34 Vectors in R^n 35 Trigonometric Ratios Review 36 Vectors in Two Dimensions 37 Set Theory Fundamentals 38 Probability Axioms 39 Covalent Bonding 40 Introduction to Organic ChemistryPast the textbook frontier, reach narrows but deepens.
41 Quantum Numbers 42 Emission and Absorption Spectra 43 Hydrogen Bonding: Energetics and Thermodynamics 44 Epsilon-Delta Continuity 45 Separation of Variables for Partial Differential Equations 46 The Wave Equation and Vibrating Strings 47 Bohr Model of the Hydrogen Atom 48 The One-Dimensional Wave Equation 49 Blackbody Radiation and Planck's Law 50 Solving the Schrödinger Equation for Hydrogen Atom