01

Stage 1: Foundation Level

Building the Essential Mathematical Base (Ages 5-12)

1.1 Number Sense & Arithmetic

1.2 Fractions, Decimals & Percentages

1.3 Basic Geometry

1.4 Measurement

1.5 Introduction to Data

02

Stage 2: Intermediate Level

Developing Mathematical Thinking (Ages 12-15)

2.1 Pre-Algebra

2.2 Algebra I

2.3 Euclidean Geometry

2.4 Statistics & Probability

2.5 Number Theory Basics

03

Stage 3: Advanced Secondary Level

Deepening Understanding (Ages 15-18)

3.1 Algebra II

3.2 Trigonometry

3.3 Analytic Geometry

3.4 Pre-Calculus

3.5 Calculus (Introduction)

3.6 Probability & Statistics

04

Stage 4: Undergraduate Level

Building Mathematical Maturity (Bachelor's Degree)

4.1 Single Variable Calculus

4.2 Multivariable Calculus

4.3 Linear Algebra

4.4 Abstract Algebra

4.5 Real Analysis

4.6 Differential Equations

4.7 Probability Theory

4.8 Discrete Mathematics

4.9 Topology (Introduction)

4.10 Complex Analysis

05

Stage 5: Graduate Level

Specialization and Deep Theory (Master's Degree)

5.1 Advanced Real Analysis

5.2 Functional Analysis

5.3 Advanced Algebra

5.4 Algebraic Topology

5.5 Differential Geometry

5.6 Partial Differential Equations

5.7 Algebraic Geometry

5.8 Advanced Number Theory

5.9 Mathematical Logic

5.10 Stochastic Processes

06

Stage 6: Research Level

Contributing to Mathematical Knowledge (PhD and Beyond)

6.1 Pure Mathematics Research Areas

6.2 Analysis Research Areas

6.3 Number Theory Research

6.4 Applied Mathematics Research

6.5 Theoretical Computer Science

6.6 Mathematical Physics

6.7 Famous Open Problems

6.8 Research Skills

Mathematics Learning Flowchart

Visual representation of the learning progression

1 Foundation Arithmetic, Basic Geometry, Fractions
2 Intermediate Pre-Algebra, Algebra I, Euclidean Geometry
3 Advanced Secondary Algebra II, Trigonometry, Pre-Calculus, Intro Calculus
4 Undergraduate Analysis, Linear Algebra, Abstract Algebra, Topology
5 Graduate Measure Theory, Functional Analysis, Differential Geometry
6 Research Original Contributions, Open Problems, Specialization

Pure Mathematics Track

Algebra
Analysis
Geometry
Topology

Applied Mathematics Track

ODEs/PDEs
Numerical Methods
Optimization
Applications

Statistics/Probability Track

Probability
Statistics
Stochastic Processes
ML/Data Science

Mathematics Mind Map

Interconnected branches of mathematical knowledge

MATHEMATICS
ALGEBRA
Elementary Algebra Linear Algebra Abstract Algebra Commutative Algebra Homological Algebra
ANALYSIS
Real Analysis Complex Analysis Functional Analysis Harmonic Analysis Measure Theory
GEOMETRY
Euclidean Geometry Analytic Geometry Differential Geometry Algebraic Geometry Non-Euclidean Geometry
TOPOLOGY
Point-Set Topology Algebraic Topology Differential Topology Geometric Topology Knot Theory
NUMBER THEORY
Elementary Number Theory Algebraic Number Theory Analytic Number Theory Computational Number Theory Diophantine Equations
DISCRETE MATH
Combinatorics Graph Theory Logic Set Theory Cryptography
APPLIED MATH
Differential Equations Numerical Analysis Optimization Mathematical Physics Mathematical Biology
PROBABILITY
Probability Theory Statistics Stochastic Processes Bayesian Methods Information Theory

Visual Learning Roadmap

A timeline view of your mathematical journey

Years 1-6

Foundation

Numbers Basic Operations Shapes Measurement

Years 7-10

Intermediate

Algebra Geometry Statistics Number Theory

Years 11-12

Advanced Secondary

Advanced Algebra Trigonometry Calculus Coordinate Geometry

Years 13-16

Undergraduate

Real Analysis Linear Algebra Abstract Algebra Complex Analysis Topology

Years 17-18

Graduate

Measure Theory Functional Analysis Algebraic Topology Differential Geometry

Years 19+

Research

Original Research Specialization Open Problems Publication

Key Prerequisites Path

Arithmetic
Algebra
Calculus
Analysis
Research
Geometry
Linear Algebra
Abstract Algebra
Topology
Research

⚠️ Educational Disclaimer

This resource is for educational purposes only and does not constitute professional academic advice. The roadmap represents a general guide to mathematical education. Individual learning paths may vary based on personal goals, institutional requirements, and career objectives. Always consult with academic advisors for personalized educational planning.