: The study of algebraic structures such as groups, rings, and fields. These concepts govern symmetries in physics and data encryption.
Pure mathematics is the study of mathematical concepts for their own sake, independent of any application outside of the field. This territory is divided into several major provinces.
Thanks to creators like Dominic Walliman (of Domain of Science ) and other educators, the "Map of Mathematics" poster has gone viral. And now, having a on your device is one of the smartest study tools you can download.
A direct PDF version is hosted by King Saud University .
Often called "rubber-sheet geometry." It studies properties of spaces that remain unchanged when stretched, twisted, or crumpled, but not torn or glued. 5. Changes: The Mathematics of Motion
The study of vectors, matrices, and multi-dimensional spaces. This is the core engine behind modern artificial intelligence and computer graphics.
If you are a computer science major, you will see a clear path from Discrete Math to Data Structures. If you are interested in Engineering, you will see how Vector Calculus leads directly into Fluid Dynamics. By using the map as a diagnostic tool, you can identify "knowledge gaps" that might be making your current coursework difficult. Conclusion
: Algebra (Linear and Abstract), Number Theory, and Combinatorics. Spaces : Geometry, Topology, and Trigonometry.
The investigation of the relationship between formal languages and their interpretations.
The second province is Algebra. While elementary algebra introduces variables to solve for unknowns, advanced algebra deals with structures. Here, mathematicians study groups, rings, and fields—frameworks that define how operations like addition and multiplication work in abstract spaces.
Applied mathematics takes the abstract tools created in pure mathematics and uses them to solve real-world problems. It bridges the gap between theory and reality. 1. Mathematical Physics
The Map of Mathematics PDF: A Comprehensive Guide to the Branches of Math
Differential calculus finds the rate of change (slopes), while integral calculus finds the accumulation of quantities (areas under curves).
Solving for unknown variables and understanding basic relationships like linear equations.
It highlights how different areas, such as calculus and differential equations, are related.
: Digs into the philosophical and logical roots, such as set theory and Gödel's incompleteness theorems. Educational Value
The beauty of the Map of Mathematics PDF is that it reminds us: Even PhDs specialize in one tiny dot on the map. The map simply shows you that every dot is connected—and that with patience, you can travel between them.
When studying history, a timeline helps you understand the sequence of events. When exploring geography, an atlas shows you how countries border one another. Mathematics requires the same spatial and conceptual orientation. A visual map provides several distinct advantages: