## Tuesday, November 23, 2010

### The Math Family Tree and its Branches

It's Thanksgiving week and lots of kids are out of school and heading for grandma's house for turkey dinner. Time to use our imaginations and consider math for the holidays.

Here's a Mathematics tree, looking for other members in his family. Let's say he represents math. What other branches of his family might show up for the big dinner on Thursday? He knows he has a cousin named Geometry (gee, I'm a tree).

One amateur mathematician suggested that these are the definitive various branches of math:

1. Foundations
-Logic & Model Theory
-Computability Theory & Recursion Theory
-Set Theory
-Category Theory

2. Algebra
-Group Theory -> Symmetry
-Ring Theory -> Polynomials
-Field Theory
-Module Theory -> Linear Algebra
-Galois Theory -> The Theory of Equations
-Number Theory
-Combinatorics
-Algebraic Geometry

3. Mathematical Analysis
-Real Analysis & Measure Theory -> Calculus
-Complex Analysis
-Tensor & Vector Analysis
-Differential & Integral Equations
-Numerical Analysis
-Functional Analysis & The Theory of Functions

4. Geometry & Topology
-Euclidean Geometry
-Non-Euclidean Geometry
-Absolute Geometry
-Metric Geometry
-Projective Geometry
-Affine Geometry
-Discrete Geometry & Graph Theory
-Differential Geometry
-Point-Set or General Topology
-Algebraic Topology

4. Applied Mathematics
-Probability Theory
-Statistics
-Computer Science
-Mathematical Physics
-Game Theory
-Systems & Control Theory

Ok, this is a list compiled by an expert. And there are lots of big and confusing words in the list. But did you notice that he can't count?  Or doesn't know number sequence? We teach this in Kindergarten and First Grade.

Group 1, 2, 3, 4 and 4.

But that makes sense, because he left arithmetic off the list, which is what we teach in early grades of elementary school. We could do some of this list-making ourselves, I think. Here's what I come up with if I strip off all of Mr. Tree's leaves. We see these branches:

Most of these relatives will have to be introduced to you by someone else who knows them better than I do.