meow

8 files changed, 12 insertions, 59 deletions

diff --git a/mathematics/abstract-algebra.md b/mathematics/abstract-algebra.md
deleted file mode 100644
index c2446cd..0000000
--- a/mathematics/abstract-algebra.md
+++ /dev/null
@@ -1,13 +0,0 @@
----
-layout: algebra
-title: mathematics/algebra/abstract algebra
----
-
-# various notes on topics in abstract algebra
-
-## groups
-
-## rings
-
-## fields
-
diff --git a/mathematics/algebra.md b/mathematics/algebra.md
index 4b9a097..3756604 100644
--- a/mathematics/algebra.md
+++ b/mathematics/algebra.md
@@ -5,8 +5,8 @@ title: mathematics/algebra
 
 # algebra
 
-modern algebra is the study of **algebraic structures**: groups, rings, fields, modules, vector spaces, lattices, and the like.
-these structures are very general: and so results from abstract algebra can be applied to a wide variety of situations.
+modern algebra is the study of **algebraic structures**: groups, rings, fields, modules, and the like.
+these structures are very abstract: and so results can be applied to a wide variety of situations.
 
 ## structures
 
@@ -34,9 +34,9 @@ A **ring** $R$ is a set with two binary operations $+$ and $×$ satisfying the f
   - $∀a,b,c : (a+b) × c = (a×c)+(b×c)$
   - $∀a,b,c : a × (b+c) = (a×b) + (a×c)$
 - An Abelian or **commutative ring** satisfies an additional axiom:
-  - commutativity (of ×): $∀a,b : a×b=b×a$
+  - commutativity (of $×$): $∀a,b : a×b=b×a$
 
-A **field** is a *commutative ring* where $0 ≠ 1$ and all elements sans $0$ have an inverse $a^{-1}$ under multiplication.
+A **field** is a *commutative ring* where all elements sans $0$ have an inverse $a^{-1}$ under multiplication. Subsequently, $0 ≠ 1$. A field may be also thought of as a set on which addition, subtraction, multiplication, and division are defined and behave as they do on $ℝ$.
 
 A **vector space** $V$ over a field $F$ of scalars is a set with a binary operation $+$ and a binary function satisfying the following axioms:
 - $(V, +)$ is a *commutative group*:
@@ -53,7 +53,7 @@ A **vector space** $V$ over a field $F$ of scalars is a set with a binary operat
 
 A **module** $M$ is a generalization of a *vector space* to function over a ring $R$ instead of a field.
 
-A **lattice** $L$ is a set with two binary operations ∧ and ∨ satisfying the following axioms:
+A **lattice** $L$ is a set with two binary operations $∧$ and $∨$ satisfying the following axioms:
 - commutativity:
   - $∀a,b : a ∧ b = b ∧ a$
   - $∀a,b : a ∨ b = b ∨ a$
@@ -67,22 +67,14 @@ A **lattice** $L$ is a set with two binary operations ∧ and ∨ satisfying the
   - $∀a : a ∧ a = a$
   - $∀a : a ∨ a = a$
 
-## group theory
+## [group theory](group-theory.md)
 
-...
+## [ring theory](ring-theory.md)
 
-## ring theory
+## [galois theory](galois-theory.md)
 
-...
+## [linear algebra](linear-algebra.md)
 
-## galois theory
+## [order theory](order-theory.md)
 
-...
-
-## linear algebra
-
-...
-
-## order theory
-
-a lattice may alternatively be defined as...
+## [coding theory](coding-theory.md)
diff --git a/mathematics/calculus.md b/mathematics/calculus.md
deleted file mode 100644
index d78b7e7..0000000
--- a/mathematics/calculus.md
+++ /dev/null
@@ -1,6 +0,0 @@
----
-layout: analysis
-title: mathematics/analysis/calculus
----
-
-# calculus
diff --git a/mathematics/complex-analysis.md b/mathematics/complex-analysis.md
deleted file mode 100644
index 26e1ff0..0000000
--- a/mathematics/complex-analysis.md
+++ /dev/null
@@ -1,5 +0,0 @@
----
-layout: analysis
-title: mathematics/analysis/complex analysis
----
-
diff --git a/mathematics/lambdas.md b/mathematics/lambdas.md
deleted file mode 100644
index 1c93818..0000000
--- a/mathematics/lambdas.md
+++ /dev/null
@@ -1,5 +0,0 @@
----
-layout: foundations
-title: mathematics/foundations/lambdas
----
-
diff --git a/mathematics/linear-algebra.md b/mathematics/linear-algebra.md
index 5fe2210..6853121 100644
--- a/mathematics/linear-algebra.md
+++ b/mathematics/linear-algebra.md
@@ -1,6 +1,6 @@
 ---
 layout: algebra
-title: mathematics/algebra/linear algebra
+title: mathematics/linear algebra
 ---
 
 # Linear Algebra
diff --git a/mathematics/real-analysis.md b/mathematics/real-analysis.md
deleted file mode 100644
index 9c0b134..0000000
--- a/mathematics/real-analysis.md
+++ /dev/null
@@ -1,5 +0,0 @@
----
-layout: analysis
-title: mathematics/analysis/real analysis
----
-
diff --git a/mathematics/types.md b/mathematics/types.md
deleted file mode 100644
index 577e610..0000000
--- a/mathematics/types.md
+++ /dev/null
@@ -1,5 +0,0 @@
----
-layout: foundations
-title: mathematics/foundations/types
----
-