Merge branch 'master' of ssh://bnewbold@animus.robocracy.org/srv/git/knowledge

10 files changed, 121 insertions, 116 deletions

diff --git a/MIT Courses b/MIT Courses
index 33dfcbe..31ebaf1 100644
--- a/MIT Courses
+++ b/MIT Courses
@@ -48,19 +48,18 @@ humanities concentration in philosophy.
     + **21F.052** - French Film Classics (spring, in english) 

     + **18.100b** - Analysis

 

-* Fall 2008 (planned)

-    + 8.05  - Quantum Mechanics II

-    + 18.901 - Topology

-    + 24.118 - Paradox and Infinity

-    + 24.209 - Philosophy in Film

-    + 6.111 - Digital Systems Lab (FPGA Design)

+* Fall 2008

+    + **8.05**  - Quantum Mechanics II

+    + **24.118** - Paradox and Infinity

+    + **24.209** - Philosophy in Film

+    + **6.111** - Digital Systems Lab (FPGA Design)

 

 * Spring 2009 (planned)

     + 8.06 - Quantum Mechanics III

-    + 8.08 - Statistical Physics II

-    + 8.962 (cosmo) or 8.942 (GR)

+    + 8.962 - General Relativity

+    + 6.945 - Adventures in Symbolic Programming

+    + 4.602 - Modern Art and Mass Culture

     + 8.ThU - Thesis

-    + Pop Culture HASSD

 

 Other interesting courses:

     + 24.215 - Topics in the Philosophy of Science (fall)

@@ -75,6 +74,7 @@ Other interesting courses:
     + 18.565 - Recursion Theory

     + 18.703 - Modern Algebra (spring)

     + 18.701/702 - Algebra I/II (fall/spring)

+    + 18.901 - Topology

     + 18.950 - Differential Geometry

     + 8.261J - Introduction to Computational Neuroscience (fall)

     + 8.292J - Fluid Physics (spring)

@@ -82,3 +82,4 @@ Other interesting courses:
     + 8.594J - Introduction to Neural Networks (grad, fall)

     + 8.284 - Modern Astrophysics (spring)

     + 8.942 - Cosmology (grad, spring)

+

diff --git a/books/WantedBooks b/books/WantedBooks
deleted file mode 100644
index 51b0361..0000000
--- a/books/WantedBooks
+++ /dev/null
@@ -1,33 +0,0 @@
-=================================
-Wanted Books
-=================================
-
-These are some books i'd love to own a copy of or at least read through 
-carefully.
-
-Technical 
-------------
-
- * **Visual Complex Analysis** by Tristan Needham
- * **Visualizing Data: Exploring and Explaining Data with the Processing Environment** by Ben Fry
- * **General Theory of Relativity** by P. A.M. Dirac
- * **Computability and Unsolvability** by Martin Davis
- * **Mathematical Foundations of Quantum Mechanics** by John von Neumann
- * **Real and Complex Analysis** by Walter Rudin
- * **Art of Computer Programming** by Donald E. Knuth
- * **Gravitation** by MTW
- * **Euclid's Elements**
- * **C Programming Language** by Brian W. Kernighan
- * **Mathematical Physics** by Robert Geroch
-
-Novels
------------
-
- * **Return From the Stars** by Stanislaw Lem
- * **Mortal Engines** by Stanislaw Lem
- * **V.** by Thomas Pynchon
-
-Other
--------
- * **Pictures Showing What Happens on Each Page of Thomas Pynchon's Novel Gravity's Rainbow** by Zak Smith
-
diff --git a/books/wanted books b/books/wanted books
new file mode 100644
index 0000000..6c29a2e
--- /dev/null
+++ b/books/wanted books
@@ -0,0 +1,53 @@
+=================================
+Wanted Books
+=================================
+
+These are some books i'd love to own a copy of or at least read through 
+carefully.
+
+Technical 
+------------
+
+ * **Visual Complex Analysis** by Tristan Needham
+ * **Visualizing Data: Exploring and Explaining Data with the Processing Environment** by Ben Fry
+ * **General Theory of Relativity** by P. A.M. Dirac
+ * **Computability and Unsolvability** by Martin Davis
+ * **Mathematical Foundations of Quantum Mechanics** by John von Neumann
+ * **Real and Complex Analysis** by Walter Rudin
+ * **Art of Computer Programming** by Donald E. Knuth
+ * **Gravitation** by MTW
+ * **Euclid's Elements**
+ * **C Programming Language** by Brian W. Kernighan
+ * **Mathematical Physics** by Robert Geroch
+
+Math
+~~~~~~~~~~~~~~
+(I haven't really looked in to most of these, just sound interesting)
+
+
+ * `On formally undecidable propositions of Principa Mathematica and related systems`:title:, by Kurt Godel. 
+ * `Computability and Unsolvability`:title:, by Martin Davis. 
+ * `Mathematical Foundations of Information Theory`:title:, by A.I. Khinchin. 
+ * `Calculus of Variations with Applications to Physics and Engineering`:title:, by Robert Weinstock. 
+ * `Relativity, Thermodynamics, and Cosmology`:title:, by Richard Tolman.
+ * `Mathematics Applied to Continuum Mechanics`:title:, by Lee Segel.
+ * `Optimization Theory and Applications`:title:, by Donald Pierre.
+ * `The Variational Principles of Mechanics`:title:, by Cornelius Lanczos.
+ * `Tensor Analysis for Physicists`:title:, by J.A. Schonten.
+ * `Investigations on the Theory of Brownian Movement`:title:, by Albert Einstein.
+ * `Great Experiments in Physics`:title:, ed. by ???.
+ * `Curvature and Homology`:title:, by Samuel Goldberd.
+ * `The Philosophy of Mathematics`:title:, by Stephan Korner.
+ * `The Various and Ingenious Machines of Agostino Ramelli`:title:, by A. Ramelli (!).
+ * `Experiments in Topology`:title:, by Stephan Barr.
+
+Novels
+-----------
+
+ * **Return From the Stars** by Stanislaw Lem
+ * **Mortal Engines** by Stanislaw Lem
+
+Other
+-------
+ * **Pictures Showing What Happens on Each Page of Thomas Pynchon's Novel Gravity's Rainbow** by Zak Smith
+
diff --git a/math/algebra b/math/algebra
index b337a2e..3e39ddb 100644
--- a/math/algebra
+++ b/math/algebra
@@ -5,42 +5,50 @@ Algebra
 .. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
 
 .. list-table:: Closure of binary operators on given sets of numbers
-    * Operation
-     - :latex:`$+$`
-     - :latex:`$\times$`
-     - :latex:`$-$`
-     - :latex:`$\divide$`
-     - :latex:`$^$`
-     - :latex:`$\sqrt{\text{ }}$`
-    * Positive Integers
+
+   * - Operation name
+     - addition
+     - product
+     - subtraction
+     - division
+     - power
+     - root
+   * - Operation symbol
+     - :latex:`$a + b$`
+     - :latex:`$a\times b$`
+     - :latex:`$a-b$`
+     - :latex:`$\frac{a}{b}$`
+     - :latex:`$a^b$`
+     - :latex:`$\sqrt{\text{a}}$`
+   * - Positive Integers
      - Y
      - Y
      - N
      - N
      - Y
      - N
-    * Positive rationals
+   * - Positive rationals
      - Y
      - Y
      - N
      - Y
      - Y
      - N
-    * Rationals (and zero)
+   * - Rationals (and zero)
      - Y
      - Y
      - Y
      - Y
      - Y
      - N
-    * Reals wrt positive integers
+   * - Reals wrt positive integers
      - Y
      - Y
      - Y
      - Y
      - Y
      - Y
-    * Complex numbers
+   * - Complex numbers
      - Y
      - Y
      - Y
diff --git a/math/books to read b/math/books to read
deleted file mode 100644
index ba75d8e..0000000
--- a/math/books to read
+++ /dev/null
@@ -1,33 +0,0 @@
-===============================================
-Math books that look interesting
-===============================================
-
-`On formally undecidable propositions of Principa Mathematica and related systems`:title:, by Kurt Godel. 
-
-`Computability and Unsolvability`:title:, by Martin Davis. 
-
-`Mathematical Foundations of Information Theory`:title:, by A.I. Khinchin. 
-
-`Calculus of Variations with Applications to Physics and Engineering`:title:, by Robert Weinstock. 
-
-`Relativity, Thermodynamics, and Cosmology`:title:, by Richard Tolman.
-
-`Mathematics Applied to Continuum Mechanics`:title:, by Lee Segel.
-
-`Optimization Theory and Applications`:title:, by Donald Pierre.
-
-`The Variational Principles of Mechanics`:title:, by Cornelius Lanczos.
-
-`Tensor Analysis for Physicists`:title:, by J.A. Schonten.
-
-`Investigations on the Theory of Brownian Movement`:title:, by Albert Einstein.
-
-`Great Experiments in Physics`:title:, ed. by ???.
-
-`Curvature and Homology`:title:, by Samuel Goldberd.
-
-`The Philosophy of Mathematics`:title:, by Stephan Korner.
-
-`The Various and Ingenious Machines of Agostino Ramelli`:title:, by A. Ramelli (!).
-
-`Experiments in Topology`:title:, by Stephan Barr.
diff --git a/math/good books b/math/good books
deleted file mode 100644
index bc3efe5..0000000
--- a/math/good books
+++ /dev/null
@@ -1,5 +0,0 @@
-==========================================
-Recommended Math Reading
-==========================================
-
-BLANK
diff --git a/math/tensors b/math/tensors
index 42fa841..d46810e 100644
--- a/math/tensors
+++ b/math/tensors
@@ -8,20 +8,28 @@ Tensors, Differential Geometry, Manifolds
 
 On a manifold, only "short" vectors exist. Longer vectors are in a space tangent to the manifold.
 
-There are points (P), separation vectors (\Delta \vector P), curves ( Q(\zeta) ), tangent vectors ( \delta P / \delta \zeta \equiv \lim_{\Delta \zeta \rightarrow 0} \frac{ \vector{ Q(\zeta+\delta \zeta) - Q(\zeta) } }{\delta \zeta} )
+There are points (:m:`$P$`), separation vectors (:m:`$\Delta \vector P$`),
+curves (:m:`$Q(\zeta)$`), tangent vectors (:m:`$\delta P / \delta \zeta \equiv
+\lim_{\Delta \zeta \rightarrow 0} \frac{ \vector{ Q(\zeta+\delta \zeta) -
+Q(\zeta) } }{\delta \zeta}$`)
 
-Coordinates: \Chi^\alpha (P), where \alpha = 0,1,2,3; Q(\Chi_0, \Chi_1, ...)
+Coordinates: :m:`$\Chi^\alpha (P)$`, where :m:`$\alpha = 0,1,2,3$`;
+:m:`$Q(\Chi_0, \Chi_1, ...)$`
     there is an isomorphism between points and coordinates
 
-Coordinate basis: \vector{e_\alpha} \equiv \left( \frac{\partial Q}{\partial \Chi^\alpha} \right)
-    for instance, on a sphere with angles \omega, \phi: 
-        \vector{e_\phi} = \left( \frac{\partial Q(\phi, \theta)}{\partial \phi}\right)_\theta
+Coordinate basis: :m:`$\vector{e_\alpha} \equiv \left( \frac{\partial
+Q}{\partial \Chi^\alpha} \right$`)
+    
+    for instance, on a sphere with angles :m:`$\omega, \phi$`: 
+    
+    :m:`$\vector{e_\phi} = \left( \frac{\partial Q(\phi, \theta)}{\partial \phi}\right)_\theta$`
 
 Components of a vector:
-    \vector{A} = \frac{\partial P}{\partial \Chi^\alpha }
+
+    :m:`$\vector{A} = \frac{\partial P}{\partial \Chi^\alpha }$`
 
 Directional Derivatives: consider a scalar function defined on a manifold \Psi(P)
-    \partial_\vector{A} \Psi = A^\alpha \frac{\partial \Psi}{\partial \Chi^\alpha}
+    :m:`$\partial_\vector{A} \Psi = A^\alpha \frac{\partial \Psi}{\partial \Chi^\alpha}$`
 
 Mathematicians like to say that the coordinate bases are actually directional derivatives
 
@@ -32,24 +40,24 @@ A **tensor** :m:`$\bold{T}$` has a number of slots (called it's **rank**), takes
 as an example for a rank-3 tensor:
 
 :m:`$$\bold{T} ( \alpha \vector{A} + \beta \vector{B}, \vector{C}, \vector{D}) =
-   \alpha \bold{T} (\vector{A}, \vector{C}, \vector{D}) +
-   \beta \bold{T} (\vector{B}, \vector{C}, \vector{D}) $$`
+\alpha \bold{T} (\vector{A}, \vector{C}, \vector{D}) + \beta \bold{T}
+(\vector{B}, \vector{C}, \vector{D}) $$`
 
 Even a regular vector is a tensor: pass it a second vector and take the 
 inner product (aka dot product) to get a real.
 
 Define the **metric tensor** 
-:m:`$\bold{g}(\vector{A}, \vector{B}) = \vector{A} \dot \vector{B}$`. The 
+:m:`$\bold{g}(\vector{A}, \vector{B}) = \vector{A} \cdot \vector{B}$`. The 
 metric tensor is rank two and symetric (the vectors A and B could be swapped 
 without changing the scalar output value) and is the same as the inner product. 
 
-:m:`$$\Delta P \dot \Delta P \equiv \Delta P^2 \equiv (length of \Delta P)^2 A \dot B = 1/4[ (A+B)^2 - (A-B)^2 ]$$`
+:m:`$$\Delta P \cdot \Delta P \equiv \Delta P^2 \equiv (length of \Delta P)^2 A \cdot B = 1/4[ (A+B)^2 - (A-B)^2 ]$$`
 
 Starting with individual vectors, we can construct tensors by taking the 
 product of their inner products with empty slots; for example
 
 :m:`$$\vector{A} \crossop \vector{B} \crossop \vector{C} (\_ ,\_ ,\_)$$` 
-:m:`$$\vector{A} \crossop \vector{B} \crossop \vector{C} (\vector{E}, \vector{F}, \vector{G}) = ( \vector{A} \dot \vector{E})(\vector{B} \dot \vector{F})(\vecotr{C} \dot \vector{G}) $$` 
+:m:`$$\vector{A} \crossop \vector{B} \crossop \vector{C} (\vector{E}, \vector{F}, \vector{G}) = ( \vector{A} \cdot \vector{E})(\vector{B} \cdot \vector{F})(\vecotr{C} \cdot \vector{G}) $$` 
 
 Spacetime
 --------------
@@ -57,10 +65,10 @@ Spacetime
 Two types of vectors.
 
 Timelike: :m:`$\vector{\Delta P}$`
-    (\vector{\Delta P})^2 = -(\Delta \Tau)^2
+    :m:`$(\vector{\Delta P})^2 = -(\Delta \Tau)^2$`
 
-Spacelike: \vector{\Delta Q}
-    (\vector{\Delta Q})^2 = +(\Delta S)^2
+Spacelike: :m:`$\vector{\Delta Q}$`
+    :m:`$(\vector{\Delta Q})^2 = +(\Delta S)^2$`
 
 Because product of "up" and "down" basis vectors must be a positive Kronecker 
 delta, and timelikes squared come out negative, the time "up" basis must be  negative of the time "down" basis vector.
diff --git a/physics/general relativity b/physics/general relativity
index 7521db5..7fc29eb 100644
--- a/physics/general relativity
+++ b/physics/general relativity
@@ -8,8 +8,9 @@ General Relativity
 .. note:: Most of this content is based on a 2002 Caltech course taught by
     Kip Thorn [PH237]_
 
-*See also `math/tensors </k/math/tensors>`_*
+*See also `math/tensors </k/math/tensors>`__*
 
+(no content)
 
 References
 ----------------
diff --git a/physics/gravitational waves b/physics/gravitational waves
index ab7174e..5aa1744 100644
--- a/physics/gravitational waves
+++ b/physics/gravitational waves
@@ -38,9 +38,11 @@ Fifth term: current quadrupole
 Energy
 ----------------
 
-Quick calculation: for a source with mass M, size L, period P, the quadrupole moment $M_2 \approx M L^2$, h \approx 1/c^2 (Newtonian potential energy) ????
+Quick calculation: for a source with mass M, size L, period P, the quadrupole
+moment :m:`$M_2 \approx M L^2$`, :m:`$h \approx 1/c^2` (Newtonian potential
+energy) ????
 
-h on the order of $10^{-22}$
+h on the order of :m:`$10^{-22}$`
 
 Propagation
 -----------------
diff --git a/physics/special relativity b/physics/special relativity
index 41bf4b8..37fd3e9 100644
--- a/physics/special relativity
+++ b/physics/special relativity
@@ -8,7 +8,7 @@ Special Relativity
 .. note:: Most of this content is based on a 2002 Caltech course taught by
     Kip Thorn [PH237]_
 
-*See also `physics/general relativity</k/physics/generalrelativity/>`_*
+*See also `physics/general relativity</k/physics/generalrelativity/>`__*
 
 As opposed to general relativity, special relativity takes place in a *flat*
 Minkowski space time: a 4-space with three spatial dimensions and one time
@@ -17,22 +17,25 @@ dimension.
 +----------------+--------------------+
 | Index notation | Variable | Type    |
 +----------------+--------------------+
-| `$x^\0`:m:     | `$t$`:m: | Time    |
-| `$x^\1`:m:     | `$x$`:m: | Spatial |
-| `$x^\2`:m:     | `$y$`:m: | Spatial |
-| `$x^\3`:m:     | `$z$`:m: | Spatial |
+| `$x^0$`:m:     | `$t$`:m: | Time    |
+| `$x^1$`:m:     | `$x$`:m: | Spatial |
+| `$x^2$`:m:     | `$y$`:m: | Spatial |
+| `$x^3$`:m:     | `$z$`:m: | Spatial |
 +----------------+--------------------+
 
 Separations
 -------------
 
-The separation `$(\Delta s)^2`:m: between two events in space time, in a given
+The separation `$(\Delta s)^2$`:m: between two events in space time, in a given
 Lorentzian/inertial frame, is defined
 as:
 
 :m:`$$ (\Delta s)^2 \equiv -(\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 $$`
+
 or
+
 :m:`$$ (\Delta s)^2 \equiv -(\Delta x^0)^2 + \sum_{i,j} \delta_{ij} \Delta x^i \Delta x^j$$`
+
 where :m:`$\delta_{ij}$` is the Kronecker delta (unity or 1 when 
 :m:`$i=j$`; zero otherwise), and the indices i and j are over the spatial
 dimensions 1,2,3 (corresponding to x,y,z). It can be shown that this separation