clean up some typos

Author: ericung

Chapters/Chapter3.tex

@@ -474,7 +474,7 @@ \section{Rules of a Field}
 
 The first equation is bold and italicized in the set to make a decider.
 
-
+$\\ $
 
 $
 \begin{matrix}
@@ -486,7 +486,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-Operations for the right hand side (RHS) versus the left hand side (LHS) represents different operations of the string in different scenarios.
+Operations for the right hand side (RHS) evaluation for -b.
 
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@@ -530,7 +530,7 @@ \section{Rules of a Field}
 
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-Q is the quotient space represented in topology such that A/~ where are sets and ~ is the divisions of A
+Q is the quotient space represented in topology such that $A/\sim$ are sets and $\sim$ is the representation of the operations of division of A.
 
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@@ -546,7 +546,7 @@ \section{Rules of a Field}
 
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-Q-rational-deciders are the possible monomial deciders of Q-rational-string. Use the picking function, PF, to choose one decision function in Q-rational-deciders, we see a mapping from Q-rational => R-rational.
+Q-rational-deciders are the possible monomial deciders of Q-rational-string. Use the picking function, PF, to choose one decision function in Q-rational-deciders, we see a mapping from Q-rational to R-rational.
 
 \begin{figure}[H]
   \centering
@@ -821,11 +821,11 @@ \section{Rules of a Field}
 
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-Given the following equation above, it has the following matrix representations forming a free skew field.
+Given the following equation above, it has the following matrix representations forming a free skew field. The elaboration of the free skew field matrix representation of $a + bc$ consists of the following set of representations.
 
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-The free skew field matrix representation of $a + bc$ consists of the following set of representations.
+$\textbf{Free Skew Field}.$ $a + b + c$
 
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@@ -854,7 +854,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $a + b + c$
+$\textbf{Free Skew Field}.$ $a + b + c$
 
 
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@@ -886,7 +886,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $ab + c$
+$\textbf{Free Skew Field}.$ $ab + c$
 
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@@ -933,7 +933,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $a + bc$
+$\textbf{Free Skew Field}.$ $a + bc$
 
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@@ -964,7 +964,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $a + b + c$
+$\textbf{Free Skew Field}.$ $a + b + c$
 
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@@ -995,7 +995,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $ab + c$
+$\textbf{Free Skew Field}.$ $ab + c$
 
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@@ -1039,7 +1039,7 @@ \section{Rules of a Field}
 
 $\\ $
 
-$\textit{Free Skew Field}.$ $a + b + c$
+$\textbf{Free Skew Field}.$ $a + b + c$
 
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@@ -1070,7 +1070,7 @@ \section{Rules of a Field}
 
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-$\textit{Free Skew Field}.$ $a b + a c$
+$\textbf{Free Skew Field}.$ $a b + a c$
 
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@@ -1110,7 +1110,7 @@ \section{Rules of a Field}
 
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-$\textit{Free Skew Field}.$ $a b + a c$
+$\textbf{Free Skew Field}.$ $a b + a c$
 
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