Fix typo. (#327)

* Fix typo ("fo" to "for").

* Fix typo in "README.md" ("gitbook" -> "GitBook").

* Improve spelling and fix multiple typos.

* Improve spelling in a few places.

Author: june128

README.md

@@ -21,7 +21,7 @@ Unfortunately, this means that we will probably never cover every algorithm ever
 That said, we'll still cover a few algorithms for fun that have very little, if any practical purpose.
 
 If you would like to contribute, feel free to go to any chapter with code associated with it and implement that algorithm in your favorite language,
-and then submit the code via pull request, following the submission guidelines found in `contents/how_to_contribute/how_to_contribute.md` (or [here](contents/how_to_contribute/how_to_contribute.md) if you are reading this on gitbook).
+and then submit the code via pull request, following the submission guidelines found in `contents/how_to_contribute/how_to_contribute.md` (or [here](contents/how_to_contribute/how_to_contribute.md) if you are reading this on GitBook).
 
 Hopefully, this project will grow and allow individuals to learn about and try their hand at implementing different algorithms for fun and (potentially) useful projects.
 If nothing else, it will be an enjoyable adventure for our community.

contents/bitlogic/bitlogic.md

@@ -92,7 +92,7 @@ There are more complicated things that can be done with the bitshift operators;
 
 #### Logic gates
 In addition to the bitshift operations, there are a number of logical operations that can be performed on one or two bits together.
-These operations are called *gates*, and follow soemwhat straightforward logic.
+These operations are called *gates*, and follow somewhat straightforward logic.
 The *AND* gate, for example, reads in 2 bits and will only output a 1 value if both inputs are 1. This can be seen in the corresponding truth table:
 
 <p>

contents/cooley_tukey/cooley_tukey.md

@@ -97,7 +97,7 @@ M = [1.0+0.0im  1.0+0.0im           1.0+0.0im          1.0+0.0im;
 
 It was amazing to me when I saw the transform for what it truly was: an actual transformation matrix!
 That said, the Discrete Fourier Transform is slow -- primarily because matrix multiplication is slow, and as mentioned before, slow code is not particularly useful.
-So what was the trick that everyone used to go from a Discrete fourier Transform to a *Fast* Fourier Transform?
+So what was the trick that everyone used to go from a Discrete Fourier Transform to a *Fast* Fourier Transform?
 
 Recursion!
 

contents/euclidean_algorithm/euclidean_algorithm.md

@@ -1,6 +1,6 @@
 # Euclidean Algorithm
 
-Computer science is (almost by definition) a science about computers -- a device first conceptualized in the 1800's. Computers have become so revolutionary, that it is difficult to think of our lives today without them. That said, *algorithms* are much older and have existed in the world for millenia. Incredibly, a few of the algorithms created before the Common Era (AD) are still in use today. One such algorithm was first described in Euclid's *Elements* (~ 300 BC) and has come to be known as the *Euclidean Algorithm*.
+Computer science is (almost by definition) a science about computers -- a device first conceptualized in the 1800's. Computers have become so revolutionary, that it is difficult to think of our lives today without them. That said, *algorithms* are much older and have existed in the world for millennia. Incredibly, a few of the algorithms created before the Common Era (AD) are still in use today. One such algorithm was first described in Euclid's *Elements* (~ 300 BC) and has come to be known as the *Euclidean Algorithm*.
 
 The algorithm is a simple way to find the *greatest common divisor* (GCD) of two numbers, which is useful for a number of different applications (like reducing fractions). The first method (envisioned by Euclid) uses simple subtraction:
 
@@ -80,7 +80,7 @@ Here, we set `b` to be the remainder of `a%b` and `a` to be whatever `b` was las
     <img  class="center" src="res/modulus.png" width="500" />
 </p>
 
-The Euclidean Algorithm is truly fundamental to many other algorithms throughout the history of computer science and will definitely be used again later. At least to me, it's amazing how such an ancient algorithm can still have modern use and appeal. That said, there are still other algorithms out there that can find the greatest common divisor of two numbers that are arguably better in certain cases than the Euclidean algorithm, but the fact that we are discussing Euclid two millenia after his death shows how timeless and universal mathematics truly is. I think that's pretty cool.
+The Euclidean Algorithm is truly fundamental to many other algorithms throughout the history of computer science and will definitely be used again later. At least to me, it's amazing how such an ancient algorithm can still have modern use and appeal. That said, there are still other algorithms out there that can find the greatest common divisor of two numbers that are arguably better in certain cases than the Euclidean algorithm, but the fact that we are discussing Euclid two millennia after his death shows how timeless and universal mathematics truly is. I think that's pretty cool.
 
 ## Example Code
 

contents/forward_euler_method/forward_euler_method.md

@@ -73,7 +73,7 @@ If we were to take the Euler method's solution as valid, we would incorrectly as
     <img  class="center" src="res/instability.png" />
 </p>
 
-Like above, the blue line is the analytical solution, the green is with a timestep of 0.5 and the red is with a tiemstep of 1.
+Like above, the blue line is the analytical solution, the green is with a timestep of 0.5 and the red is with a timestep of 1.
 Here, it's interesting that we see 2 different instability patterns.
 The green is initially unstable, but converges onto the correct solution, but the red is wrong from the get-go and only gets more wrong as time goes on.