Some small fixes

Author: VaclavMacha

docs/src/lecture_03/exercises.md

@@ -10,7 +10,7 @@ The universe of the Game of Life is an infinite, two-dimensional orthogonal grid
 
 The first generation must be initialized. Every new generation is created by applying the above rules simultaneously to every cell in the previous generations; births and deaths occur simultaneously. The moment when this happens is called a tick. Since every generation depends only on the previous one, this process is a [Markov chain](https://en.wikipedia.org/wiki/Markov_chain).
 
-The following few exercises will implement the Game of Life. We will consider finite university with periodic boundary conditions.
+The following few exercises will implement the Game of Life. We will consider finite universe with periodic boundary conditions.
 
 ```@raw html
 <div class = "exercise-body">
@@ -115,7 +115,7 @@ Write a function `willsurvive` that returns `true` if the cell will survive base
 <summary class = "solution-header">Solution:</summary><p>
 ```
 
-This function can be written using the `if-elseif-else` statement. Since `cell` is a boolean value, we do not need to compare with one as in `call == 1`.
+This function can be written using the `if-elseif-else` statement. Since `cell` is a boolean value, we do not need to compare with one as in `cell == 1`.
 
 ```julia
 function willsurvive(cell, k)

docs/src/lecture_03/functions.md

@@ -44,7 +44,7 @@ end
 plus (generic function with 1 method)
 ```
 
-The example above contains the `println` function on the last line. However, if the function is called, nothing is printed into the REPL. The happened because expressions after the `return` keyword are never evaluated.
+The example above contains the `println` function on the last line. However, if the function is called, nothing is printed into the REPL. This is because expressions after the `return` keyword are never evaluated.
 
 ```jldoctest functions
 julia> plus(4, 5)
@@ -75,7 +75,7 @@ julia> typeof(ps)
 NTuple{4,Int64}
 ```
 
-Since the function returns a tuple, returned values can be directly unpacked into multiple variables. This can be done in the same way as unpacking [tuples](@ref Tuples).
+Note that the function returns `NTuple{4, Int64}` which is a compact way of representing the type for a tuple of length `N = 4` where all elements are of the same type. Since the function returns a tuple, returned values can be directly unpacked into multiple variables. This can be done in the same way as unpacking [tuples](@ref Tuples).
 
 ```jldoctest functions
 julia> x1, x2, x3, x4 = powers(2)
@@ -105,7 +105,7 @@ To use recursion, we have to split the computation into three parts:
 - `p > 0`: the function should be called recursively with arguments `x`, `p - 1` and the result should be multiplied by `x`.
 - `p < 0`: then it is equivalent to call the power function with arguments `1/x`, `-p`.
 
-These three cases can be defined in one `if` condition as follows:
+These three cases can be defined using the `if-elseif` as follows:
 
 ```jldoctest functions_ex; output = false
 function power(x::Real, p::Integer)
@@ -401,7 +401,7 @@ julia> linear(2; a = 2, b = 4)
 The semicolon is not mandatory and can be omitted. Moreover, the order of keyword arguments is arbitrary. It is even possible to mix keyword arguments with positional arguments, as shown in the following example.
 
 ```jldoctest key_args
-julia> linear(b = 4, 2, a = 2) # If you use this, you will burn in hell. Also, Vasek does not check my changes :D
+julia> linear(b = 4, 2, a = 2) # If you use this, you will burn in hell :D
 8
 ```
 
@@ -714,7 +714,7 @@ Those two function declarations create functions with automatically generated na
 ```@example
 using Plots
 
-f(x,a) = (x+a)^2
+f(x,a) = (x + a)^2
 plot(-1:0.01:1, x -> f(x,0.5))
 
 savefig("Plots.svg") # hide

docs/src/lecture_03/methods.md

@@ -116,7 +116,7 @@ The `supertypes_tree` function can be defined by:
 
 ```jldoctest methods; output = false
 function supertypes_tree(T::Type, level::Int = 0)
-    T === Any && return
+    isequal(T, Any) && return
     println(repeat("   ", level), T)
     supertypes_tree(supertype(T), level + 1)
     return
@@ -411,7 +411,7 @@ Write the `salary_yearly` function which computes the yearly salary for both stu
 <details class = "solution-body">
 <summary class = "solution-header">Solution:</summary><p>
 ```
-Julia prefers to write many simple functions. We write `salary_yearly` based on the not-yet-defined `salary_yearly` function.
+Julia prefers to write many simple functions. We write `salary_yearly` based on the not-yet-defined `salary_monthly` function.
 ```@example methods
 salary_yearly(s::Student) = 12*salary_monthly(s)