diff --git a/Day_4/Day_4.jl b/Day_4/Day_4.jl
index 664eb80..a4281e6 100644
--- a/Day_4/Day_4.jl
+++ b/Day_4/Day_4.jl
@@ -4,6 +4,12 @@
 using Markdown
 using InteractiveUtils
 
+# ╔═╡ 7a9ccfbc-bd2e-41d0-be5d-dea04b90d397
+using BenchmarkTools
+
+# ╔═╡ 8b1dfee2-bd8b-4d23-b9f8-9406002e0eaa
+using Random
+
 # ╔═╡ 1fb7d9af-333e-44f2-b693-09ff97937d4c
 # Oh, no, you found my secret! 😱
 # Don't change this hidden cell!
@@ -135,8 +141,164 @@ If you want syntax highlighting in your REPL, add the package `OhMyREPL` to your
 	https://kristofferc.github.io/OhMyREPL.jl/latest/installation/
 """
 
-# ╔═╡ d21771de-272e-4d57-8c76-c75be709ad0a
+# ╔═╡ 0e53e4ee-16a7-47ef-9992-77cbfd1ed258
+md"""
+# Benchmarking
+"""
 
+# ╔═╡ d86e4a2f-e737-49a4-bc16-a149e81785bd
+function normal_for_loop(N)
+	factorials = zeros(BigInt, N)
+	
+	for i in 1:N
+		factorials[i] = factorial(big(i))
+	end
+
+	return
+end
+
+# ╔═╡ bc777c73-9573-41c3-8ab5-843335539f96
+N = 5000
+
+# ╔═╡ 55d1d616-b6ee-40dd-a0ed-6274a98b1e73
+@benchmark normal_for_loop(N)
+
+# ╔═╡ 00c27927-9c72-417a-862f-9b66318d9751
+@btime normal_for_loop(N)
+
+# ╔═╡ d21771de-272e-4d57-8c76-c75be709ad0a
+md"""
+# Multithreading
+Julia is built as a modern language with parallel and asynchronous programming in mind.
+
+You can use run Julia code on the GPU, on multiple CPU threads (multithreading) and with multiple processes (multiprocessing).
+
+In this course, only multithreading will be presented.
+
+The easiest way to use multithreading in Julia is by letting a `for` loop run on multiple threads. This can be achieved by only addy the macro `@threads` before the `for` loop.
+
+Before trying to use multithreading, make sure that you launch Julia with multiple threads. To do so, run the following to launch Julia:
+
+	julia -t auto
+
+You can append `--project=.` and other arguments to it.
+
+`-t` is an alias to `--threads`. `auto` automatically determins how many threads your PC supports. You can also replace `auto` by the number of threads that you want to use. This number can not be bigger than the number of threads that your computer supports.
+"""
+
+# ╔═╡ 2cf5f891-8d8f-477d-8ef1-9b4b9480d477
+# Show available number of threads
+# If this is 1, then you can not use multithreading!
+# If your PC has only one core and one thread, then you can do nothing about it.
+# Otherwise, you have to tell Julia how many threads to use with the `-t` argument.
+Threads.nthreads()
+
+# ╔═╡ 76866972-0290-4e33-93de-b6128ba11994
+md"""
+## `@threads`
+"""
+
+# ╔═╡ cacc94b4-21e0-410e-acaa-80e37b447f94
+function multithreaded_for_loop(N)
+	factorials = zeros(BigInt, N)
+	
+	Threads.@threads for i in 1:N
+		factorials[i] = factorial(big(i))
+	end
+
+	return
+end
+
+# ╔═╡ a3029480-bcdc-44f3-b504-8bd3bf3aa14d
+@btime multithreaded_for_loop(N)
+
+# ╔═╡ f141dbb4-bdc5-4f16-8d97-fc0a3d5981f2
+function shuffle_multithreaded_for_loop(N)
+	factorials = zeros(BigInt, N)
+	
+	Threads.@threads for i in shuffle(1:N)
+		factorials[i] = factorial(big(i))
+	end
+
+	return
+end
+
+# ╔═╡ e9dcda88-1eef-4c0a-99b2-12eaec56186b
+@btime shuffle_multithreaded_for_loop(N)
+
+# ╔═╡ 009bb2e8-f03e-40f7-a66b-166dc6a1962d
+md"""
+## Thread safety
+"""
+
+# ╔═╡ dd5e5073-be29-47e7-91c5-9e47c35f905c
+function thread_unsafe()
+	N = 100000
+	var = 0
+
+	Threads.@threads for i in 1:N
+		var += 1
+	end
+
+	return var
+end
+
+# ╔═╡ 4554cbf0-36f5-45c6-a966-ad18b1592a60
+# Run this cell multiple times.
+# The output is random 🤯
+thread_unsafe()
+
+# ╔═╡ ec08a80c-8886-4312-9481-5c89951681e1
+function thread_unsafe_sum(N)
+	sum_of_sums = 0
+
+	Threads.@threads for i in 1:N
+		sum_of_sums = sum(1:i)
+	end
+
+	return sum_of_sums
+end
+
+# ╔═╡ 3b5d9f7c-1fc9-4e85-8c07-8b5709895a10
+N2 = 1000000
+
+# ╔═╡ fbd2423b-aaea-47a7-a3cf-537860e11a93
+thread_unsafe_sum(N2)
+
+# ╔═╡ e65ad214-33ba-4d08-81f0-5f98022a9f78
+function thread_safe_sum(N)
+	sums = zeros(Int64, N)
+
+	Threads.@threads for i in 1:N
+		sums[i] = sum(1:i)
+	end
+
+	return sum(sums)
+end
+
+# ╔═╡ 8ad3daa6-d221-4ff7-9bc2-8e8a66bdd8c7
+@btime thread_safe_sum(N2)
+
+# ╔═╡ 95dffc7f-3393-487e-8521-c96291cdc7bf
+typemax(Int64)
+
+# ╔═╡ ebd3a9d9-7a12-4001-9b53-913f664fb1c8
+function shuffle_safe_thread_sum(N)
+	sums = zeros(Int64, N)
+
+	Threads.@threads for i in shuffle(1:N)
+		sums[i] = sum(1:i)
+	end
+
+	return sum(sums)
+end
+
+# ╔═╡ ddd2409e-de34-4eb9-a0b7-e10cc6c0ce9f
+# This is worse than the version without shuffeling.
+# In this case, shuffling is too expensive compared with its benefit
+# Especially for multithreading, there is no silver bullet.
+# Always benchmark! This is the only method to make sure that an "optimization" indeed an optimization is
+@btime shuffle_safe_thread_sum(N2)
 
 # ╔═╡ 09f71a9e-6798-492f-98df-45087d0c4c8b
 md"""
@@ -146,15 +308,94 @@ Julia has a focus on high performance. But if you don't pay attention, you might
 In this section, tools and tips for performance optimization in Julia are presented.
 """
 
-# ╔═╡ 2a24aebc-0654-4d00-bdab-627a8e1a75f2
+# ╔═╡ 6509dddd-ff17-49db-8e5e-fcea1ef0026c
+N3 = 1000000
 
+# ╔═╡ 2a24aebc-0654-4d00-bdab-627a8e1a75f2
+begin
+	sin_vals = []
+	
+	function global_allocating_access(N)
+		for i in 1:N
+			push!(sin_vals, sin(i))
+		end
+	
+		return
+	end
+
+	@btime global_allocating_access(N3)
+end
+
+# ╔═╡ 56058ab1-4ea2-479d-88f9-5da6ac8c39c2
+begin
+	typed_sin_vals = Float64[]
+	
+	function typed_global_allocating_access(N)
+		for i in 1:N
+			push!(typed_sin_vals, sin(i))
+		end
+	
+		return
+	end
+
+	@btime typed_global_allocating_access(N3)
+end
+
+# ╔═╡ ef164e7c-668a-4312-83f1-687ca7d4c8f9
+begin
+	preallocated_sin_vals = zeros(Float64, N3)
+	
+	function global_preallocated_access(N)
+		for i in 1:N
+			preallocated_sin_vals[i] = sin(i)
+		end
+	
+		return
+	end
+
+	@btime global_preallocated_access(N3)
+end
+
+# ╔═╡ ebc621b5-3aa3-4cf7-bcdf-e4c5fbb79f50
+begin
+	passed_preallocated_sin_vals = zeros(Float64, N3)
+	
+	function local_preallocated_access(N, sin_vals)
+		for i in 1:N
+			sin_vals[i] = sin(i)
+		end
+	
+		return
+	end
+
+	@btime local_preallocated_access(N3, passed_preallocated_sin_vals)
+end
+
+# ╔═╡ afcc15de-81e0-484f-80cf-3d805517c6e8
+# Here, the difference of preallocation is clearer
+begin
+	passed_sin_vals = Float64[]
+	
+	function local_access(N, sin_vals)
+		for i in 1:N
+			push!(sin_vals, sin(i))
+		end
+	
+		return
+	end
+
+	@btime local_access(N3, passed_sin_vals)
+end
 
 # ╔═╡ 00000000-0000-0000-0000-000000000001
 PLUTO_PROJECT_TOML_CONTENTS = """
 [deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [compat]
+BenchmarkTools = "~1.3.1"
 PlutoUI = "~0.7.38"
 """
 
@@ -180,6 +421,12 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[deps.BenchmarkTools]]
+deps = ["JSON", "Logging", "Printf", "Profile", "Statistics", "UUIDs"]
+git-tree-sha1 = "4c10eee4af024676200bc7752e536f858c6b8f93"
+uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+version = "1.3.1"
+
 [[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
 git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
@@ -298,6 +545,10 @@ version = "0.7.38"
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[deps.Profile]]
+deps = ["Printf"]
+uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -369,9 +620,38 @@ uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 # ╟─7f45c502-0909-42df-b93d-384f743df6a9
 # ╟─f23ad33d-af1d-40c2-9efc-17ef8c4d1fb8
 # ╟─6340aec8-6f77-4a30-8815-ce76ddecd6e8
-# ╠═d21771de-272e-4d57-8c76-c75be709ad0a
+# ╠═0e53e4ee-16a7-47ef-9992-77cbfd1ed258
+# ╠═7a9ccfbc-bd2e-41d0-be5d-dea04b90d397
+# ╠═d86e4a2f-e737-49a4-bc16-a149e81785bd
+# ╠═bc777c73-9573-41c3-8ab5-843335539f96
+# ╠═55d1d616-b6ee-40dd-a0ed-6274a98b1e73
+# ╠═00c27927-9c72-417a-862f-9b66318d9751
+# ╟─d21771de-272e-4d57-8c76-c75be709ad0a
+# ╠═2cf5f891-8d8f-477d-8ef1-9b4b9480d477
+# ╟─76866972-0290-4e33-93de-b6128ba11994
+# ╠═cacc94b4-21e0-410e-acaa-80e37b447f94
+# ╠═a3029480-bcdc-44f3-b504-8bd3bf3aa14d
+# ╠═8b1dfee2-bd8b-4d23-b9f8-9406002e0eaa
+# ╠═f141dbb4-bdc5-4f16-8d97-fc0a3d5981f2
+# ╠═e9dcda88-1eef-4c0a-99b2-12eaec56186b
+# ╠═009bb2e8-f03e-40f7-a66b-166dc6a1962d
+# ╠═dd5e5073-be29-47e7-91c5-9e47c35f905c
+# ╠═4554cbf0-36f5-45c6-a966-ad18b1592a60
+# ╠═ec08a80c-8886-4312-9481-5c89951681e1
+# ╠═3b5d9f7c-1fc9-4e85-8c07-8b5709895a10
+# ╠═fbd2423b-aaea-47a7-a3cf-537860e11a93
+# ╠═e65ad214-33ba-4d08-81f0-5f98022a9f78
+# ╠═8ad3daa6-d221-4ff7-9bc2-8e8a66bdd8c7
+# ╠═95dffc7f-3393-487e-8521-c96291cdc7bf
+# ╠═ebd3a9d9-7a12-4001-9b53-913f664fb1c8
+# ╠═ddd2409e-de34-4eb9-a0b7-e10cc6c0ce9f
 # ╟─09f71a9e-6798-492f-98df-45087d0c4c8b
+# ╠═6509dddd-ff17-49db-8e5e-fcea1ef0026c
 # ╠═2a24aebc-0654-4d00-bdab-627a8e1a75f2
+# ╠═56058ab1-4ea2-479d-88f9-5da6ac8c39c2
+# ╠═ef164e7c-668a-4312-83f1-687ca7d4c8f9
+# ╠═ebc621b5-3aa3-4cf7-bcdf-e4c5fbb79f50
+# ╠═afcc15de-81e0-484f-80cf-3d805517c6e8
 # ╟─1fb7d9af-333e-44f2-b693-09ff97937d4c
 # ╟─00000000-0000-0000-0000-000000000001
 # ╟─00000000-0000-0000-0000-000000000002