docs: fix typos in tutorial

docs/tutorial/getting_started.md

@@ -14,7 +14,7 @@ Algobattle website. On the specific problem's page you can then download an Algo
 file with the `.algo` extension. This file contains all the information we need.
 
 !!! info "A peek behind the curtain" Despite their very fancy looking extension, `.algo` files
-really just zip files with a few files inside. Algobattle uses these to set up your project folders
+really are just zip files with a few files inside. Algobattle uses these to set up your project folders
 for you, but it doesn't handle things very well if you feed it data that doesn't have that
 structure, so the file extension is there to remind you that you're not meant to process these files
 manually. If you're curious you can unzip them and take a look inside yourself.

docs/tutorial/installation.md

@@ -63,7 +63,7 @@ For more examples and ideas, visit:
 
 ## Installing Algobattle
 
-Algobattle is a Python package and unfortunately Python version and depenency management is kind of
+Algobattle is a Python package and unfortunately Python version and dependency management is kind of
 a mess. Luckily there's a great tool called uv that solves all of those hassles for us. Throughout
 this tutorial, we'll show you the correct commands to use when you have it installed, but if you
 prefer to manage your Python setup yourself you can just install the `algobattle-base` package

docs/tutorial/match.md

@@ -50,12 +50,12 @@ Algobattle is doing and what the interface is trying to tell us.
 
 ## Building programs
 
-The First part of a match is building every team's programs. Depending on how complicated they are this may take a
+The first part of a match is building every team's programs. Depending on how complicated they are this may take a
 little while. During this step Algobattle gets all the programs ready for execution, compiles and installs them, etc.
 
 ??? question "You can't just skip over what's actually happening!"
     Yes I can :wink:. The actual details of this are somewhat complicated if you're not familiar with Docker (and if
-    you are, you'll have already figured our what's going on) so we recommend skipping over this for now. We recommend
+    you are, you'll have already figured out what's going on) so we recommend skipping over this for now. We recommend
     skipping over the details here for now and if you still want to learn more later you can check out the
     [advanced guide on Docker](../advanced/docker.md#building-images).
 

docs/tutorial/programs.md

@@ -117,7 +117,7 @@ The important file here is `generator.py`, we need to put the code that we want
     already filled out with the data we need so we can just leave it as is for now.
 
 ??? question "What's `Dockerfile`?"
-    This is the file that specified what Docker is supposed to do with our code. What exactly Docker does and what the
+    This is the file that specifies what Docker is supposed to do with our code. What exactly Docker does and what the
     Dockerfile says is rather complicated and not super important for us right now. It's explained in detail in the
     [Docker guide](../advanced/docker.md).
 
@@ -171,7 +171,7 @@ us to stick to some given upper limit of size of instance we make.
 The code then writes things to the output directory, but it doesn't just write the instance, it also writes a solution.
 It might seem weird at first, but many problems do require the generator to not only come up with an instance, but also
 solve it. This is to make sure that the instance does indeed have a solution. Otherwise, we could just make some list
-of numbers were no two pairs have the same sum and then always win no matter how good the other teams' solvers are!
+of numbers where no two pairs have the same sum and then always win no matter how good the other teams' solvers are!
 
 
 ### Writing the code
@@ -262,7 +262,7 @@ The solver takes an instance and should produce a solution for it. Similar to th
 `/input` and `/output` directory, but this time called `/input/instance.json` and `/output/solution.json` as you'd
 expect. Since we're already familiar with this I/O structure we can get right into writing the actual program.
 
-This will again widely vary based on how you choose to do things, We've got our rust example solver here:
+This will again vary widely based on how you choose to do things. We've got our rust example solver here:
 
 !!! example "Example solver"
     This solver just iterates over all possible combinations of four numbers in the input list and checks if they form