docs: improve language in root files (#2894)

I asked Gemini to review the English for inconsistencies and grammar
mistakes. This is the result and I hope it's useful!

As a non-native speaker, it is hard for me to evaluate the finer
details, so let me know if you would like to see changes (or even
better: make them directly in the PR with the suggestion function).

Author: mgeisler

README.md

@@ -18,14 +18,14 @@ Read the course at **https://google.github.io/comprehensive-rust/**.
 
 ## Course Format and Target Audience
 
-The course is used internally at Google when teaching Rust to experienced
-software engineers. They typically have a background in C++ or Java.
-
-The course is taught in a classroom setting and we hope it will be useful for
-others who want to teach Rust to their team. The course will be less useful for
-self-study since you miss out on the discussions happening in the classroom. You
-don't see the questions and answers and you don't see the compiler errors we
-trigger when going through the code samples. We hope to improve on this via
+The course is used internally at Google to teach Rust to experienced software
+engineers, typically with a background in C++ or Java.
+
+The course is taught in a classroom setting, and we hope it will be useful for
+others who want to teach Rust to their team. The course is less ideal for
+self-study, since you would miss out on classroom discussions. You would not see
+the questions and answers, nor the compiler errors we trigger when going through
+the code samples. We hope to improve the self-study experience via
 [speaker notes](https://github.com/google/comprehensive-rust/issues/53) and by
 [publishing videos](https://github.com/google/comprehensive-rust/issues/52).
 
@@ -44,7 +44,7 @@ Articles and blog posts from around the web which cover Comprehensive Rust:
   About how Microsoft, Google, and others are training people in Rust.
 - 2024-10-18:
   _[Rust Training at Scale | Rust Global @ RustConf 2024](https://youtu.be/7h5KyMqt2-Q?si=4M99HdWWxMaqN8Zr)_.
-  What Google learnt from teaching Comprehensive Rust for more than two years.
+  What Google learned from teaching Comprehensive Rust for more than two years.
 
 ## Setup
 
@@ -57,7 +57,7 @@ The course is built using a few tools:
 - [mdbook-course](mdbook-course/)
 - [mdbook-linkcheck2](https://github.com/marxin/mdbook-linkcheck2)
 
-First install Rust by following the instructions on https://rustup.rs/. Then
+First, install Rust by following the instructions on https://rustup.rs/. Then
 clone this repository:
 
 ```shell
@@ -93,8 +93,8 @@ Here are some of the commonly used commands you can run in the project. Run
 
 ## Contributing
 
-We would like to receive your contributions. Please see
-[CONTRIBUTING.md](CONTRIBUTING.md) for details.
+We welcome contributions. Please see [CONTRIBUTING.md](CONTRIBUTING.md) for
+details.
 
 ## Contact
 

src/index.md

@@ -32,7 +32,7 @@ Building on this, you're invited to dive into one or more specialized topics:
 
 - [Android](android.md): a half-day course on using Rust for Android platform
   development (AOSP). This includes interoperability with C, C++, and Java.
-- [Chromium](chromium.md): a half-day course on using Rust within Chromium based
+- [Chromium](chromium.md): a half-day course on using Rust in Chromium-based
   browsers. This includes interoperability with C++ and how to include
   third-party crates in Chromium.
 - [Bare-metal](bare-metal.md): a whole-day class on using Rust for bare-metal

src/welcome-day-1.md

@@ -26,9 +26,10 @@ Please remind the students that:
 - They should ask questions when they get them, don't save them to the end.
 - The class is meant to be interactive and discussions are very much encouraged!
   - As an instructor, you should try to keep the discussions relevant, i.e.,
-    keep the discussions related to how Rust does things vs some other language.
-    It can be hard to find the right balance, but err on the side of allowing
-    discussions since they engage people much more than one-way communication.
+    keep the discussions related to how Rust does things vs. some other
+    language. It can be hard to find the right balance, but err on the side of
+    allowing discussions since they engage people much more than one-way
+    communication.
 - The questions will likely mean that we talk about things ahead of the slides.
   - This is perfectly okay! Repetition is an important part of learning.
     Remember that the slides are just a support and you are free to skip them as