docs fix spelling issues

CONTRIBUTING.md

@@ -5,7 +5,7 @@
 
 Thank you for considering making contributions to `arkworks-rs/$REPO_NAME`!
 
-Contributing to this repo can be done in several forms, such as participating in discussion or proposing code changes. 
+Contributing to this repo can be done in several forms, such as participating in discussions or proposing code changes. 
 To ensure a smooth workflow for all contributors, the following general procedure for contributing has been established:
 
 1) Either open or find an issue you'd like to help with
@@ -33,7 +33,7 @@ All other branches should be assumed to be miscellaneous feature development bra
 All downstream users of the library should be using tagged versions of the library pulled from cargo.
 
 ## How to work on a fork
-Please skip this section if you're familiar with contributing to opensource github projects.
+Please skip this section if you're familiar with contributing to open-source github projects.
 
 First fork the repo from the github UI, and clone it locally.
 Then in the repo, you want to add the repo you forked from as a new remote. You do this as:
@@ -53,16 +53,16 @@ and then work as normal on that branch, and pull request to upstream master when
 ## Updating documentation
 
 All PRs should aim to leave the code more documented than it started with.
-Please don't assume that its easy to infer what the code is doing,
+Please don't assume that it's easy to infer what the code is doing,
 as that is almost always not the case for these complex protocols.
 (Even when you understand the paper!)
 
-Its often very useful to describe what is the high level view of what a code block is doing,
+It's often very useful to describe what is the high level view of what a code block is doing,
 and either refer to the relevant section of a paper or include a short proof/argument for why it makes sense before the actual logic.
 
 ## Performance improvements
 
 All performance improvements should be accompanied with benchmarks improving, or otherwise have it be clear that things have improved.
 For some areas of the codebase, performance roughly follows the number of field multiplications, but there are also many areas where
 hard to predict low level system effects such as cache locality and superscalar operations become important for performance.
-Thus performance can often become very non-intuitive / diverge from minimizing the number of arithmetic operations.
+Thus performance can often become very non-intuitive / diverge from minimizing the number of arithmetic operations.

README.md

@@ -33,7 +33,7 @@ verification logic can be delayed to query and decision phase.
 - This implementation has low-degree test built-in, and can handle RS-IOP.
 - Multiple oracles with same evaluation domain share a merkle tree and be submitted in one round, which greatly reduces
   verification overhead and number of constraints.
-- Each leaf of an low-degree oracle is a coset instead of an individual field element, which significantly reduces
+- Each leaf of a low-degree oracle is a coset instead of an individual field element, which significantly reduces
   merkle tree overhead on FRI query.
 
 ## Build Guide
@@ -67,7 +67,7 @@ This library is licensed under either of the following licenses, at your discret
 * [Apache License Version 2.0](LICENSE-APACHE)
 * [MIT License](LICENSE-MIT)
 
-Unless you explicitly state otherwise, any contribution that you submit to this library shall be dual licensed as
+Unless you explicitly state otherwise, any contribution that you submit to this library shall be dual-licensed as
 above (as defined in the Apache v2 License), without any additional terms or conditions.
 
 ## Reference papers

sumcheck/src/protocol.rs

@@ -195,7 +195,7 @@ impl<F: PrimeField + Absorb> UnivariateSumcheck<F> {
         );
     }
 
-    // there is no need to do query phase. LDT will fail is sum is incorrect.
+    // there is no need to do query phase. LDT will fail if sum is incorrect.
 }
 
 #[cfg(test)]