README.md

@@ -1,53 +1,54 @@
 # KMath
-Kotlin MATHematics library is intended as a kotlin based analog of numpy python library. Contrary to `numpy`
-and `scipy` it is modular and has a lightweight core.
+The Kotlin MATHematics library is intended as a Kotlin-based analog to Python's `numpy` library. In contrast to `numpy` and `scipy` it is modular and has a lightweight core.
 
 ## Features
 
 * **Algebra**
-    * Mathematical operation entities like rings, spaces and fields with (**TODO** add example to wiki) 
-    * Basic linear algebra operations (summs products, etc) backed by `Space` API.
-    * Complex numbers backed by `Field` API (meaning that they will be useable in any structures like vectors and NDArrays).
-    * [In progress] advanced linear algebra operations like matrix inversions.
-* **Array-like structures** Full support of numpy-like ndarray including mixed arithmetic operations and function operations
-on arrays and numbers just like it works in python (with benefit of static type checking).
+    * Algebraic structures like rings, spaces and field (**TODO** add example to wiki)
+    * Basic linear algebra operations (sums, products, etc.), backed by the `Space` API.
+    * Complex numbers backed by the `Field` API (meaning that they will be usable in any structure like vectors and N-dimensional arrays).
+    * [In progress] advanced linear algebra operations like matrix inversion and LU decomposition.
+* **Array-like structures** Full support of [numpy-like ndarrays](https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.ndarray.html) including mixed arithmetic operations and function operations over arrays and numbers just like in Python (with the added benefit of static type checking).
 
-* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
-expression once an then apply it to different types of objects by providing different context. Exception could be used
-for a wide variety of purposes from high performance calculations to code generation.
+* **Expressions** Expressions are one of the ultimate goals of KMath. By writing a single mathematical expression
+once, users will be able to apply different types of objects to the expression by providing a context. Exceptions
+can be used for a wide variety of purposes from high performance calculations to code generation.
 
 ## Planned features
 
 * **Common mathematics** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/) 
-library in kotlin code and maybe rewrite some parts to better suite kotlin programming paradigm. There is no fixed priority list for that. Feel free
-to submit a future request if you want something to be done first.
+library in Kotlin code and maybe rewrite some parts to better suit the Kotlin programming paradigm, however there is no fixed roadmap for that. Feel free
+to submit a feature request if you want something to be done first.
 
 * **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.
 
 ## Multi-platform support
-KMath is developed as a multi-platform library, which means that most of interfaces are declared in common module.
-Implementation is also done in common module wherever it is possible. In some cases features are delegated to 
-platform even if they could be done in common module because of platform performance optimization. 
-Currently the main focus of development is the JVM platform, contribution of implementations for Kotlin - Native and
-Kotlin - JS is welcome. 
+
+KMath is developed as a multi-platform library, which means that most of interfaces are declared in the [common module](kmath-core/src/commonMain).
+Implementation is also done in the common module wherever possible. In some cases, features are delegated to
+platform-specific implementations even if they could be done in the common module for performance reasons.
+Currently, the JVM is the main focus of development, however Kotlin/Native and Kotlin/JS contributions are also welcome.
 
 ## Performance
-The calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve 
-both performance and flexibility. We expect to firstly focus on creating convenient universal API and then work on 
-increasing performance for specific cases. We expect the worst KMath performance still be better than natural python,
-but worse than optimized native/scipy (mostly due to boxing operations on primitive numbers). The best performance 
-of optimized parts should be better than scipy.
+
+Calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve
+both performance and flexibility. We expect to focus on creating convenient universal API first and then work on
+increasing performance for specific cases. We expect the worst KMath benchmarks will perform better than native Python,
+but worse than optimized native/SciPy (mostly due to boxing operations on primitive numbers). The best performance
+of optimized parts should be better than SciPy.
 
 ## Releases
 
-The project is currently in pre-release stage. Nightly builds could be used by adding additional repository to (groovy) gradle config:
+The project is currently in pre-release stage. Nightly builds can be used by adding an additional repository to the Gradle config like so:
+
 ```groovy
 repositories {
     maven { url = "http://npm.mipt.ru:8081/artifactory/gradle-dev" }
     mavenCentral()
 } 
 ```
-or for kotlin gradle dsl:
+
+or for the Gradle Kotlin DSL:
 
 ```kotlin
 repositories {
@@ -56,16 +57,20 @@ repositories {
 } 
 ```
 
-Then use regular dependency like
+Then use a regular dependency like so:
+
 ```groovy
 compile(group: 'scientifik', name: 'kmath-core', version: '0.0.1-SNAPSHOT')
 ```
-or in kotlin
+
+or in the Gradle Kotlin DSL:
+
 ```kotlin
 compile(group = "scientifik", name = "kmath-core", version = "0.0.1-SNAPSHOT")
 ```
 
-Work builds could be obtained with [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath). 
+Working builds can be obtained here: [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath).
 
 ## Contributing
-The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.
+
+The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.