Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/erikaduan/introductory_maths

A repository of tutorials to revise mathematical concepts required for statistics and machine learning
https://github.com/erikaduan/introductory_maths

algebra calculus linear-algebra mathematics matrices python r

Last synced: about 2 months ago
JSON representation

A repository of tutorials to revise mathematical concepts required for statistics and machine learning

Awesome Lists containing this project

README 

        
# Introductory mathematics in R and Python    

This repository contains tutorials on the introductory mathematical concepts required for studying statistics and machine learning. Code to solve mathematical problems is written in `R`, `Python` and `Julia`.      



![](./figures/repo_logo.jpg)



## Tutorials    

|Topics|Tutorials|  

|:-----|:--------|  

|:1234:|[Introduction to numbers](./tutorials/numbers-introduction.md) (Updated)|    

|:1234:|[Introduction to algebra](./tutorials/algebra-introduction.md) (Updated)|   

|:1234:|[Introduction to functions](./tutorials/functions-introduction.md)|      

|:1234:|Introduction to summations|   

|:cookie:|[Introduction to set theory](./tutorials/set_theory-introduction.md)|  

|:cookie:|[Introduction to combinatorics](./tutorials/combinatorics-introduction.md)|   

|:black_joker:|[Introduction to probability theory](./tutorials/probability-introduction.md)|   

|:black_joker:|[Conditional probability](./tutorials/probability-conditional_probability.md)|   

|:black_joker:|Bayes theorem|   

|:roller_coaster:|[Introduction to derivatives](./tutorials/calculus-derivatives.md)|    

|:roller_coaster:| Introduction to integration |    

|:roller_coaster:| Differential equations |     

|:roller_coaster:| Multivariable functions  |      

|:roller_coaster:| Differentiation of multivariable functions  |    

|:1234:|Exponents and logarithms|   

|:1234:|Logarithms and information theory|  

|:compass:|Introduction to trigonometry|  

|:compass:|Introduction to distance metrics|   

|:compass:|Cosine similarity applications|   

|:chopsticks:|[Introduction to linear systems](./tutorials/linear_algebra-linear_systems.md)|   

|:chopsticks:|[Introduction to vectors](./tutorials/linear_algebra-vectors.md)|   

|:chopsticks:|Vector norms and embeddings|    

|:department_store:|[Introduction to matrices](./tutorials/linear_algebra-matrices.md)|    

|:chopsticks:|[Linear transformations](./tutorials/linear_algebra-linear_transformations.md)|    

|:chopsticks:|Applications of eigenvalues and eigenvectors|      



## Contributors

+ [Erika Duan](https://github.com/erikaduan/)  

+ [Chuanxin Liu](https://github.com/codetrainee)   



## Project setup   

This project was created using the following setup:     

+ R package dependencies are managed using renv for R version 4.1.2 (2021-11-01).   

+ Python virtual environment and package dependencies are managed using [`poetry`](https://python-poetry.org/docs/basic-usage/) for `Python 3.9.6`. A local version of `Python 3.9.6` was installed and activated using `pyenv local 3.9.6` via the terminal.      

+ The Julia version used is `julia version 1.7.3`.    



## Guide to writing mathematical proofs    

Writing mathematical proofs might feel archaic but they are a great way to help you reason why mathematical concepts should behave consistently (and not just because your textbook says so). There are multiple approaches to proving a mathematical statement or concept. Sadly, there is no magical rule to selecting the correct method for each scenario - mathematicians often have to try multiple approaches before they find the right one.        



**Direct proof**   

+ Occurs when you need to prove that A and B are equivalent.   

+ Start by assuming A is true.   

+ Construct a definition statement for A (use a fixed but arbitary example of A).   

+ Extend and simplify mathematical definitions derived from A to reach B.   

+ When you are asked if A and **only** A is true, then B is true, first suppose A to reach B. Then suppose B to reach A.   



**Induction proof**  

+ Occurs when you need to prove that something is true for all cases.  

+ Start by proving the base case when $n = 1$.  

+ Assume that the case is also true for some integer $k$.  

+ Prove that the case for $k + 1$ also holds i.e. prove the next incremental step up a ladder stretching to infinity.  



**Uniqueness proof**  

+ Occurs when you need to prove that a solution is unique.  

+ Show that there is one solution first.   

+ Show that there is a second solution and that the first and second solutions must be equal.   



**Proof by contradiction**   

+ Start by assuming that the incorrect state is true i.e. that eigenvectors are linearly dependent.    

+ Prove that the assumption does not hold and contradicts itself.    

+ Therefore prove that the reverse state is actually true.   



## References  

+ A guide to [linear algebra](https://pabloinsente.github.io/intro-linear-algebra) for applied machine learning by Pablo Caceres

+ The [Mathematics for Machine Learning textbook](https://mml-book.github.io/book/mml-book.pdf) by Marc Peter Deisenroth, A Aldo Faisal and Cheng Soon Ong - Cambridge University Press

+ The [Probability for Data Science textbook](https://probability4datascience.com/) by Stanley H Chan - Michigan Publishing

+ The [Probabilistic modelling tutorials](https://betanalpha.github.io/writing/) by Michael Betancourt - GitHub

+ Writing [mathematical operations in LaTex/R](https://en.wikibooks.org/wiki/LaTeX/Mathematics#Fractions_and_Binomials) - Wikibooks  

+ Introduction to university mathematics [YouTube lecture series ]https://www.youtube.com/playlist?list=PL4d5ZtfQonW1xKVEtYJd1iu9m52ATG7SV by the Department of Mathematics - Oxford University.