{"id":13680847,"url":"https://github.com/erikaduan/introductory_maths","last_synced_at":"2025-04-30T00:31:08.713Z","repository":{"id":40341466,"uuid":"227992771","full_name":"erikaduan/introductory_maths","owner":"erikaduan","description":"Simple summaries of mathematical concepts required for statistics and machine learning","archived":false,"fork":false,"pushed_at":"2025-01-30T05:15:44.000Z","size":12326,"stargazers_count":8,"open_issues_count":0,"forks_count":6,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-01-30T06:20:54.843Z","etag":null,"topics":["algebra","calculus","linear-algebra","mathematics","matrices","python","r"],"latest_commit_sha":null,"homepage":"","language":"HTML","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"cc0-1.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/erikaduan.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2019-12-14T08:48:26.000Z","updated_at":"2025-01-30T05:27:51.000Z","dependencies_parsed_at":"2023-11-28T03:50:34.473Z","dependency_job_id":null,"html_url":"https://github.com/erikaduan/introductory_maths","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/erikaduan%2Fintroductory_maths","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/erikaduan%2Fintroductory_maths/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/erikaduan%2Fintroductory_maths/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/erikaduan%2Fintroductory_maths/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/erikaduan","download_url":"https://codeload.github.com/erikaduan/introductory_maths/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":251607506,"owners_count":21616776,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["algebra","calculus","linear-algebra","mathematics","matrices","python","r"],"created_at":"2024-08-02T13:01:22.772Z","updated_at":"2025-04-30T00:31:03.702Z","avatar_url":"https://github.com/erikaduan.png","language":"HTML","funding_links":[],"categories":["1B. Learning Resources - Programming"],"sub_categories":["Table of Contents"],"readme":"# Introductory mathematics in R and Python    \r\nThis 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`.      \r\n\r\n![](./figures/repo_logo.jpg)\r\n\r\n## Tutorials    \r\n|Topics|Tutorials|  \r\n|:-----|:--------|  \r\n|:1234:|[Introduction to numbers](./tutorials/numbers-introduction.md) (Updated)|    \r\n|:1234:|[Introduction to algebra](./tutorials/algebra-introduction.md) (Updated)|   \r\n|:1234:|[Introduction to functions](./tutorials/functions-introduction.md)|      \r\n|:1234:|Introduction to summations|   \r\n|:cookie:|[Introduction to set theory](./tutorials/set_theory-introduction.md)|  \r\n|:cookie:|[Introduction to combinatorics](./tutorials/combinatorics-introduction.md)|   \r\n|:black_joker:|[Introduction to probability theory](./tutorials/probability-introduction.md)|   \r\n|:black_joker:|[Conditional probability](./tutorials/probability-conditional_probability.md)|   \r\n|:black_joker:|Bayes theorem|   \r\n|:roller_coaster:|[Introduction to derivatives](./tutorials/calculus-derivatives.md)|    \r\n|:roller_coaster:| Introduction to integration |    \r\n|:roller_coaster:| Differential equations |     \r\n|:roller_coaster:| Multivariable functions  |      \r\n|:roller_coaster:| Differentiation of multivariable functions  |    \r\n|:1234:|Exponents and logarithms|   \r\n|:1234:|Logarithms and information theory|  \r\n|:compass:|Introduction to trigonometry|  \r\n|:compass:|Introduction to distance metrics|   \r\n|:compass:|Cosine similarity applications|   \r\n|:chopsticks:|[Introduction to linear systems](./tutorials/linear_algebra-linear_systems.md)|   \r\n|:chopsticks:|[Introduction to vectors](./tutorials/linear_algebra-vectors.md)|   \r\n|:chopsticks:|Vector norms and embeddings|    \r\n|:department_store:|[Introduction to matrices](./tutorials/linear_algebra-matrices.md)|    \r\n|:chopsticks:|[Linear transformations](./tutorials/linear_algebra-linear_transformations.md)|    \r\n|:chopsticks:|Applications of eigenvalues and eigenvectors|      \r\n\r\n## Contributors\r\n+ [Erika Duan](https://github.com/erikaduan/)  \r\n+ [Chuanxin Liu](https://github.com/codetrainee)   \r\n\r\n## Project setup   \r\nThis project was created using the following setup:     \r\n+ R package dependencies are managed using renv for R version 4.1.2 (2021-11-01).   \r\n+ 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.      \r\n+ The Julia version used is `julia version 1.7.3`.    \r\n\r\n## Guide to writing mathematical proofs    \r\nWriting 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.        \r\n\r\n**Direct proof**   \r\n+ Occurs when you need to prove that A and B are equivalent.   \r\n+ Start by assuming A is true.   \r\n+ Construct a definition statement for A (use a fixed but arbitary example of A).   \r\n+ Extend and simplify mathematical definitions derived from A to reach B.   \r\n+ 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.   \r\n\r\n**Induction proof**  \r\n+ Occurs when you need to prove that something is true for all cases.  \r\n+ Start by proving the base case when $n = 1$.  \r\n+ Assume that the case is also true for some integer $k$.  \r\n+ Prove that the case for $k + 1$ also holds i.e. prove the next incremental step up a ladder stretching to infinity.  \r\n\r\n**Uniqueness proof**  \r\n+ Occurs when you need to prove that a solution is unique.  \r\n+ Show that there is one solution first.   \r\n+ Show that there is a second solution and that the first and second solutions must be equal.   \r\n\r\n**Proof by contradiction**   \r\n+ Start by assuming that the incorrect state is true i.e. that eigenvectors are linearly dependent.    \r\n+ Prove that the assumption does not hold and contradicts itself.    \r\n+ Therefore prove that the reverse state is actually true.   \r\n\r\n## References  \r\n+ A guide to [linear algebra](https://pabloinsente.github.io/intro-linear-algebra) for applied machine learning by Pablo Caceres\r\n+ 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\r\n+ The [Probability for Data Science textbook](https://probability4datascience.com/) by Stanley H Chan - Michigan Publishing\r\n+ The [Probabilistic modelling tutorials](https://betanalpha.github.io/writing/) by Michael Betancourt - GitHub\r\n+ Writing [mathematical operations in LaTex/R](https://en.wikibooks.org/wiki/LaTeX/Mathematics#Fractions_and_Binomials) - Wikibooks  \r\n+ Introduction to university mathematics [YouTube lecture series ]https://www.youtube.com/playlist?list=PL4d5ZtfQonW1xKVEtYJd1iu9m52ATG7SV by the Department of Mathematics - Oxford University.  \r\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ferikaduan%2Fintroductory_maths","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ferikaduan%2Fintroductory_maths","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ferikaduan%2Fintroductory_maths/lists"}