{"id":21451761,"url":"https://github.com/ostad-ai/computer-science","last_synced_at":"2025-03-17T02:42:36.677Z","repository":{"id":139753289,"uuid":"419758667","full_name":"ostad-ai/Computer-Science","owner":"ostad-ai","description":"Computer Science and related topics are the main focus of this repository. Mainly, Python language is used here.","archived":false,"fork":false,"pushed_at":"2025-01-08T17:37:17.000Z","size":3621,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-01-23T12:29:44.482Z","etag":null,"topics":["algorithms","computer-science","cramers-rule","divide-and-conquer","dynamic-programming","fast-fourier-transform","linked-list","matrix-inversion","python","root-finding"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ostad-ai.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"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":"2021-10-21T14:33:53.000Z","updated_at":"2025-01-08T17:37:20.000Z","dependencies_parsed_at":"2024-12-30T18:29:37.399Z","dependency_job_id":"fdda3f26-0735-421d-8f0a-616e12496a8c","html_url":"https://github.com/ostad-ai/Computer-Science","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/ostad-ai%2FComputer-Science","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ostad-ai%2FComputer-Science/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ostad-ai%2FComputer-Science/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ostad-ai%2FComputer-Science/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ostad-ai","download_url":"https://codeload.github.com/ostad-ai/Computer-Science/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243964489,"owners_count":20375786,"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":["algorithms","computer-science","cramers-rule","divide-and-conquer","dynamic-programming","fast-fourier-transform","linked-list","matrix-inversion","python","root-finding"],"created_at":"2024-11-23T04:25:43.343Z","updated_at":"2025-03-17T02:42:36.656Z","avatar_url":"https://github.com/ostad-ai.png","language":"Jupyter Notebook","readme":"# Computer-Science \nPrograms related to the field of Computer Science are expessed here. More on Computer Science is at the following link:\nhttps://www.pinterest.com/HamedShahHosseini/\n\n1) **Determinant from scratch** with Python by converting matrix to triangular one.\n2) **Cramer's rule** for solving a system of linear equations.\n3) **Matrix inversion by the cofactor matrix** from scratch in Python. \n4) **Matrix inversion by Gauss-Jordan elimination** from scratch in Python. \n5) **Fast Fourier Transform (FFT), one-dimensional,** from scratch in Python. Also, Discrete Fourier Transform (DFT) from scratch is also included.\n6) **Divide and Conquer:** Quicksort from scratch in Python. \n7) **Dynamic Programming:** Fibonacci numbers in Python.\n8) **Singly Linked Lists** from scratch with Python. An example is also given to implement a stack having functions: push and pop. \n9) **Complex numbers, introduction:** Here, we review complex numbers in both rectangular and polar forms by reminding Euler's formula and De Moivre's formula. Also, we review doing arithmetic for complex numbers in Python.\n10) **Absolute and relative errors** are reviewed. When we don't know the true value, we may use approximate value in measuring the mentioned errors. A Python example is also provided.\n11) **Root finding, Bisection method:** It is a bracketing method to find one root of a continuous function, given the interval [a,b] in which the root exists. It is assumed that f(a)f(b)\u003c0. \n12) **Root finding, False Position method:** This root finding method is also a bracketing method with the same assumptions we make for the bisection method. However, it is usually faster than the bisection method.\n13) **Root finding, Fixed Point Iteration:** This is an open method such that it starts by an initial guess of the root, and then it uses an iteration to get closer to the real root.\n14) **Root finding, Secant method:** We give two initial guesses of the root. Then, the method creates a secant line which intersects the x-axis at a value that is usually a better estimate of the root.\n15) **Matrix-vector multiplication as a linear combination:** It is possible to express the product of a matrix by a vector as a linear combination of the columns of the matrix by the components of the vector as weights. Here, we mention this property with an example in Python code.\n16) **Trace of a matrix:** *Trace* is defined on a *square* matrix, which is the sum of the elements on the *main diagonal* of the matrix. We review the trace function with some properties of the trace. Also, we check those properties in an example with Python code.\n17) **Determinant:** Determinant is reviewed again here with some of its properties. The *Laplace expansion* is also mentioned. Moreover, **minors** and **cofactors** of the given matrix are computed. 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