> For the complete documentation index, see [llms.txt](https://panav.gitbook.io/robotics-handbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://panav.gitbook.io/robotics-handbook/mathematical-and-programming-foundations/mathematical-and-programming-foundations.md).

# Mathematical & Programming Foundations (overview)

Mathematical and programming foundations - discrete math, graph theory, numerical methods, optimization, and advanced algorithms.

Beyond linear algebra and calculus, robotics requires discrete math (graph theory, optimization), numerical stability, and algorithm design.

### In this section

<table data-view="cards"><thead><tr><th></th><th data-type="content-ref"></th><th data-hidden data-card-cover data-type="files"></th></tr></thead><tbody><tr><td>Discrete Mathematics &#x26; Graph Theory</td><td><a href="/robotics-handbook/mathematical-and-programming-foundations/discrete-math.md">Discrete Mathematics &amp; Graph Theory</a></td><td><a href="https://923066007-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FJR2yBCOFnSaxfostbWYx%2Fuploads%2Fgit-blob-9ed35c5f0b20e2e54d95373352a26d0212fd51e8%2Fastar-pathfinding.gif?alt=media">astar-pathfinding.gif</a></td></tr><tr><td>Optimization Methods</td><td><a href="/robotics-handbook/mathematical-and-programming-foundations/optimization-methods.md">Optimization Methods</a></td><td><a href="https://923066007-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FJR2yBCOFnSaxfostbWYx%2Fuploads%2Fgit-blob-bc7d4b2caef841341dec83d28c434215076d8cf6%2Fgradient-descent.gif?alt=media">gradient-descent.gif</a></td></tr><tr><td>Numerical Methods</td><td><a href="/robotics-handbook/mathematical-and-programming-foundations/numerical-methods.md">Numerical Methods</a></td><td><a href="https://923066007-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FJR2yBCOFnSaxfostbWYx%2Fuploads%2Fgit-blob-019833b2d5b01cfd5af5d5ce33935e7c66834cb2%2Fnumerical-integration.gif?alt=media">numerical-integration.gif</a></td></tr><tr><td>Advanced Algorithms</td><td><a href="/robotics-handbook/mathematical-and-programming-foundations/advanced-algorithms.md">Advanced Algorithms</a></td><td><a href="https://923066007-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FJR2yBCOFnSaxfostbWYx%2Fuploads%2Fgit-blob-0153992d2be6effcd329fdf429c7cd6e8940dd15%2Frrt-path-planning.gif?alt=media">rrt-path-planning.gif</a></td></tr></tbody></table>