![3Blue1Brown]({"thumbnails":[{"url":"https://i.ytimg.com/vi/rB83DpBJQsE/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDT2cDGyrvrrQyrcLKyysFOprEd4w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/rB83DpBJQsE/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLD_RCemXOTkm2qkqrWTV3DdsfjXkA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/rB83DpBJQsE/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLBe7-WEzW0IFjK1IXVbHGZdVdCBGA","width":246,"height":138},{"url":"https://i.ytimg.com/vi/rB83DpBJQsE/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCkCF3FNk9jDl8-Nz_2ND4-TXmHuQ","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/rB83DpBJQsE/maxresdefault.webp","width":1920,"height":1080}]})
Transcripts of 3Blue1Brown - 49 Videos
49 videos•212.0M views•156.4K words•Avg 4.3M views per video•Avg 3.2K words per transcript•Avg 9 words per title
3Blue1Brown videos - Read, search, and download full transcripts from all 49 videos. Access transcripts with timestamps, word counts, and more.
Page 1 of 3Next
Related Channels
About 3Blue1Brown Transcripts
Browse and read full transcripts from 3Blue1Brown's videos. We've transcribed 49 videos with a total of 156.4K words. Perfect for studying, referencing, or catching up on content you might have missed.
![But what is the Central Limit Theorem?]({"thumbnails":[{"url":"https://i.ytimg.com/vi/zeJD6dqJ5lo/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDBkMnok-8C6V0vg_HbH4cSu6zb-A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/zeJD6dqJ5lo/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLCsa00yelckra46ZpfQLETNj63Ucw","width":196,"height":110},{"url":"https://i.ytimg.com/vi/zeJD6dqJ5lo/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCdfmxWri_0bMLvRK422_hes6zVpw","width":246,"height":138},{"url":"https://i.ytimg.com/vi/zeJD6dqJ5lo/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCndMa7zReeqw_AcKPUOUo6XO7Uyg","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/zeJD6dqJ5lo/maxresdefault.webp","width":1920,"height":1080}]})
![But what is a Fourier series? From heat flow to drawing with circles | DE4]({"thumbnails":[{"url":"https://i.ytimg.com/vi/r6sGWTCMz2k/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLD8gpzbpv6rYHdfJfrjfivoDQXc5g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/r6sGWTCMz2k/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLBxrZVfIC2t_GQSlvGSlI58a8bCRQ","width":196,"height":110},{"url":"https://i.ytimg.com/vi/r6sGWTCMz2k/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDhOse5eTTPD5ANfixiS_4oMqum-Q","width":246,"height":138},{"url":"https://i.ytimg.com/vi/r6sGWTCMz2k/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDtf1d2LLjZjC4StbwOlwCVz7Y9UA","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/r6sGWTCMz2k/maxresdefault.webp","width":1920,"height":1080}]})
![What makes a great math explanation? | SoME2 results]({"thumbnails":[{"url":"https://i.ytimg.com/vi/cDofhN-RJqg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDzuBY33Usa3masj9k1-5TiAp8-fw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/cDofhN-RJqg/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLB76Tzbm_Gnrv1GcFbeLsE84XzeOg","width":196,"height":110},{"url":"https://i.ytimg.com/vi/cDofhN-RJqg/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLBv16p9dV6xmU5-7wRDVA_sDe5CVg","width":246,"height":138},{"url":"https://i.ytimg.com/vi/cDofhN-RJqg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAD9tktzIOgh6mVxbseZbFUBdQbYA","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/cDofhN-RJqg/maxresdefault.webp","width":1920,"height":1080}]})
![Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/k7RM-ot2NWY/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLAwpFZgZ5FDjBLvCTQfheYF15x5yw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/k7RM-ot2NWY/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLBgos5R2VcbMF_vkVw6HjUReNIIMA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/k7RM-ot2NWY/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAnYLor7URvaQcYu4O2748vD5Tiew","width":246,"height":138},{"url":"https://i.ytimg.com/vi/k7RM-ot2NWY/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLB18MevnnLPiyJ0V7i6NhGgG_Bxow","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/k7RM-ot2NWY/maxresdefault.webp","width":1920,"height":1080}]})
![Linear transformations and matrices | Chapter 3, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/kYB8IZa5AuE/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLCsXtktTzOBi9zzA4aT2RsUgV3eMw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/kYB8IZa5AuE/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLCDNzrHjqSacu65M40IBqQGXGd0qA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/kYB8IZa5AuE/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCyDwI2iW0oYklBUcLK4pP_EZpnmw","width":246,"height":138},{"url":"https://i.ytimg.com/vi/kYB8IZa5AuE/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAS8UbhRPQiVi2HR6jc1wWst-RF3A","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/kYB8IZa5AuE/maxresdefault.webp","width":1920,"height":1080}]})
![Attention in transformers, visually explained | DL6]({"thumbnails":[{"url":"https://i.ytimg.com/vi/eMlx5fFNoYc/hqdefault.jpg?sqp=-oaymwEmCKgBEF5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLAMDJ6VmxTiQdr44_eKBclWSA00mg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/eMlx5fFNoYc/hqdefault.jpg?sqp=-oaymwEmCMQBEG5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLCRazq5jewxTL3CvZRTWoVrc7AKcA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/eMlx5fFNoYc/hqdefault.jpg?sqp=-oaymwEnCPYBEIoBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLDNEVO04pVWwfB0FEDpGZraWYgggA","width":246,"height":138},{"url":"https://i.ytimg.com/vi/eMlx5fFNoYc/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLDyNnrTCksDmoyiwj9S_a51WSU_LQ","width":336,"height":188},{"url":"https://i.ytimg.com/vi/eMlx5fFNoYc/maxresdefault.jpg","width":1920,"height":1080}]})
![But what is the Fourier Transform? A visual introduction.]({"thumbnails":[{"url":"https://i.ytimg.com/vi/spUNpyF58BY/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLB_6ArRDuk8DgQa8OcFW9YrFWKpyQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/spUNpyF58BY/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLA1Ybu84FFPmCP3x1L28kSvEhcasA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/spUNpyF58BY/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLABCyD3VVctqDt4wbODVkQufJjX6A","width":246,"height":138},{"url":"https://i.ytimg.com/vi/spUNpyF58BY/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAV7TBVafnzr4YjqpUFsazhAbdivg","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/spUNpyF58BY/maxresdefault.webp","width":1920,"height":1080}]})
![Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLD1-NoCqVbo6D5jYH3BrdtXQO1m7g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDiDR_aeL2JQPztFxO0wPn3fr7uPA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLABeAIQGaD6TAHv5qC2fQfbKdmqIg","width":246,"height":138},{"url":"https://i.ytimg.com/vi/PFDu9oVAE-g/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDrj_RNyJZk3-SATcjV0k78CL65zA","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/PFDu9oVAE-g/maxresdefault.webp","width":1920,"height":1080}]})
![Taylor series | Chapter 11, Essence of calculus]({"thumbnails":[{"url":"https://i.ytimg.com/vi/3d6DsjIBzJ4/hqdefault.jpg?sqp=-oaymwEmCKgBEF5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLAAo9aoPZJsgUVE5N3fHrF5fsLd3A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/3d6DsjIBzJ4/hqdefault.jpg?sqp=-oaymwEmCMQBEG5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLD3PjmyzMHCyuYXF2cvm9W0nd36uA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/3d6DsjIBzJ4/hqdefault.jpg?sqp=-oaymwEnCPYBEIoBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLAxG-gBpeo4OwJui3IR5j-ojeOBXA","width":246,"height":138},{"url":"https://i.ytimg.com/vi/3d6DsjIBzJ4/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLC7eY5y0O1TVSsRdlgveqLyyJGQyg","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/3d6DsjIBzJ4/maxresdefault.webp","width":1920,"height":1080}]})
![How are holograms possible?]({"thumbnails":[{"url":"https://i.ytimg.com/vi/EmKQsSDlaa4/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLATsGYNiP74EuiyHVy_CiClvBf48Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/EmKQsSDlaa4/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLAQZZJ0dzilvYUM0b66ZxAOYTw3mw","width":196,"height":110},{"url":"https://i.ytimg.com/vi/EmKQsSDlaa4/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCWXdYBWxuUKCbi3po1VSeTnm8FMQ","width":246,"height":138},{"url":"https://i.ytimg.com/vi/EmKQsSDlaa4/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAg-dA-dW_qZQXE6Y1H0TJflQqqIA","width":336,"height":188},{"url":"https://i.ytimg.com/vi/EmKQsSDlaa4/maxresdefault.jpg","width":1920,"height":1080}]})
![How I animate 3Blue1Brown | A Manim demo with Ben Sparks]({"thumbnails":[{"url":"https://i.ytimg.com/vi/rbu7Zu5X1zI/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLAqItEYWT4ugumr-C0G16As-chPxw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/rbu7Zu5X1zI/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDDmKosVnzdiPlccX5pgiXBP6W5oA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/rbu7Zu5X1zI/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAbbqsnOTEA-HiuYg0IqMrjlPOQEQ","width":246,"height":138},{"url":"https://i.ytimg.com/vi/rbu7Zu5X1zI/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAelba4twblsla_QutoOFP7e0m5zA","width":336,"height":188},{"url":"https://i.ytimg.com/vi/rbu7Zu5X1zI/maxresdefault.jpg","width":1920,"height":1080}]})
![Essence of linear algebra preview]({"thumbnails":[{"url":"https://i.ytimg.com/vi/kjBOesZCoqc/hqdefault.jpg?sqp=-oaymwEmCKgBEF5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLChD12Q1aDB0LME9QIFMFUXmTcqjQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/kjBOesZCoqc/hqdefault.jpg?sqp=-oaymwEmCMQBEG5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLDVABZP5eM7Y22iPASiPkU-4jU2HQ","width":196,"height":110},{"url":"https://i.ytimg.com/vi/kjBOesZCoqc/hqdefault.jpg?sqp=-oaymwEnCPYBEIoBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLBmyF9FWdPHX0mzExsa4_hyfOQfQA","width":246,"height":138},{"url":"https://i.ytimg.com/vi/kjBOesZCoqc/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLDdpYiLF5Cn6Fst6lkzFGcoB-ybRw","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/kjBOesZCoqc/maxresdefault.webp","width":1920,"height":1080}]})
![Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/uQhTuRlWMxw/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLCXREsxJtBFl3nfjorgsObx9YGWkA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/uQhTuRlWMxw/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLCGxdXuHPtcs3TkIgmZJMWWfSSA1A","width":196,"height":110},{"url":"https://i.ytimg.com/vi/uQhTuRlWMxw/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCkrhh6_t6e9m0RAar62qW74kHfTg","width":246,"height":138},{"url":"https://i.ytimg.com/vi/uQhTuRlWMxw/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDfGQCz2VDfpNAXkW9Q7lHCS2klqg","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/uQhTuRlWMxw/maxresdefault.webp","width":1920,"height":1080}]})
![Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/v8VSDg_WQlA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDbXmCmuL1yYgnjv_cRduYOeCY-xg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/v8VSDg_WQlA/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLChPiiZhcTblFLhka7nYxSl61hBDQ","width":196,"height":110},{"url":"https://i.ytimg.com/vi/v8VSDg_WQlA/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDW8qDTCGJIBFAZ4YqtCfM3kOH79A","width":246,"height":138},{"url":"https://i.ytimg.com/vi/v8VSDg_WQlA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLCJ_au0UF8uBV25Pb5koD0DOGPAEg","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/v8VSDg_WQlA/maxresdefault.webp","width":1920,"height":1080}]})
![Dot products and duality | Chapter 9, Essence of linear algebra]({"thumbnails":[{"url":"https://i.ytimg.com/vi/LyGKycYT2v0/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDQmiDcBHc_4ghUsY72sssNZ6b44w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/LyGKycYT2v0/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLDn-SaSOlB4MOAR9SsU0GfMTb5MWA","width":196,"height":110},{"url":"https://i.ytimg.com/vi/LyGKycYT2v0/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLAF27Kgm2Fp901hDPiCPSaYK8ZG9g","width":246,"height":138},{"url":"https://i.ytimg.com/vi/LyGKycYT2v0/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLDaCESW-1JF0Cu9BNFBd3Lkpwx_Sw","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/LyGKycYT2v0/maxresdefault.webp","width":1920,"height":1080}]})
![The essence of calculus]({"thumbnails":[{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEmCKgBEF5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLDRlHsdhFFIgUSKO-_kOU9Ci7ch8A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEmCMQBEG5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLDLdWQew2QR6WXhhBQoNn1827RX0g","width":196,"height":110},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEnCPYBEIoBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLAho-_ZSh9AmJ03F-yeIq5RbavgCw","width":246,"height":138},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLCgnHS8Wdxu2vA1ZOUZiqYavkUIdw","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/WUvTyaaNkzM/maxresdefault.webp","width":1920,"height":1080}]})
![Bayes theorem, the geometry of changing beliefs]({"thumbnails":[{"url":"https://i.ytimg.com/vi/HZGCoVF3YvM/hqdefault.jpg?sqp=-oaymwEmCKgBEF5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLCX-FcXOahGdEKern_9VgEXaDs5FA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/HZGCoVF3YvM/hqdefault.jpg?sqp=-oaymwEmCMQBEG5IWvKriqkDGQgBFQAAiEIYAdgBAeIBCggYEAIYBjgBQAE=&rs=AOn4CLDlYneVBW6w62cZMm-Y76XuJc2LcQ","width":196,"height":110},{"url":"https://i.ytimg.com/vi/HZGCoVF3YvM/hqdefault.jpg?sqp=-oaymwEnCPYBEIoBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLDWq8tGZ0S-1pmxG8h0vPqFedd_lw","width":246,"height":138},{"url":"https://i.ytimg.com/vi/HZGCoVF3YvM/hqdefault.jpg?sqp=-oaymwEnCNACELwBSFryq4qpAxkIARUAAIhCGAHYAQHiAQoIGBACGAY4AUAB&rs=AOn4CLB7PbUtb2TA6YPbsygmV1qkD3TJ5w","width":336,"height":188},{"url":"https://i.ytimg.com/vi/HZGCoVF3YvM/maxresdefault.jpg","width":1920,"height":1080}]})
![The essence of calculus]({"thumbnails":[{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLB8Jxf9oUNefs7k6wSyOERV_koIng","width":168,"height":94},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEbCMQBEG5IVfKriqkDDggBFQAAiEIYAXABwAEG&rs=AOn4CLAafAa4zUqKWQo_vuFRzRnovdcdBg","width":196,"height":110},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEcCPYBEIoBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLACPVawwVSH0zhZJyAXqsLY__WZ9g","width":246,"height":138},{"url":"https://i.ytimg.com/vi/WUvTyaaNkzM/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg==&rs=AOn4CLA_5XRUf6tNT9RrWAdcdiQzlrpmRA","width":336,"height":188},{"url":"https://i.ytimg.com/vi_webp/WUvTyaaNkzM/maxresdefault.webp","width":1920,"height":1080}]})
