{"id":1553,"date":"2025-05-28T17:00:16","date_gmt":"2025-05-28T17:00:16","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1553"},"modified":"2025-05-29T23:42:43","modified_gmt":"2025-05-29T23:42:43","slug":"announcing-think-linear-algebra","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2025\/05\/28\/announcing-think-linear-algebra\/","title":{"rendered":"Announcing Think Linear Algebra"},"content":{"rendered":"\n

I’ve been thinking about Think Linear Algebra<\/em> for more than a decade, and recently I started working on it in earnest. If you want to get a sense of it, I’ve posted a draft chapter as a Jupyter notebook<\/strong><\/a>.<\/p>\n\n\n\n

In one way, I am glad I waited — I think it will be better, faster [to write], and stronger [?] because of AI tools. To be clear, I am writing this book, not AI. But I’m finding ChatGPT helpful for brainstorming and Copilot and Cursor helpful for generating and testing code.<\/p>\n\n\n\n

If you are curious, here’s my discussion with ChatGPT about that sample chapter<\/strong><\/a>. Before you read it, I want to say in my defense that I often ask questions where I think I know the answer, as a way of checking my understanding without leading too strongly. That way I avoid one of the more painful anti-patterns of working with AI tools, the spiral of confusion that can happen if you start from an incorrect premise.<\/p>\n\n\n\n

My next step is to write a proposal, and I will probably use AI tools for that, too. Here’s a first draft that outlines the features I have in mind:<\/p>\n\n\n\n

\n

1. Case-Based, Code-First<\/h3>\n\n\n\n

Each chapter is built around a case study\u2014drawn from engineering, physics, signal processing, or beyond\u2014that demonstrates the power of linear algebra methods. These examples unfold in Jupyter notebooks that combine explanation, Python code, visualizations, and exercises, all in one place.<\/p>\n\n\n\n

2. Multiple Computational Perspectives<\/h3>\n\n\n\n

The book uses a variety of tools\u2014NumPy for efficient arrays, SciPy for numerical methods, SymPy for symbolic manipulation, and even NetworkX for graph-based systems. Readers see how different libraries offer different lenses on the same mathematical ideas\u2014and how choosing the right one can make thinking and doing more effective.<\/p>\n\n\n\n

3. Top-Down Learning<\/h3>\n\n\n\n

Rather than starting from scratch with low-level implementations, we use robust, well-tested libraries from day one. That way, readers can solve real problems immediately, and explore how the algorithms work only when it\u2019s useful to do so. This approach makes linear algebra more motivating, more intuitive\u2014and more fun.<\/p>\n\n\n\n

4. Linear Algebra as a Language for Thought<\/h3>\n\n\n\n

Vectors and matrices are more than data structures\u2014they\u2019re conceptual tools. By expressing problems in linear algebra terms, readers learn to think in higher-level chunks and unlock general-purpose solutions. Instead of custom code for each new problem, they learn to use elegant, efficient abstractions. As I wrote in Programming as a Way of Thinking<\/em><\/a>, modern programming lets us collapse the gap between expressing, exploring, and executing ideas.<\/p>\n<\/div><\/div>\n\n\n\n

Finally, here’s what ChatGPT thinks the cover should look like:<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

I’ve been thinking about Think Linear Algebra for more than a decade, and recently I started working on it in earnest. If you want to get a sense of it, I’ve posted a draft chapter as a Jupyter notebook. In one way, I am glad I waited — I think it will be better, faster [to write], and stronger [?] because of AI tools. To be clear, I am writing this book, not AI. But I’m finding ChatGPT helpful for…<\/p>\n

Read More Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[98],"class_list":["post-1553","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-linear-algebra"],"yoast_head":"\nAnnouncing Think Linear Algebra - Probably Overthinking It<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.allendowney.com\/blog\/2025\/05\/28\/announcing-think-linear-algebra\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Announcing Think Linear Algebra - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"I’ve been thinking about Think Linear Algebra for more than a decade, and recently I started working on it in earnest. 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You can read them here or follow these links to run the notebooks on Colab. Here are the chapters I have so far: Chapter 1: The Power of Linear AlgebraIntroduces matrix multiplication and eigenvectors through a network-based model of\u2026","rel":"","context":"In "Announcement"","block_context":{"text":"Announcement","link":"https:\/\/www.allendowney.com\/blog\/category\/announcement\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/06\/image.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/06\/image.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/06\/image.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2025\/06\/image.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":220,"url":"https:\/\/www.allendowney.com\/blog\/2019\/05\/16\/foundations-of-data-science\/","url_meta":{"origin":1553,"position":1},"title":"Foundations of data science?","author":"AllenDowney","date":"May 16, 2019","format":false,"excerpt":"\"Foundation\" is one of several words I would like to ban from all discussion of higher education. \u00a0Others include \"liberal arts\", \"rigor\", and \"service class\", but I'll write about them another time. \u00a0Right now, \"foundation\" is on my mind because of a new book from Microsoft Research, Foundations of Data\u2026","rel":"","context":"In \"data science\"","block_context":{"text":"data science","link":"https:\/\/www.allendowney.com\/blog\/tag\/data-science\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1627,"url":"https:\/\/www.allendowney.com\/blog\/2025\/10\/22\/the-foundation-fallacy\/","url_meta":{"origin":1553,"position":2},"title":"The Foundation Fallacy","author":"AllenDowney","date":"October 22, 2025","format":false,"excerpt":"At Olin College recently, I met with a group from the Kyiv School of Economics who are creating a new engineering program. 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Last Tuesday I presented a talk and co-presented a workshop at ODSC, and on Thursday I presented a tutorial at PyCon. If you would like to follow along with my very\u2026","rel":"","context":"In \"bayesian statistics\"","block_context":{"text":"bayesian statistics","link":"https:\/\/www.allendowney.com\/blog\/tag\/bayesian-statistics\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/img.youtube.com\/vi\/foMbacbuAQk\/0.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":586,"url":"https:\/\/www.allendowney.com\/blog\/2021\/04\/30\/whats-new-in-think-bayes-2\/","url_meta":{"origin":1553,"position":4},"title":"What’s new in Think Bayes 2?","author":"AllenDowney","date":"April 30, 2021","format":false,"excerpt":"I'm happy to report that the second edition of Think Bayes is available for preorder now. What's new in the second edition? I wrote a new Chapter 1 that introduces conditional probability using the Linda the Banker problem and data from the General Social Survey.I added new chapters on survival\u2026","rel":"","context":"In \"bayesian statistics\"","block_context":{"text":"bayesian statistics","link":"https:\/\/www.allendowney.com\/blog\/tag\/bayesian-statistics\/"},"img":{"alt_text":"Cover of Think Bayes second edition","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2021\/04\/think_bayes_2e_cover.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1050,"url":"https:\/\/www.allendowney.com\/blog\/2023\/10\/06\/how-does-world-population-grow\/","url_meta":{"origin":1553,"position":5},"title":"How Does World Population Grow?","author":"AllenDowney","date":"October 6, 2023","format":false,"excerpt":"Recently I posed this question on Twitter: \"Since 1960, has world population grown exponentially, quadratically, linearly, or logarithmically?\" Here are the responses: By a narrow margin, the most popular answer is correct -- since 1960 world population growth has been roughly linear. I know this because it's the topic of\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-at-2023-10-06-18-00-06.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-at-2023-10-06-18-00-06.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-at-2023-10-06-18-00-06.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-at-2023-10-06-18-00-06.png?resize=700%2C400&ssl=1 2x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1553","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/comments?post=1553"}],"version-history":[{"count":6,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1553\/revisions"}],"predecessor-version":[{"id":1566,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/1553\/revisions\/1566"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=1553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=1553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=1553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}