{"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_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_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},"jetpack_post_was_ever_published":false},"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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