Not entirely sure what this is but it's definitely something interactive and interesting
Mathematics
Essays/Tweet threads
Reading
- A Computational Introduction to Number Theory and Algebra - Victor Shoup
- A Computational Logic (1979) - Robert S. Boyer and J Strother Moore (PDF)
- A First Course in Complex Analysis - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
- A First Course in Linear Algebra - Rob Beezer
- A Friendly Introduction to Mathematical Logic - Christopher C. Leary and Lars Kristiansen
- A Gentle Introduction to the Art of Mathematics - Joseph E. Fields
- A Programmer's Introduction to Mathematics - Jeremy Kun
- Abstract Algebra: Theory and Applications - Tom Judson
- Active Calculus - Matt Boelkins
- Advanced Algebra - Anthony W. Knapp (PDF)
- Algebra: Abstract and Concrete - Frederick Goodman
- Algebra: An Elementary Text-Book, Part I (1904) - G. Chrystal (PDF)
- Algebra: An Elementary Text-Book, Part II (1900) - G. Chrystal (PDF)
- Algebraic Topology - Allen Hatcher (PDF)
- An Introduction to the Theory of Numbers - Leo Moser (PDF)
- Analytic Geometry (1922) - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (PDF)
- APEX Calculus - Gregory Hartman, Brian Heinold, Troy Siemers, and Dimplekumar Chalishajar
- Applied Combinatorics - Mitchel T. Keller and William T. Trotter
- Applied Discrete Structures - Alan Doerr and Kenneth Levasseur
- Basic Algebra - Anthony W. Knapp (PDF)
- Basic Analysis: Introduction to Real Analysis - Jiří Lebl
- Basics of Algebra, Topology, and Differential Calculus (PDF)
- Bayesian Methods for Hackers - Cameron Davidson-Pilon
- Beginning and Intermediate Algebra - Tyler Wallace
- Book of Proof - Richard Hammack (PDF)
- Calculus - Gilbert Strang
- Calculus I - Jerrold E. Marsden and Alan Weinstein
- Calculus in Context - James Callahan
- Calculus Made Easy - Silvanus P. Thompson (PDF)
- Category Theory for the Sciences - David I. Spivak
- Choose your own adventure Calculus - Tomas Petricek
- CK-12 Probability and Statistics - Advanced
- CLP-1 Differential Calculus - Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
- CLP-2 Integral Calculus - Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
- CLP-3 Multivariable Calculus - Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
- CLP-4 Vector Calculus - Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
- Collaborative Statistics
- College Trigonometry - Carl Stitz, Jeff Zeager (PDF)
- Combinatorics Through Guided Discovery - Kenneth Bogart
- Complex Analysis - George Cain
- Computational and Inferential Thinking. The Foundations of Data Science
- Computational Geometry
- Computational Mathematics with SageMath - Paul Zimmermann, Alexandre Casamayou, Nathann Cohen, Guillaume Connan, et al. (PDF)
- Concepts & Applications of Inferential Statistics
- Convex Optimization - Stephen Boyd and Lieven Vandenberghe
- Coordinate Geometry (1911) - Henry Buchard Fine and Henry Dallas Thompson (PDF)
- "Efforts to decolonise the curriculum in mathematics": Origins of maths around circles and "360 degrees in a circle" - Jacqui Ramagge
- Differential Equations - Paul Dawkins (PDF, use download menu to download)
- Differential Equations (1922) - H. B. Phillips (PDF)
- Discrete Mathematics: An Open Introduction - Oscar Levin
- Discrete Mathematics: First and Second Course - Edward A. Bender and S. Gill Williamson
- Elementary Differential Equations - William F. Trench (PDF)
- Elementary Differential Equations (with Boundary Value Problems) - William F. Trench
- Elementary Number Theory: Primes, Congruences, and Secrets - William Stein
- Elementary Real Analysis - Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner
- Elements of Abstract and Linear Algebra - E. H. Connell
- Elements of Differential and Integral Calculus (1911) - William Anthony Granville (PDF)
- Essentials of Metaheuristics - Sean Luke
- First Course in Algebra (1910) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (PDF)
- Foundations of Combinatorics with Applications - Edward A. Bender and S. Gill Williamson
- Foundations of Constructive Probability Theory - Yuen-Kwok Chan (PDF)
- Geometry with an Introduction to Cosmic Topology - Michael P. Hitchman
- Graph Theory
- How We Got from There to Here: A Story of Real Analysis - Robert Rogers and Eugene Boman
- Introduction to Probability - Charles M. Grinstead and J. Laurie Snell
- Introduction to Probability and Statistics Spring 2014
- Introduction to Proofs - Jim Hefferon
- Introduction to Real Analysis - William F. Trench
- Introduction to Statistical Thought - Michael Lavine
- Introductory Statistics for the Life and Biomedical Sciences - Julie Vu and David Harrington
- Kalman and Bayesian Filters in Python
- Knapsack Problems - Algorithms and Computer Implementations - Silvano Martello and Paolo Toth
- Lecture Notes of Linear Algebra - Dr. P. Shunmugaraj, IIT Kanpur (PDF)
- Lecture Notes on Linear Algebra - Dr. Arbind K Lal, Sukant Pati (PDF) (:construction: in process)
- Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics - Jonathan A. Poritz (PDF)
- Linear Algebra (PDF)
- Linear Algebra - Jim Hefferon
- Linear Algebra Done Wrong - Sergei Treil
- Linear Algebra, Infinite Dimensions, and Maple - James Herod
- Linear Methods of Applied Mathematics - Evans M. Harrell II and James V. Herod
- Magic Squares and Cubes (1917) - W. S. Anderson (PDF)
- Math in Society - David Lippman
- Mathematical Analysis I - Elias Zakon
- Mathematical Discovery - Andrew M. Bruckner, Brian S. Thomson, and Judith B. Bruckner
- Mathematical Logic - an Introduction (PDF)
- Mathematical Reasoning: Writing and Proof - Ted Sundstrom
- Mathematics, MTH101A - P. Shunmugaraj, IIT Kanpur
- Modern Statistics for Modern Biology - Susan Holmes and Wolfgang Huber
- Multivariable Calculus - George Cain and James Herod
- Non-Uniform Random Variate Generation - Luc Devroye (PDF)
- Notes on Diffy Qs - Jiří Lebl
- Number Theory - Holden Lee MIT
- Number Theory: In Context and Interactive - Karl-Dieter Crisman
- Odds and Ends: Introducing Probability & Decision with a Visual Emphasis - Jonathan Weisberg
- Online Statistics Education - David Lane
- OpenIntro Statistics - David M. Diez, Christopher D. Barr, Mine Çetinkaya-Rundel
- ORCCA: Open Resources for Community College Algebra - Portland Community College
- Ordinary Differential Equations - Wikibooks
- Paul's Online Notes: Algebra, Calculus I-III and Differential Equations - Paul Dawkins @ Lamar University
- Plane Geometry (1913) - George Wentworth and David Eugene Smith (PDF)
- Planes and Spherical Trigonometry (1915) - George Wentworth and David Eugene Smith (PDF)
- Precalculus - Carl Stitz and Jeff Zeager (PDF)
- Probability and Statistics Cookbook
- Probability and Statistics EBook
- Probability: Lectures and Labs - Mark Huber
- Recreations in Math - H. E. Licks (PDF)
- Sage for Undergraduates - Gregory Bard
- Second Course in Algebra - Herbert E. Hawkes, William A. Luby, Frank C. Touton (PDF)
- Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong and David I. Spivak (PDF)
- Statistical Thinking for the 21st Century - Russell A. Poldrack
- Statistics Done Wrong - Alex Reinhart
- SticiGui - Philip Stark
- Tea Time Numerical Analysis - Leon Q. Brin
- The Elements of Data Analytic Style - Jeff Leek (HTML, PDF, EPUB, Kindle) (Leanpub account or valid email requested)
- The Open Logic Text - Open Logic Project (PDF)
- Think Bayes: Bayesian Statistics Made Simple - Allen B. Downey
- Think Stats: Probability and Statistics for Programmers - Allen B. Downey (using Python)
- Vector Calculus - Michael Corral
- Yet Another Introductory Number Theory Textbook - Jonathan A. Poritz (PDF)
Mathematics For Computer Science
Philosophy
General
Software
- "A closer look at Software Development": Purportedly offers a "solution" to some of the problems with software dev. References UBizz, which seems like a product from the company hosting this page. May need to relocate this to "tools" sometime in the future.
Psychology
"The conceptual structure of human relationships across modern and historical cultures": "A defining characteristic of social complexity in Homo sapiens is the diversity of our relationships. We build connections of various types in our families, workplaces, neighbourhoods and online communities. How do we make sense of such complex systems of human relationships? The basic organization of relationships has long been studied in the social sciences, but no consensus has been reached. Here, by using online surveys, laboratory cognitive tasks and natural language processing in diverse modern cultures across the world (n = 20,427) and ancient cultures spanning 3,000 years of history, we examined universality and cultural variability in the ways that people conceptualize relationships. We discovered a universal representational space for relationship concepts, comprising five principal dimensions (formality, activeness, valence, exchange and equality) and three core categories (hostile, public, and private relationships). Our work reveals the fundamental cognitive constructs and cultural principles of human relationship knowledge and advances our understanding of human sociality."
"That is not how your brain works": Debunking certain psychological myths:
1. ... that specific parts of the human brain have specific psychological jobs.
2. ... that your brain reacts to events in the world.
3. ... that there’s a clear dividing line between diseases of the body, such as cardiovascular disease, and diseases of the mind, such as depression.
The manifold effects of partisan media on viewers' beliefs and attitudes: A field experiment with Fox News viewers
"Human Brain Compresses Working Memories into Low-Res 'Summaries'": "The findings... show that the visual cortex--the brain’s primary region for receiving, integrating, and processing visual information from the eye’s retina--acts more like a blackboard than a camera. That is, the visual cortex doesn’t photograph all the complex details of a visual image, such as the color of paper on which your password is written or the precise series of lines that make up the letters. Instead, it recodes visual information into something more like simple chalkboard sketches. The discovery suggests that those pared down, low-res representations serve as a kind of abstract summary, capturing the relevant information while discarding features that aren’t relevant to the task at hand. It also shows that different visual inputs, such as spatial orientation and motion, may be stored in virtually identical, shared memory formats."
"Adversarial Collaboration" by Daniel Kahneman -- "The power of reasons is an illusion. The belief will not change when the reasons are defeated. The causality is reversed. People believe the reasons because they believe in the conclusion." "The normal flow of reasoning is forward from what you believe to a possible consequence. When someone proposes a serious critical test, you cannot get from your theory to the result without adding an extra wrinkle to the theory. The extra wrinkle is hard to find—if it were easy, this would not be a serious critical test. On the other hand, the result probably follows from the adversary's theory. The lazy solution is to concede provisionally. The situation changes completely when the result is known. It is a constraint and working backward to a slightly wrinkled theory is much easier. It's not the case that people refuse to admit that they had been wrong. From their perspective they were only wrong in failing to see that the experiment didn't prove anything. This is where the extra 15 IQ points come from. You can explain surprises that you could not anticipate."
"Problem Space and Solution Space": "'Any product that you actually build exists in solution space[…]. Solution space includes any product or representation of a product that is used by or intended for use by a customer. It is the opposite of a blank slate. When you build a product, you have chosen a specific implementation. Whether you’ve done so explicitly or not, you’ve determined how the product looks, what it does, and how it works. […] [P]roblem space is where all the customer needs that you’d like your product to deliver live. You shouldn’t interpret the word "needs" too narrowly: Whether it’s a customer pain point, a desire, a job to be done, or a user story, it lives in problem space.' --from "The Lean Product Playbook", chap 2 ... Connecting the problem space and the solution space is where the magic happens. This is where value is created. A solution s can be connected to a problem p if s solves p. The problem p could be "remembering which groceries I need to buy" and a matching s could be a shopping list app. ... Firstly, for any point p in problem space, there are many points in solution space that can be mapped to p. For example, you can solve the problem of taking notes using pen and paper or a voice recording device. The converse is also true: One single solution might address several needs. Pen and paper can be mapped to both filing your taxes and to taking notes. Let us call these respective sets projections: The projection onto problem space P(s) of a solution s is the set of all problems that the solution s solves. Conversely, the projection onto solution space S(p) of a problem p is the set of all solutions that solve problem p. ... Another important observation is that the mapping between problem space and solution space is not a continuous function: If two points in problem space p and p’ are very close to each other by some measure, this does not necessarily mean that S(p) and S(p’) have a lot of points in common. This explains why, when business people ask engineers for estimates during a roadmap exercise, the conversation is often difficult. The engineers usually come back with a ton of detailed questions. However, during early planning, all that is known is a vague area somewhere in problem space. If this area is narrowed down one way, an easy solution exists."
Fallacies
"Characteristics of Pseudoscience" (graphic):
- Is UNFALSIFIABLE (can't be proven wrong); makes vague or unobservable claims.
- Relies heavily on ANECDOTES, personal experiences, and testimonials.
- CHERRY PICKS confirming evidence while ignoring/minimizing disconfirming evidence.
- Uses TECHNOBABBLE: words that sound scientific but don't make sense.
- Lacks PLAUSIBLE MECHANISM: No way to explain it based on existing knowledge.
- Is UNCHANGING: Doesn't self-correct or progress.
- Makes EXTRAORDINARY/EXAGGERATED CLAIMS with insufficient evidence.
- Professes CERTAINTY: Talks of "proof" with great confidence.
- Commits LOGICAL FALLACIES: Arguments contain errors in reasoning.
- Lacks PEER REVIEW: Goes directly to the public, avoiding scientific scrutiny.
- Claims there's a CONSPIRACY to suppress their ideas.
"It was safer back in my day" takedown: "The findings ... suggest there is a pervasive illusion of moral decline that is the result, at least in part, of two common psychological biases." ... "Mastroianni also noted that a study published last year, which analyzed 511 studies conducted over the course of 61 years, found evidence that cooperative behavior had actually increased over time." -- Study: "The illusion of moral decline"
Random shit that I find interesting but not high priority
Detail Pages:
- 50 Big Ideas A collection of ideas that define our world.
- 50 Philosophy Ideas A collection of philosophy ideas.
- 50 Psychology Ideas A collection of ideas from psychology.
- 8 Pillars of Greek Philosophy 8 core greek philosophies.
- Atomic Habits Notes from the book.
- Brain Rules Rules for how the brain works.
- Category Theory A collection of links on category theory.
- Concept Maps A page of resources for Concept Maps.
- Crucial Conversations How to have important emotional conversations with people (when opinions vary, stakes are high, and emotions run strong).
- Economics Collections of articles and books on economics.
- Finite and Infinite Games A Vision of Life and Possibility
- Good Strategy Bad Strategy A book on how to differentiate good strategy from bad strategy.
- Inverted Computer Culture A thought experiment.
- Pragmatic Thinking & Learning Andy Hunt's thoughts on thinking.
- Quit Notes from the book.
- Simple Rules Descriptions of how to guide behavior using simple rules.
- Simplexity "Why Simple Things Become Complex (and how Complex Things Can Be Made Simple)." Simplexity is a whole new science redefining how we look at the world; seen through this lens, the world becomes a more delicate place filled with predictable patterns, which we often fail to see as we're time and again fooled by our instincts, our fear, the size of things, or even their beauty.
- Superforecasting: The Art and Science of Prediction Notes on the book, about how non-experts can often outpredict the experts by following some remarkably straightforward approaches.
- Sway The irresistable pull of irrational behavior
- Systems Thinking Collection of notes links, articles, blog posts and other resources on systems thinking.
- Tempo "timing, tactics and strategy in narrative-driven decision-making." Tempo is a modern treatment of decision-making that weaves together concepts and principles from the mathematical decision sciences, cognitive psychology, philosophy and theories of narrative and metaphor.
- The Edge of Sentience Notes on (and links to) the book.
- The Elephant in the Brain Hidden motives in everyday life; a study of the intrinsic selfishness of the human brain.
- The Red Team Handbook The Army's guide to making better decisions.
- The Subtle Art of Not Giving a F*ck Interesting modern take on Stoic thought and philosophy.
- Thinking Fast and Slow System 1 and System 2 types of thinking and how to move from one to another.
- Thinking in Bets How to make decisions with less than perfect information.
- Thinking in Systems A primer on systems thinking.
- Untools Collection of thinking tools and frameworks to help you solve problems, make decisions and understand systems.
- Voiceliner Hold record, say what you want, and release. Just like you'd expect from an outliner, create hierarchies and rearrange. Notes are auto-transcribed and searchable, but you can always play back the audio. Automatically attach location to notes. Remember walks you took, and which places sparked what ideas.
Last modified 26 April 2025