[Illustrative Mathematics Accelerated Grade 6, Unit 5 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/1/5/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 5 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/1/5/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 6 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/1/6/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 6 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/1/6/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 7 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/1/7/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 7 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/1/7/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 8 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/1/8/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 8 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/1/8/index.html) [Illustrative Mathematics Accelerated Grade 6, Unit 9 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/1/9/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 1 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/1/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 1 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/1/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 2 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/2/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 2 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/2/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 3 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/3/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 3 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/3/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 4 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/4/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 4 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/4/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 5 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/5/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 5 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/5/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 6 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/6/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 6 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/6/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 7 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/7/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 7 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/7/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 8 - Families | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/families/2/8/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 8 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/8/index.html) [Illustrative Mathematics Accelerated Grade 7, Unit 9 - Teachers | Kendall Hunt](https://im.kendallhunt.com/MS_ACC/teachers/2/9/index.html) [Illustrative Mathematics 6-8 Math version 3.1415 | Kendall Hunt](https://im.kendallhunt.com/MS/index.html) [Illustrative Mathematics Algebra 1, Geometry, Algebra 2 | Kendall Hunt](https://im.kendallhunt.com/HS/index.html) [Basic Algebra](https://www.intmath.com/basic-algebra/basic-algebra-intro.php) [Purpose and structure of algebra | Britannica](https://www.britannica.com/summary/algebra) [Properties of arithmetic - commutative, associative, and distributive | Britannica](https://www.britannica.com/summary/arithmetic) [Algebra | Hacker News](https://news.ycombinator.com/item?id=38044997) [The Feynman Lectures on Physics Vol. I Ch. 22: Algebra](https://www.feynmanlectures.caltech.edu/I_22.html) NOTE: CLARIFY WHAT A LOGARITHM IS (REF FROM FIXING) NOTE: CLARIFY CARTESIAN COORDINATES (REF FROM 3D PRINTER) TT Algebra - make sure to indicate radial degrees (from TT GPS) Higher-order math just uses fractions, NOT division, since division gets messy and vague When you get into more complex formulas, implied multiplication is treated as higher priority than operators for multiplication. "6 ÷ 2y, y=3" would almost universally be interpreted as 1 even without parenthesis. This is all a moot point because "÷" is almost never used in higher mathematics because it creates either ambiguity or very messy equations requiring a ton of parentheses. Fractions are used instead. See in this thread even calculators disagreeing on the answer. Algebra is basically calculations by completing and balancing [Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009) | Hacker News](https://news.ycombinator.com/item?id=37774580) [Pythagoras: Everyone knows his famous theorem, but not who discovered it 1000 years before him | Journal of Targeting, Measurement and Analysis for Marketing](https://link.springer.com/article/10.1057/jt.2009.16) [Alice's adventures in algebra: Wonderland solved | New Scientist](https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/) [Only one pair of distinct positive integers satisfy the equation m^n = n^m | Hacker News](https://news.ycombinator.com/item?id=35635491) [Only One Pair of Distinct Positive Integers Satisfy The Equation n^m = m^n | by Keith McNulty | Medium](https://keith-mcnulty.medium.com/only-one-pair-of-distinct-integers-satisfy-this-equation-76ea45469a96) [saw that video where everybody shared what they used 'k' for : sciencememes](https://old.reddit.com/r/sciencememes/comments/12luzp8/saw_that_video_where_everybody_shared_what_they/) [128: dPain over dt - explain xkcd](https://www.explainxkcd.com/wiki/index.php/128:_dPain_over_dt) [184: Matrix Transform - explain xkcd](https://www.explainxkcd.com/wiki/index.php/184:_Matrix_Transform) [207: What xkcd Means - explain xkcd](https://www.explainxkcd.com/wiki/index.php/207:_What_xkcd_Means) [Google Trying to Solve a UUID | Hacker News](https://news.ycombinator.com/item?id=32367982) [0e2b835d-4d9a-4b8b-b009-988741022e8c - Google Search](https://www.google.com/search?q=0e2b835d-4d9a-4b8b-b009-988741022e8c&ie=UTF-8) [Subtraction is functionally complete | Hacker News](https://news.ycombinator.com/item?id=37800062) [Subtraction Is Functionally Complete | orlp.net](https://orlp.net/blog/subtraction-is-functionally-complete/) [π in Other Universes | Hacker News](https://news.ycombinator.com/item?id=38063536) [π in Other Universes | Azeem Bande-Ali | azeemba.com](https://azeemba.com/posts/pi-in-other-universes.html) [Running Speeds | Hacker News](https://news.ycombinator.com/item?id=38056227) [Why are you so slow? - Probably Overthinking It](https://www.allendowney.com/blog/2023/10/28/why-are-you-so-slow/) [Othello Is Solved? | Hacker News](https://news.ycombinator.com/item?id=38141366) [[2310.19387] Othello is Solved](https://arxiv.org/abs/2310.19387) [37, the median value for the second prime factor of an integer | Hacker News](https://news.ycombinator.com/item?id=38242946) [A truly incredible fact about the number 37 | Chris Grossack's Blog](https://grossack.site/2023/11/08/37-median.html) [Exponentially Better Rotations (2022) | Hacker News](https://news.ycombinator.com/item?id=40684901) [Exponentially Better Rotations](https://thenumb.at/Exponential-Rotations/) [A wonderful coincidence or an expected connection: why π² ≈ g | Hacker News](https://news.ycombinator.com/item?id=41208988) [A wonderful coincidence or an expected connection: why π² ≈ g.](https://roitman.io/blog/91) ## fibonacci Fibonacci sequence - ON TT: indicate the difference between the fibonacci sequence/golden mean and the "computer sequence" ## functions (CS-based?) NOTE: A HUGE PART OF COMPUTER MATH, SO MAY NEED ITS OWN MAJOR SECTION OR A WHOLE NEW PAGE ## constraints [Fitting an elephant with four non-zero parameters | Hacker News](https://news.ycombinator.com/item?id=40961163) [[2407.07909] Fitting an Elephant with Four non-Zero Parameters](https://arxiv.org/abs/2407.07909) ## specific algebra [Differential equation - Wikipedia](https://en.wikipedia.org/wiki/Differential_equation) [Cameras and Lenses | Hacker News](https://news.ycombinator.com/item?id=25357315) [Cameras and Lenses - Bartosz Ciechanowski](https://ciechanow.ski/cameras-and-lenses/) [Poisson's Equation | Hacker News](https://news.ycombinator.com/item?id=27748967) [Poisson's Equation is the Most Powerful Tool not yet in your Toolbox](https://mattferraro.dev/posts/poissons-equation) [Show HN: Markov chains explained visually | Hacker News](https://news.ycombinator.com/item?id=8103240) [Markov Chains](https://setosa.io/blog/2014/07/26/markov-chains/index.html) [Sigmoid function - Wikipedia](https://en.wikipedia.org/wiki/Sigmoid_function) [The Rule of 72: Definition, Usefulness, and How to Use It](https://www.investopedia.com/terms/r/ruleof72.asp) [Up and Down the Ladder of Abstraction](http://worrydream.com/LadderOfAbstraction/) http://worrydream.com/refs [Function Sets and Specification • Buttondown](https://buttondown.email/hillelwayne/archive/function-sets-and-specification) [What is a Factorial? How to Calculate Factorials with Examples](https://www.freecodecamp.org/news/what-is-a-factorial) [What Is the Rule of 70? Definition, Example and Calculation](https://www.investopedia.com/terms/r/rule-of-70.asp) [Arithmetic Mean vs. Geometric Mean: What's the Difference?](https://www.investopedia.com/ask/answers/06/geometricmean.asp) [A list of advanced math tricks by Terence Tao | Hacker News](https://news.ycombinator.com/item?id=33952515) [Terence Tao: "Perhaps Mathstodon can be a pl…" - Mathstodon](https://mathstodon.xyz/@tao/109451634735720062) [Numbers every programmer should know | Hacker News](https://news.ycombinator.com/item?id=39657675) [Numbers](https://samwho.dev/numbers/?fo) ## linear algebra [Seven sins of numerical linear algebra | Hacker News](https://news.ycombinator.com/item?id=33173443) [Seven Sins of Numerical Linear Algebra - Nick Higham](https://nhigham.com/2022/10/11/seven-sins-of-numerical-linear-algebra/) [He made linear algebra fun | Hacker News](https://news.ycombinator.com/item?id=36168068) [He made linear algebra fun | MIT News | Massachusetts Institute of Technology](https://news.mit.edu/2023/gilbert-strang-made-linear-algebra-fun-0531) [A little bit of slope makes up for a lot of Y-intercept (2012) | Hacker News](https://news.ycombinator.com/item?id=34766444) [A little bit of slope makes up for a lot of y-intercept](https://gist.github.com/gtallen1187/e83ed02eac6cc8d7e185) [Free Linear Algebra textbook, from Jim Hefferon](https://hefferon.net/linearalgebra/) [An Intuitive Guide to Linear Algebra - BetterExplained](https://betterexplained.com/articles/linear-algebra-guide/) [Breaking Down The "Cosine Fourth Power Law"](https://www.photonicsonline.com/doc/breaking-down-the-cosine-fourth-power-law-0001) [Ask HN: Best beginner friendly linear algebra book? | Hacker News](https://news.ycombinator.com/item?id=31707163) [Front Matter](https://textbooks.math.gatech.edu/ila/index.html) [Coding The Matrix](https://codingthematrix.com/) [GitHub - mikeroyal/Linear-Algebra-Guide: Linear Algebra Guide](https://github.com/mikeroyal/Linear-Algebra-Guide) [Immersive Linear Algebra (2015) | Hacker News](https://news.ycombinator.com/item?id=40329388) [Immersive Math](https://immersivemath.com/ila/index.html) ## differential equations [Lessons I wish I had learned before teaching differential equations [pdf] (1997) | Hacker News](https://news.ycombinator.com/item?id=38248532) [Lessons I wish I had learned before I started teaching differential equations [pdf] (1997) | Hacker News](https://news.ycombinator.com/item?id=32530035) [Ten lessons I wish I had learned - Rota.pdf](https://web.williams.edu/Mathematics/lg5/Rota.pdf) ## discrete mathematics [Discrete Mathematics – An Open Introduction, 4th edition | Hacker News](https://news.ycombinator.com/item?id=41267478) [Discrete Mathematics - An Open Introduction](https://discrete.openmathbooks.org/dmoi4.html) ## kaprekar's constant [6174 | Hacker News](https://news.ycombinator.com/item?id=39018769) [6174 - Wikipedia](https://en.wikipedia.org/wiki/6174) ## quaternions [Visualizing quaternions, an explorable video series](https://eater.net/quaternions) [Quaternions | Hacker News](https://news.ycombinator.com/item?id=29510237) [Quaternions: Part 1 - Lior Sinai](https://liorsinai.github.io/mathematics/2021/11/05/quaternion-1-intro.html) [Let's remove Quaternions from every 3D Engine (An Interactive Introduction to Rotors from Geometric Algebra) - Marc ten Bosch](https://marctenbosch.com/quaternions/) [Look, ma, no matrices | Hacker News](https://news.ycombinator.com/item?id=39538670) [Look, Ma, No Matrices!](https://enkimute.github.io/LookMaNoMatrices/) ## sum of cubes [Visual Sum of Cubes | Hacker News](https://news.ycombinator.com/item?id=32528769) [Visual Sum of Cubes](https://x.st/visual-sum-of-cubes/) ## recaman sequence [Recamán Sequence](https://xeniasuper.github.io/recaman-sequence/) ## optimization [Encyclopedia of Optimization | Hacker News](https://news.ycombinator.com/item?id=41238130) [Encyclopedia of Optimization | SpringerLink](https://link.springer.com/referencework/10.1007/978-0-387-74759-0)