Visualizing Basic Algebra Last weekend, I shared some interesting properties of numbers with my kids. The great thing about explaining something to a non-expert is that you have to actually understand the topic. (This is why making teaching universities and research universities the same actually makes sense.) If you hide behind a formalism, the explanation won’t work. Usually, this means that you didn’t understand why the formalism worked either. This is why I thought “why are far away things smaller?” Some of the interesting properties of numbers are: that (n + 1)×(n-1)=n2-1: that the perfect squares (0,1,4,9,…) go up by successive odd numbers (1,3,5,…); and that the area of a triangular number (1+2+…+n) has a closed form. Multiplication and division are grounded in visuospatial concepts, which is why these number theoretical results are easy to understand. Properties of Addition Addition is associative: and commutative: Multiplication is Commutative The commutative law is that a×b=b×a. Distributive Law ! Addendum
30 Best Math Books to Learn Advanced Mathematics for Self-Learners Skip to content Menu Deudas sistémicas s Introduction to Complex Systems by David Kirshbaum I. Introduction: Complex Systems Theory : Basic Definition II. Four Important Characteristics of Complexity: III. I. A Complex System is any system which involves a number of elements, arranged in structure(s) which can exist on many scales. Previously, when studying a subject, researchers tended to use a reductionist approach which attempted to summarize the dynamics, processes, and change that occurred in terms of lowest common denominators and the simplest, yet most widely provable and applicable elegant explanations. But since the advent of powerful computers which can handle huge amounts of data, researchers can now study the complexity of factors involved in a subject and see what insights that complexity yields without simplification or reduction. Scientists are finding that complexity itself is often characterized by a number of important characteristics: (II.1) Self-Organization(II.2) Non-Linearity(II.3) Order/Chaos Dynamic(II.4) Emergent Properties. Examples
's AI Journal • Primers • Math Linear Algebra Linear Algebra is the branch of mathematics that studies vector spaces and linear transformations between vector spaces, such as rotating a shape, scaling it up or down, translating it (i.e., moving it), etc. Machine Learning relies heavily on Linear Algebra, so it is essential to understand what vectors and matrices are, what operations you can perform with them, and how they can be useful. Vectors Definition A vector is a quantity defined by a magnitude and a direction. Purpose Vectors have many purposes in Machine Learning, most notably to represent observations and predictions. Vectors in Python In python, a vector can be represented in many ways, the simplest being a regular python list of numbers: Since we plan to do quite a lot of scientific calculations, it is much better to use NumPy’s ndarray, which provides a lot of convenient and optimized implementations of essential mathematical operations on vectors (for more details about NumPy, check out the NumPy tutorial).
Moodle The UN Sustainable Development Goals (SDGs) offer a blueprint to help simultaneously tackle humanitarian and environmental crises. On this six-week course from RMIT University, you’ll take a guided tour with world experts through the UN SDGs. During this exploration, you’ll discover how digital technology can help achieve different SDGs and drive social impact. Using carefully curated case studies, you’ll discover the real-world applications of digital technology. You’ll then develop an action plan for your organisation to adapt this approach and work toward relevant SDGs. You’ll start by delving into the SDGs that promote equal opportunity. Exploring quality education, reduced inequality, and gender equality, you’ll discover the digital technology solutions that can help achieve these goals. Understand how digital technology can build sustainable cities Explore case studies on clean water and sanitation and good health and wellbeing
Dave's short course in trigonometry Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Ptolemy’s sum and difference formulas Ptolemy’s theorem The sum formula for sines The other sum and difference formulas Summary of trigonometric formulas Formulas for arcs and sectors of circles Formulas for right triangles Formulas for oblique triangles Formulas for areas of triangles Summary of trigonometric identities More important identities Less important identities Truly obscure identities About the Java applet. Images in Dave’s Short Trig Course are illustrated with a Java applet. Note that some web browsers do not allow printers to print images created by Java applets.
Lic. Melina Mariel Losada on LinkedIn: #datavisualization #visualization #datascience #datamanagement #python… | 12 comments A Gentle Introduction To Learning Calculus I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. Calculus is similarly enlightening. They are. Unfortunately, calculus can epitomize what’s wrong with math education. It really shouldn’t be this way. Math, art, and ideas I’ve learned something from school: Math isn’t the hard part of math; motivation is. Teachers focused more on publishing/perishing than teachingSelf-fulfilling prophecies that math is difficult, boring, unpopular or “not your subject”Textbooks and curriculums more concerned with profits and test results than insight ‘A Mathematician’s Lament’ [pdf] is an excellent essay on this issue that resonated with many people: Imagine teaching art like this: Kids, no fingerpainting in kindergarten. Poetry is similar. Feisty, are we? Yowza!
The open source learning curve for AI researchers Tri Dao, the creator of an increasingly popular technique in language model development, is running head-first into a new problem for AI researchers: working with the incredibly fast LLM open source community. Dao is one of the creators of FlashAttention, a technique now adopted by some developers to increase the amount of information that can go into a context window for a large language model more efficiently. The theory goes that if you can find ways to get larger amounts of useful information into that window (without going overboard), you could achieve better outcomes because the model has a better idea of what you’re trying to do. Dao this week joined Together, a startup that aims to build open source language models and associated technology, where he’ll work as chief scientist. FlashAttention, which speeds up training and fine-tuning of LLMs, could help solve an important piece of the puzzle for making large language models address more practical use cases. Share