Quanta Magazine’s Post

https://lnkd.in/eKCBnXwT An introduction to the fascinating subject of linear algebra. Major topics of linear algebra are presented in detail, with proofs of important theorems provided. #algebra #linearalgebra #mathematics

Geometry is self-founded! Professor F. William Lawvere's ‘Introduction to Linear Categories and Applications’ (https://lnkd.in/g8c4KDMg) along with his ‘Categories of Space and of Quantity’ (https://lnkd.in/g8c4KDMg), where contrasting linear and distributive categories are compared to the dual: quantity vs. space, respectively, provide an in-depth discussion of the categories encountered in linear algebra. Linear categories and linear algebra are also discussed in Lawvere & Schanuel ‘Conceptual Mathematics’ textbook (https://lnkd.in/g8c4KDMg) and in Lawvere & Rosebrugh ‘Sets for Mathematics’ (https://lnkd.in/g8c4KDMg). Categories of linear algebra are also discussed in Arbib and Manes ‘Arrows, Structures, and Functors’ textbook. It is interesting to note that the categories of linear structures quantifying spaces are within the categories of spaces (https://lnkd.in/g8c4KDMg). https://lnkd.in/gKvhQhdk #Mathematics #Geometry #Foundations #Linear #Algebra #Distributive #Category #Quantity #Space #Set #Vector #CategoryTheory #ConceptualMathematics #Axiomatization #Education #Science #FWilliamLawvere

Really fun series of lecture slides by Tim Cochran on Untying Knots in 4D. From: Rice University’s Dean’s Lecture Series, April 19, 2017. Link(s) below. Knots really don’t exists in high-dimensional spaces and the ones that do are trivial. There are also those who think there is a curse of high dimensionality because the math is complicated (see, e.g. three-body problem). Both are interesting to think about. It requires a change from algebra and linear thinking to geometry and then to topology (different than geometry, especially in high dimensional spaces). …sort of like synergism being “more than additive.” Our human semantics in any given language make the concepts clunky/difficult to convey. https://lnkd.in/gBKpCSGu https://math(.)rice(.)edu/~cochran/ResearchLectures/Deans_Lecture(.)pdf [delete parentheticals for link]

Normal and General Form of Equation of a Line Unlock the secrets of line equations with our guide on Normal and General Forms. Essential for geometry, trigonometry, and linear algebra applications. #OwnPetz #LineEquations #MathematicsExplained #GeometryInsights #TrigonometryBasics #AlgebraicForms #Learning #LinkedinLearning https://lnkd.in/gJPE4HTU

https://lnkd.in/eGaVP-RF A self-contained detailed exposition of the #algorithmic real algebraic geometry. Look for "Read and Download Links" section to download the book. #Algorithms #RealAlgebraicGeometry #AlgebraicGeometry #geometry #math Mathematics

Learn real-world math skills in 2024 with our free and fabulous new Finite Mathematics course! https://lnkd.in/gaCrNTCp

Today's word: Linear Algebra. Linear algebra is a type of math that deals with lines, planes, and spaces. Click the link in the comments section to learn more.

Introduction to Symplectic Geometry by Jean-Louis Koszul with forewords by Michel Nguiffo-Boyon, Frédéric Barbaresco & Charles-Michel Marle https://lnkd.in/eREw6Uyn https://lnkd.in/ePh6FGc2 Video: https://lnkd.in/drn6Z6F About this book This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric. Reviews “This book is of great interest for the emerging field of Geometric Science of Information, in which the generalization of the Fisher metric is at the heart of the extension of classical tools from Machine Learning and Artificial Intelligence to deal with more abstract objects living in homogeneous manifolds, groups, and structured matrices.’”

Bredec Group Bredec Group Tell HN: Comp Sci, Algebra and Calculus Resources I Like: Below is a list of resources that I personally like, because most of them emphasize derivations/motivations (e.g., deriving the cross product out of 3 assumptions/axioms) over (mechanical) memorization (e.g., just showing the mechanics of matrix multiplication/determinants without derivations/motivations): - Bari A., Algorithms, YouTube (playlist), https://lnkd.in/d7sH939d - Frenkel E., UC Berkeley: MATH 53 - Multivariable Calculus with Edward Frenkel, YouTube (playlist) https://lnkd.in/djWWsJCb - Hower V., Linear Algebra Full Course, YouTube (playlist), https://lnkd.in/dp7ds-zB - Lockhart P., Measurement - Axler S., Linear Algebra, Springer, 2024, https://lnkd.in/gNagvHma - Ström et al., Immersive Linear Algebra, https://lnkd.in/d5EfWD4D (online book) - Margalit et al., Interactive Linear Algebra, https://lnkd.in/gZeGtVvY (online textbook) - Macdonald A., Linear and Geometric Algebra - Macdonald A., Vector and Geometric Calculus - Ramirez et al., From Vectors to Geometric Algebra, 2018, https://lnkd.in/dFJQVQvE - Hertzmann et al., Computer Graphics Lecture Notes, Computer Science Department - University Toronto, 2005, https://lnkd.in/d8DD2R-t Further, see Sergey Trail's "Linear Algebra Done Wrong" and watch Grant Sanderson, Easy Theory (theoretical CS), Jacob Sorber (operating systems), Graphics in 5 Minutes, Sam Buss (computer graphics), Dr. Daniel Page (theory of computation, data structures and algorithms), First Principles of Computer Vision on YouTube. Mr. Hertzmann has some more resources (that I haven't checked out yet): https://lnkd.in/d4g47ViC --- Comments URL: https://lnkd.in/dUdxDQMh Points: 1 # Comments: 0 info@bredec.com Inquiry@bredec.com

🧮Monday Math Moment 🧮 Classroom-Ready Math Tasks Geometry: Scale Model Creation: Objective: To apply concepts of scale and proportion. Activity: Students choose a real-world object or structure and create a scale model of it. This could involve calculating scale factors and dimensions. Extension: Host a gallery walk where students display and explain their models and the mathematical process behind their creation. #cesa3 #empoweringeducators