STEMCstudio, Episode 00: Why STEMCstudio?
SUMMARY: Professional Software Tools require too much Software Engineering. Traditional Educational Tools are Inflexible. STEMCstudio tries to find the Sweet Spot. STEMCstudio is an online programming environment that is optimized for educational purposes and computational modeling. It is
From playlist STEMCstudio Manual
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Abstract Algebra: Motivation for the definition of a group
The definition of a group is very abstract. We motivate this definition with a simple, concrete example from basic algebra. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https:/
From playlist Abstract Algebra
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Geometric Algebra, First Course, Episode 00: High Level Overview.
Geometric Algebra is the 21st Century tool for Mathematical Physics. This video provides an introduction to the subject and announces an upcoming series of videos in which the viewer can construct their own Geometric Numbers (multivectors) in STEMCstudio, define various operators used for
From playlist Geometric Algebra, First Course, in STEMCstudio
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra