Anisogamy

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

23 Algebraic system isomorphism

Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.

From playlist Abstract algebra

Definition of a Surjective Function and a Function that is NOT Surjective

We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht

From playlist Injective, Surjective, and Bijective Functions

Isomorphisms in abstract algebra

In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4

From playlist Abstract algebra

Definition of an Injective Function and Sample Proof

We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil

From playlist Injective, Surjective, and Bijective Functions

What is an Injective Function? Definition and Explanation

An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez

From playlist Functions

Homotopy animation

An interesting homotopy (in fact, an ambient isotopy) of two surfaces.

From playlist Algebraic Topology

Isomorphisms (Abstract Algebra)

An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s

From playlist Abstract Algebra

9. The Evolution of Sex

Principles of Evolution, Ecology and Behavior (EEB 122) There are several explanations for the evolution of sex and its continued prevalence. One is facilitating the spread of helpful mutations while hastening the removal of harmful ones. Another is expediting resistance against pathoge

From playlist Evolution, Ecology and Behavior with Stephen C. Stearns

Linear regression ANOVA ANCOVA Logistic Regression

In this video tutorial you will learn about the fundamentals of linear modeling: linear regression, analysis of variance, analysis of covariance, and logistic regression. I work through the results of these tests on the white board, so no code and no complicated equations. Linear regressi

From playlist Statistics

Linear Transformations: Onto

Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

Why Did Two Sexes Evolve?

Have you ever wondered why there are two sexes? As in, why do we require sexes for sex? The origin of the sexes is actually a very interesting question in theoretical biology, and in today's video I'll be covering my favourite hypothesis for the evolution of the sexes: The Hurst-Hamilton H

From playlist Evolution Collaboration