Скачать или смотреть GF2 Function Composition & 1-1, onto maps

What is #function composition? Proof that the composition of two 1-1 functions is 1-1, and the composition of two onto functions is onto. Subscribe ‪@Shahriari‬ for math videos at the college level.
The vocabulary and the results are for general functions from one set to another (as opposed to just real valued functions on the real line) as encountered in courses in #linearalgebra #combinatorics #mathematicalanalysis or #abstractalgebra
00:00 Introduction
00:13 Definition: Function (   • GF1 What is a function? What do 1-1 and on...  )
00:54 Definition: Function Composition
02:26 Example from pre-Calculus
03:23 Example involving higher dimensions
04:27 Notation Recap
05:22 Example composing f from R^3 to R^2, and g from R^2 to R^3
08:20 Motivating Question: Does the composition inherit any properties of the original function
08:42 Definition: 1-1 &/or onto Functions (   • GF1 What is a function? What do 1-1 and on...  )
09:35 Theorem & Proof: Composition of two 1-1 functions is 1-1
12:07 Theorem & Proof: Composition of two onto functions is onto
14:39 Corollary: Composition of two bijection is a bijection
15:05 Example: Composition of two permutations (   • AG03 Permutations and Bijections form a Gr...  )

One of a series of lectures by Shahriar Shahriari on basic mathematical concepts used in undergraduate college mathematics.
The Series on Functions is as follows:
GF1: Functions, 1-1, onto Functions    • GF1 What is a function? What do 1-1 and on...  
GF2: Function Composition (this video)    • GF2 Function Composition & 1-1, onto maps  
GF3: Inverse Functions    • GF3 Inverse of Functions & Bijective maps  
GF4: Cardinality (uncountable sets, Cantor's diagonal argument, and the Continuum hypothesis)    • GF4 Cardinality--Countable & Uncountable Sets  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and five time winner of Pomona College's Wig teaching award.