3Blue1Brown
Abstract vector spaces | Essence of linear algebra, chapter 11
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
3Blue1Brown
A quick trick for computing eigenvalues | Essence of linear algebra, chapter 15
A quick way to compute eigenvalues of a 2x2 matrix
3Blue1Brown
Abstract vector spaces: Essence of Linear Algebra - Part 15 of 15
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
3Blue1Brown
Abstract vector spaces | Essence of linear algebra, chapter 15
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
Curated Video
Data Science Prerequisites - Numpy, Matplotlib, and Pandas in Python - Machine Learning Is Nothing but Geometry.
In this video, we will understand that machine learning is nothing but a geometry problem and see how it works for classification and regression. This clip is from the chapter "Machine Learning Basics" of the series "Data Science...
Brian McLogan
End Behavior Review
In this video we are going to review how to find and write the end behavior of polynomials. We will do this by covering a couple of basic examples and then work our way up to some more advanced examples ⭐ Completing the Square Problems...
Curated Video
Combining Factoring Techniques
“Combining Factoring Techniques” illustrates how to use different techniques of factoring to fully factor polynomial equations.
Curated Video
Computational Complexity and Public Key Cryptography
Quantum physicist Artur Ekert (Oxford and NUS) describes how aspects of computational complexity are harnessed by cryptosystems like RSA (Rivest–Shamir–Adleman) which is a public-key cryptosystem that is widely used for secure data...
Curated Video
Solutions by Graphing Systems
This video will discuss examples to find approximate solutions by graphing, using technology. Equations of the form f(x) = g(x) will be solved, where f(x) and g(x) may be linear, polynomial, rational, absolute value, exponential, or...
Zach Star
Why imaginary numbers are needed to understand the radius of convergence
Why imaginary numbers are needed to understand the radius of convergence
Zach Star
How you can solve dice puzzles with polynomials
How you can solve dice puzzles with polynomials
Zach Star
The Sierpinski-Mazurkiewicz Paradox (is really weird)
The Sierpinski-Mazurkiewicz Paradox (is really weird)
Why U
Algebra 85 - Building Polynomial Functions
Because of the tremendous variety of shapes of their graphs, polynomial functions are important tools for modeling phenomena in a wide range of fields such as science, engineering, medicine and finance. But since polynomial functions are...
Why U
Algebra 94 - Rational Functions with Oblique or Curvilinear Asymptotes
In the previous lecture we saw that although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Unlike vertical asymptotes, a...
Why U
Algebra 93 - Rational Functions and Nonvertical Asymptotes
Although a rational function may have any number of vertical asymptotes or no vertical asymptotes, rational functions will always have exactly one non-vertical asymptote. Since a function's value is undefined at a vertical asymptote, its...
Why U
Algebra 92 - Rational Functions and Holes
In the previous lecture, we saw examples of x values that cause a rational function's numerator to be zero, where those x values produce x-axis intercepts in the function's graph. We also saw x values that cause denominator zeros that...
Why U
Algebra 91 - Rational Functions and Vertical Asymptotes
A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a...
Why U
Algebra 90 - Dividing Polynomials
This lecture explains a procedure used to divide polynomials that is analogous to the procedure used to divide integers called "long division". Dividing one polynomial (the dividend) by another (the divisor) produces a quotient that may...
Why U
Algebra 89 - Multiplying Polynomial Functions
In the previous lecture we saw how polynomial functions could be added or subtracted, producing new polynomial functions with different characteristics. In this lecture we will see how to multiply polynomial functions and show how the...
Why U
Algebra 88 - Adding and Subtracting Polynomial Functions
Adding polynomial functions produces another polynomial function. The values of this function are the sum of the values of the polynomials that were added for every possible value of the input variable(s). Fortunately, adding polynomial...
Why U
Algebra 87 - Graphing Polynomial Functions - Part 2
When sketching the graph of a polynomial function, it may not be necessary to calculate numerous points on the graph. Many clues as to the general shape of the graph can be derived if we understand the characteristics that the graphs of...
Why U
Algebra 86 - Graphing Polynomial Functions - Part 1
Calculators and graphing utilities are available that are capable of creating accurate graphs of polynomial functions. However, it is often desirable to sketch a quick representation of a function's graph to get a general idea of its...
Why U
Algebra 84 - Monomial Building Blocks of Polynomial Functions
A polynomial is a sum of one or more terms called monomials. If we think of each monomial as a separate function, then a polynomial function can be thought of as a sum of these monomial functions. In previous lectures we have studied...
Curated Video
Factor Polynomials
A video entitled “Factor Polynomials” which models how to factor quadratic equations.