302.8A: Rings and First Examples Matthew Salomone 2013-02-25 | Definition and some first examples of rings.
202.G3 Introduction to Eigenvalues Matthew Salomone 2022-08-03 | Applet used in this video: geogebra.org/classic/hbv66hek
202.G2 Using Both Row Operations and Dimension Reduction Together for Determinants Matthew Salomone 2022-08-03 | ...
402.4Z2 Uniform Limit of Continuous Functions is Continuous Matthew Salomone 2022-07-10 | A paradigmatic analysis proof. Bookmark this one! See the playlist: http://matthematics.com/real0:00 Introduction & Necessity for this Result1:47 Setup: Unwinding the Definition3:50 Beginning from the End of the Proof4:31 Drawing an "Estimate Diagram"8:22 Claiming our Asserted "Control"8:59 Writing the Proof10:30 The "Add-Subtract Trick" Magic
402.4Z1 Our First Sequence of Functions, fₙ(x) = xⁿ Matthew Salomone 2022-07-10 | Not "does it" converge, but "how"? See the playlist: http://matthematics.com/real0:00 Introduction2:05 The sequence fₙ(x) = xⁿ3:05 Generalized definition of convergence4:10 "Just show the distances go to zero"5:34 Pointwise convergence8:28 Convergence in L¹10:49 Uniform convergence (or lack thereof)
402.3Z3 Examples of Metric Spaces Matthew Salomone 2022-07-10 | Some new examples of metrics on points of ℝⁿ and, more exciting, metrics that can measure distances between functions. See the playlist: http://matthematics.com/real0:00 Introduction1:18 Euclidean distances in ℝ and ℝⁿ2:59 The p-metrics on ℝⁿ4:32 The "taxicab" 1-metric5:51 Distances between functions: Area between graphs7:45 The Lebesgue p-metrics9:06 The uniform metric
402.3Z2 The Absolute Value Metric & The Add-Subtract Trick Matthew Salomone 2022-07-10 | Verifying that d(x,y) = |x-y| is a metric, and introducing the "add-subtract strategy". See the playlist: http://matthematics.com/real0:00 Introduction1:21 d(x,y) = |x-y| is a metric5:53 Reaching for control: The "add-subtract trick"8:57 Generalizing a definition: Continuous function
402.3Z What is a Metric Space? Matthew Salomone 2022-07-10 | Analysis is about measuring and controlling "distances". But what is the essence of a "distance"? See the playlist: http://matthematics.com/real0:00 Introduction2:34 Absolute-values are a clue!4:46 Definition of metric space6:08 Four necessary properties
202.V8 Doing Linear Algebra with Polynomials Matthew Salomone 2022-07-06 | Finding whether a set of polynomials (or whatever) are linearly independent is no more challenging than finding whether a set of vectors in ℝⁿ are linearly independent. Here's how.
202.V8 Coordinate Vectors are How We Do Linear Algebra with Other Vectors Matthew Salomone 2022-07-05 | ...
202.V8 How are Polynomials and Matrices Vectors? Matthew Salomone 2022-07-05 | "There are more vectors in heaven and earth than are dreamt of in ℝⁿ."--Shakespeare, probably
261.12.9.5 Using Stokes Theorem, and a (Bonus!) Greens Theorem appearance Matthew Salomone 2022-06-23 | ...
