Principles of Mathematical Analysis, colloquially known as "PMA" or "Baby Rudin," is an undergraduate real analysis textbook written by Walter Rudin. Initially published by McGraw Hill in 1953, it is one of the most famous mathematics textbooks ever written, and is renowned for its elegant and concise style of proof. (Wikipedia).
What are complex numbers? | Essence of complex analysis #2
A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall
From playlist Essence of complex analysis
Algebra - Ch. 0.5: Basic Concepts (1 of 26) An Overview
Visit http://ilectureonline.com for more math and science lectures! In this video I will give an overview of the basic concepts of algebra. I will review fractions operations of reducing, multiplying, dividing, adding, subtracting, and simplifying fraction. I will review number sets of re
From playlist ALGEBRA 0.5 BASIC CONCEPTS
An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger
This is a gentle introduction to curves and more specifically algebraic curves. We look at historical aspects of curves, going back to the ancient Greeks, then on the 17th century work of Descartes. We point out some of the difficulties with Jordan's notion of curve, and move to the polynu
From playlist Math Foundations
An introduction to the idea of Dimensional Analysis
From playlist Mathematical Physics I Uploads
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
Evaluate a linear expression for two variables
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
The problem with `functions' | Arithmetic and Geometry Math Foundations 42a
[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed. Here we discuss the difficulty in the context of funct
From playlist Math Foundations
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Why care about complex analysis? | Essence of complex analysis #1
Complex analysis is an incredibly powerful tool used in many applications, specifically in solving differential equations (Laplace's and others via inverse Fourier / Laplace transforms), and of course, fundamental theorem of algebra, Riemann hypothesis, as well as solving complicated integ
From playlist Essence of complex analysis
Philosophy of Mathematics & Frege (Dummett 1994)
Michael Dummett gives a talk on Frege and the philosophy of mathematics. For a good introduction to the philosophy of mathematics, check out: https://www.youtube.com/watch?v=UhX1ouUjDHE Another good introduction to the philosophy of mathematics: https://www.youtube.com/watch?v=XyXWnGFKTkg
From playlist Logic & Philosophy of Mathematics
James Arthur: The Langlands program: arithmetic, geometry and analysis
Abstract: As the Abel Prize citation points out, the Langlands program represents a grand unified theory of mathematics. We shall try to explain in elementary terms what this means. We shall describe an age old question concerning the arithmetic prime numbers, together with a profound gene
From playlist Abel Lectures
Cédric Villani: Lecture for Students [2014]
Video taken from: http://www.fields.utoronto.ca/programs/scientific/fieldsmedalsym/14-15/
From playlist Mathematics
DDPS | Toward combining principled scientific models and principled machine learning models
Toward combining principled scientific models and principled machine learning models by Michael Mahoney Description: Data-driven machine learning (ML) models have a very different basis than domain-driven physical models such as those based on partial differential equations. There have
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Ses 1: Introduction and Course Overview
MIT 15.401 Finance Theory I, Fall 2008 View the complete course: http://ocw.mit.edu/15-401F08 Instructor: Andrew Lo License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 15.401 Finance Theory I, Fall 2008
Best Books for Mathematical Analysis/Advanced Calculus
In this video I talk about three really good books on mathematical analysis which is also known as advanced calculus. There are several other really great books on the subject but I just chose three to discuss briefly in this video. I chose these mainly because I have spent a great deal of
From playlist Book Reviews
Top 4 Mathematical Analysis Books
In this video I will show you 4 mathematical analysis books. These are books you can use to learn real analysis on your own via self-study. You can also use these books to supplement any course you are taking on Advanced Calculus or Real Analysis at the undergraduate level. Knowing how to
From playlist Book Reviews
A Mathematical Analysis Book so Famous it Has a Nickname
A Mathematical Analysis Book so Famous it Has a Nickname In this video I go over the famous book "Baby Rudin", also known as "Principles of Mathematical Analysis" written by Walter B. Rudin. This book is notoriously rigorous and has some pros and cons, which I go over carefully in the vid
From playlist Cool Math Stuff
Real Analysis Lecture 1.1 The Natural Numbers
00:00 Start 00:11 Overview 01:38 Natural Numbers 08:00 A Joke 12:02 Tiling By Trominos 33:41 Integers Full Playlist: https://www.youtube.com/playlist?list=PLX2fVLMrzfneCYOpe6UrBhhFDo3JNglke Suggestion: Play at 1.25 times the normal speed. Note: The auto-generated subtitles are mostly acc
From playlist Summer of Math Exposition Youtube Videos
Terence Tao: The circle method from the perspective of higher order Fourier analysis
Higher order Fourier analysis is a collection of results and methods that can be used to control multilinear averages (such as counts for the number of four-term progressions in a set) that are out of reach of conventional linear Fourier analysis methods (i.e., out of reach of the circle m
From playlist Harmonic Analysis and Analytic Number Theory
