# Outline of mathematics

Mathematics is a field of study that investigates topics such as number, space, structure, and change. (Wikipedia).

Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44

We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge

From playlist Math Foundations

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

What is a number? | Arithmetic and Geometry Math Foundations 1 | N J Wildberger

The first of a series that will discuss foundations of mathematics. Contains a general introduction to the series, and then the beginnings of arithmetic with natural numbers. This series will methodically develop a lot of basic mathematics, starting with arithmetic, then geometry, then alg

From playlist Math Foundations

What exactly is a circle? | Arithmetic and Geometry Math Foundations 28 | N J Wildberger

Moving beyond points and lines, circles are the next geometrical objects we encounter. Here we address the question of how best to introduce this important notion, strictly in the setting of rational numbers, and without metaphysical waffling about `infinite sets.' This lecture is part of

From playlist Math Foundations

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

The basic framework for geometry (II) | Arithmetic and Geometry Math Foundations 24 | N J Wildberger

We discuss parallel and perpendicular lines, and basic notions relating to triangles, including the notion of a side and a vertex of a triangle. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discus

From playlist Math Foundations

Geometry - Ch. 1: Basic Concepts (2 of 49) Defined terms

Visit http://ilectureonline.com for more math and science lectures! In this video I will define and explain terms of point, line, plane, line segment, ray, opposite rays, intersections. Next video in this series can be seen at: https://youtu.be/fd8Reudp3gY

From playlist GEOMETRY CH 1 BASIC CONCEPTS

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

Geometry - Basic Terminology (1 of 34) Definition of Points and Lines

Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of points and lines. Next video in the Basic Terminology series can be seen at: http://youtu.be/kziFbJMWjUY

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

Learn Any Math And Science Subject

In this video I will show you some books that you can use to learn almost any math and science subject. These books are all part of the Schaum's Outline series so they have tons of worked examples which makes them great for self-study. Each book also covers more topics than what you would

From playlist Book Reviews

The Math Behind Font Rasterization | How it Works

#SoME Join the Discord: https://discord.gg/4tHeAkxNg7 If you have ever wondered how a font is rasterized, look no further. In this video I go into depth about the necessity for font rasterization, the math behind it, and how we convert the math to pixels on the screen. I also go over how

From playlist Summer of Math Exposition Youtube Videos

Epic Math Book Speed Run

In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t

From playlist Book Reviews

Everything Data Science

In this video I will give you the resources you need to learn data science from zero knowledge. We will discuss several programming books and math books that are perfect for beginners who want to acquire the skills to become a data scientist. In particular we will look at books on R, Pytho

From playlist Book Reviews

The Seduction of Curves: The Lines of Beauty That Connect Mathematics, Art and The Nude

Oxford Mathematics Public Lectures: Allan McRobie - The Seduction of Curves: The Lines of Beauty That Connect Mathematics, Art and The Nude There is a deep connection between the stability of oil rigs, the bending of light during gravitational lensing and the act of life drawing. To unde

From playlist Oxford Mathematics Public Lectures

Hierarchy of Results/Direct Proof

We look at different types of mathematical results such as Theorems, Propositions, Corollaries, and Lemmas. Next, we explore the direct method of proof, giving an outline and some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespr

From playlist Proof Writing

Learn Mathematics from START to FINISH (2nd Edition)

In this video I will show you how to learn mathematics from start to finish. I will give you three different ways to get started with mathematics. I hope this video helps someone. Here are the books Elementary Algebra https://amzn.to/3S7yG0Y Pre-Algebra https://amzn.to/3TpW8HK Discrete Ma

From playlist Book Reviews

Epicycles, complex Fourier series and Homer Simpson's orbit

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today’s video was motivated by an amazing animation of a picture of Homer Simpson being drawn using epic

From playlist Fourier

Schaum's Outline of Finite Mathematics by Lipschutz #shorts

Schaum's Outline of Finite Mathematics by Lipschutz #shorts This is the book on amazon: https://amzn.to/2GiLjaB (note this is my affiliate link) Book Review #shorts: https://www.youtube.com/playlist?list=PLO1y6V1SXjjPqMhU21NyGnwVnlF0UIheP Full Book Reviews: https://www.youtube.com/playl

From playlist Book Reviews #shorts

Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

Writing Proofs: Direct Proof

We outline the method of direct proof and give a few examples of statements that are proved using this method.

From playlist Abstract Algebra