A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. First published in 1908, it went through ten editions (up to 1952) and several reprints. It is now out of copyright in UK and is downloadable from various internet web sites. It remains one of the most popular books on pure mathematics. (Wikipedia).

The Scientific Method and the question of "Infinite Sets" | Sociology and Pure Maths| N J Wildberger

Let's get some kind of serious discussion going about the differences in methodology and philosophy between the sciences and mathematics, and how these differences manifest themselves in the attitude towards the logical foundations of mathematics. In particular we look at a bulwark notio

From playlist Sociology and Pure Mathematics

Formal Definition of a Function using the Cartesian Product

Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

Introduction and Invitation | Six: An Elementary Course in Pure Mathematics Six 1| Wild Egg

Welcome to Six --- an Elementary Course in Pure Mathematics meant for a general lay audience with a minimal amount of mathematical prerequisites! In this video we introduce the basic objects: the symbols 1,2,3,4,5 and 6 along with the basic tools to create more complex mathematical objec

From playlist Six: An elementary course in Pure Mathematics

Intro to Discrete Math - Welcome to the Course!

Welcome to Discrete Math. This is the start of a playlist which covers a typical one semester class on discrete math. I chat a little about why I love discrete math, what you should expect, and how an online discrete math course is structured. FULL PLAYLIST: https://www.youtube.com/watch

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

An invite to Pure Mathematics research: Six - an elementary course | Wild Egg mathematics courses

How do pure mathematicians think? What do they do, and how do they do it? Find out directly, by coming with me on a simple but profound journey of mathematical discovery, where we study ... Six. (Not the musical!) The Playlist https://www.youtube.com/watch?v=zrt0EKuGr5Q&list=PLzdiPTrEWyz4K

From playlist MathSeminars

The big mathematics divide: between "exact" and "approximate" | Sociology and Pure Maths | NJW

Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as "exact theories" when in fact they are really only "approximate theories". In this sense they can be viewed either as belonging more properly to applied ma

From playlist Sociology and Pure Mathematics

All of Algebraic Methods in 20 Minutes!! | Chapter 7 | A-Level Pure Maths Revision

A video revising the techniques and strategies required for all of the AS Level Pure Mathematics chapter on Algebraic Methods that you need to achieve a grade C-A* in your A-Level Pure Maths. These topics are the essential question styles that appear in the Algebraic Methods Module. This

From playlist A-Level Maths Series - Pure Mathematics

Basic Concepts of Elementary Mathematics

In this video I will show you a math book that covers a wide variety of topics. This book is very different from your typical algebra or pre-calc book in that it covers different areas of math. It is primarily written for students who want to become teachers or liberal arts majors. I think

From playlist Book Reviews

The formal definition of a sequence.

We have an intuitive picture of sequences (infinite ordered lists). But there is a formal definition of sequences based out of the idea of a specific function between sets, specifically from the positive integers to the real numbers. ►Full DISCRETE MATH Course Playlist: https://www.youtu

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

ICM 2006 Closing Round Table Are pure and applied mathematics drifting apart? Intervention by John Ball (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/table2006_ball.pdf) Intervention by Lennart Carleson (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/

From playlist Number Theory

Pure Mathematics Book with Solutions to All Problems(from 1960's England)

In this video I go over a book you have probably never heard of, I can't even find it on amazon! It is a book on Pure Mathematics written in the 1960s from London England. It covers a super wide range of topics and has solutions to every single problem in the book which is awesome. I talk

From playlist Book Reviews

Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J Wildberger

Number systems are at the heart of mathematics --- and have been for at least 4000 years. The Egyptians' had a base 10 system that used fractions, albeit not in the way we do, while the Sumerians remarkably developed a base 60 floating point system. What systems do we teach in schools?

From playlist Sociology and Pure Mathematics

Logical weakness in modern pure mathematics | Real numbers and limits Math Foundations 87

We begin PART II of this video course: "Mathematics on trial - why modern pure mathematics doesn't work". This video outlines the case for the prosecution: that modern pure mathematics suffers from: 1. Inconsistent rigour 2. Problematic definitions 3. Reliance on `axioms' 4. Computatio

From playlist Math Foundations

Towards a Sociology of Pure Mathematics | Sociology and Pure Maths | N J Wildberger

Sociology is a subversive science that delves into the complexities of human relations and interaction. Is it time for a sociology of pure mathematics? What would that involve? What new insights could it bring? This is the first video in a series that will be exploring the sometimes hidde

From playlist Sociology and Pure Mathematics

Is pure mathematics logically viable? Five Challenges! | Sociology and Pure Maths | N J Wildberger

Some tough talk directed towards the professoriat and students of the subject: is it time to re-evaluate what exactly is going on in Pure Mathematics? This is part of a series on the Sociology of Pure Mathematics, where we try to delve into and unravel some of the mysteries of the profess

From playlist Sociology and Pure Mathematics

Stanford Seminar - On the Origin of Experience: The Shaping of Sense and the Complex World

"On the Origin of Experience: The Shaping of Sense and the Complex World" -Steven Ericsson-Zenith Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to

From playlist Engineering

Basic Organization of 6 objects | Six: An Elementary Course in Pure Mathematics Six2 | Wild Egg

We continue our introduction to this elementary course in Pure Mathematics, concentrated on the magical and beautiful properties of the number 6. In our first video we introduced Nodes, Edges and Meets. In this video we review these and give a simple geometrical interpretation of them in t

From playlist Six: An elementary course in Pure Mathematics

Greek Pure Mathematics and the "Infinitude of Primes" | Sociology and Pure Maths | N J Wildberger

To understand the sociology of pure mathematics, we need to appreciate the long historical span of the subject, going back at least to ancient Greek times. Euclid's monumental work The Elements set the standard for pure mathematics research and education for more than 2000 years. Mathemati

From playlist Sociology and Pure Mathematics