These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.
Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
Homeric scholarship is the study of any Homeric topic, especially the two large surviving epics, the Iliad and Odyssey. It is currently part of the academic discipline of classical studies. The subject is one of the oldest in scholarship. For the purpose of the present article, Homeric scholarship is divided into three main phases: antiquity; the 18th and 19th centuries; and the 20th century and later.
Ancient scholarship
Scholia
Scholia are ancient commentaries, initially written in the margins of manuscripts, not necessarily at the bottom, as are their modern equivalents, the notes. The term marginalia includes them. Some are interlinear, written in very small characters. Over time the scholia were copied along with the work. When the copyist ran out of free text space, he listed them on separate pages or in separate works. Today’s equivalents are the chapter notes or the notes section at the end of the book. Notes are merely a continuation of the practice of creating or copying scholia in printed works, although the incunabula, the first printed works, duplicated some scholia. The works of Homer have been heavily annotated from their written beginnings. The total number of notes on manuscripts and printed editions of the Iliad and Odyssey are for practical purposes innumerable.
A chemical substance is a form of matter that has constant chemical composition and characteristic properties. It cannot be separated into components by physical separation methods, i.e., without breaking chemical bonds. Chemical substances can be chemical elements, chemical compounds, ions or alloys.
Chemical substances are often called 'pure' to set them apart from mixtures. A common example of a chemical substance is pure water; it has the same properties and the same ratio of hydrogen to oxygen whether it is isolated from a river or made in a laboratory. Other chemical substances commonly encountered in pure form are diamond (carbon), gold, table salt (sodium chloride) and refined sugar (sucrose). However, in practice, no substance is entirely pure, and chemical purity is specified according to the intended use of the chemical.
Chemical is the second single from the Swedishglam metal band Crashdïet's 2010 album Generation Wild. It was released on 19 September and was written by Crashdïet's guitarist Martin Sweet and the band Peep Show's singer Johnny Gunn.
Food is any substance consumed to provide nutritional support for the body. It is usually of plant or animal origin, and contains essential nutrients, such as fats, proteins, vitamins, or minerals. The substance is ingested by an organism and assimilated by the organism's cells to provide energy, maintain life, or stimulate growth.
Food Records was a record label set up in 1984 by David Balfe, who later took on Andy Ross as his partner. Originally formed as an independent record label with distribution going through Rough Trade Distribution, Food also licensed acts though WEA Records, before becoming closely associated with the EMI group's Parlophone label. EMI invested in the label and then in 1994 EMI gained complete control and folded it into Parlophone in 2000.
The Food catalogue lists the following releases under the FOOD catalog number (12inch vinyl singles have an added T after the number):
Singles
Albums
The Food Christmas EP
In December 1989, Food Records released The Food Christmas EP (FOOD 23) that featured Food artists covering each other's songs. Crazyhead covered Diesel Park West's "Like Princes Do", Jesus Jones covered Crazyhead's "I Don't Want That Kind Of Love" and Diesel Park West covered Jesus Jones' "Info-Freako". The EP was released on CD, 7" vinyl, 12" and a limited gatefold sleeve 12" vinyl.
Analysis III - Integration: Oxford Mathematics 1st Year Student Lecture
The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the course to the mathematics our students have already learnt at school and develops that knowledge, taking the students to the next, more rigorous, stage. Like all good lectures, it recaps and points forward.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4...
published: 09 May 2019
How to self study pure math - a step-by-step guide
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
---
REAL ANALYSIS
Book: “Understanding Analysis” by Stephen Abbott.
Videos: Lectures by Francis Su (https://www.youtube.com/playlist?list=PL0E754696F72137EC)
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
(https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw)
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat327/?resources)
COMPLEX ANALYSIS
Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
More Technical Book: “Complex Analysis” by Serge Lang
Videos: Wesleyan University Playlist (h...
published: 24 Dec 2021
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 write proofs is very important before jumping into analysis, but these are always fun to look at even if you aren't an expert at proof writing. I hope you enjoy this video.
Here are the books.
Principles of Mathematical Analysis by Rudin https://amzn.to/3VicMKf
Advanced Calculus by Buck https://amzn.to/3EueMbI
Advanced Calculus by Fitzpatrick https://amzn.to/3VhmzQW
Understanding Analysis by Abbott https://amzn.to/3ACUDPl
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFv...
published: 14 Dec 2022
6 Things I Wish I Knew Before Taking Real Analysis (Math Major)
Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before taking Real Analysis. Enjoy!
#realanalysis
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
published: 17 Jan 2020
The Real Analysis Survival Guide
How do you study for Real Analysis? Can you pass real analysis? In this video I tell you exactly how I made it through my analysis classes in undergrad and graduate school, and then moved on to become a professor of mathematics.
//Books
Rosenlicht (short and easy to follow) - https://amzn.to/3k9X2Zc
Rudin (gold standard, but a bit opaque) - https://amzn.to/3KeL0IC
Apostol (thorough, but long) - https://amzn.to/3LhEylx
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published: 24 Apr 2022
How to Understand Analysis
This is Understanding Analysis by Stephen Abbott. This is a wonderful book for beginners who want to learn undergraduate level real analysis/advanced calculus.
Here it is: https://amzn.to/3oGCk9b
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equat...
published: 26 May 2023
Teaching myself an upper level pure math course (we almost died)
Get 25% off a year subscription to CuriosityStream, ends Jan 3rd 2021: (use code "zachstar" at sign up): https://curiositystream.thld.co/zachstarnov18
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published: 18 Nov 2020
Lecture 1: Sets, Set Operations and Mathematical Induction
MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw
An introduction to set theory and useful proof writing techniques required for the course. We start to see the power of mathematical induction.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
published: 21 Jun 2022
The Map of Mathematics
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: ht...
published: 01 Feb 2017
Learn Real Analysis With This Excellent Book
In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone who is taking an Undergraduate level course on Advanced Calculus/Real Analysis. The book is titled Real Analysis: A Long-Form Mathematics Textbook and it was written by Jay Cummings.
Here is the book: https://amzn.to/3VkaNoN
(this is my affiliate link)
If you enjoyed this video please consider liking, sharing, and subscribing.
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The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the...
The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the course to the mathematics our students have already learnt at school and develops that knowledge, taking the students to the next, more rigorous, stage. Like all good lectures, it recaps and points forward.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the course to the mathematics our students have already learnt at school and develops that knowledge, taking the students to the next, more rigorous, stage. Like all good lectures, it recaps and points forward.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
---
REAL ANALYSIS
Boo...
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
---
REAL ANALYSIS
Book: “Understanding Analysis” by Stephen Abbott.
Videos: Lectures by Francis Su (https://www.youtube.com/playlist?list=PL0E754696F72137EC)
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
(https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw)
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat327/?resources)
COMPLEX ANALYSIS
Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
More Technical Book: “Complex Analysis” by Serge Lang
Videos: Wesleyan University Playlist (https://www.youtube.com/playlist?list=PL_onPhFCkVQjdQTbG0eQk42eH0RaBoYJf)
GROUP THEORY
Book: “Topics in Algebra” by Herstein (Chapter 2)
Videos: Lectures by Benedict Gross (https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5)
GALOIS THEORY
Notes by Tom Leinster: https://www.maths.ed.ac.uk/~tl/gt/gt.pdf
DIFFERENTIAL GEOMETRY
Book: Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby
ALGEBRAIC TOPOLOGY
Book: Algebraic Topology by Allen Hatcher (available for free on his website: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html)
Videos: Lectures by Pierre Albin (https://www.youtube.com/playlist?list=PL41FDABC6AA085E78)
Intro: (0:00)
Linear Algebra: (0:36)
Real Analysis: (2:20)
Point Set Topology: (3:19)
Complex Analysis: (4:09)
Group Theory: (5:46)
Galois Theory: (6:54)
Differential Geometry: (7:23)
Algebraic Topology: (8:44)
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
---
REAL ANALYSIS
Book: “Understanding Analysis” by Stephen Abbott.
Videos: Lectures by Francis Su (https://www.youtube.com/playlist?list=PL0E754696F72137EC)
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
(https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw)
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat327/?resources)
COMPLEX ANALYSIS
Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
More Technical Book: “Complex Analysis” by Serge Lang
Videos: Wesleyan University Playlist (https://www.youtube.com/playlist?list=PL_onPhFCkVQjdQTbG0eQk42eH0RaBoYJf)
GROUP THEORY
Book: “Topics in Algebra” by Herstein (Chapter 2)
Videos: Lectures by Benedict Gross (https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5)
GALOIS THEORY
Notes by Tom Leinster: https://www.maths.ed.ac.uk/~tl/gt/gt.pdf
DIFFERENTIAL GEOMETRY
Book: Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby
ALGEBRAIC TOPOLOGY
Book: Algebraic Topology by Allen Hatcher (available for free on his website: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html)
Videos: Lectures by Pierre Albin (https://www.youtube.com/playlist?list=PL41FDABC6AA085E78)
Intro: (0:00)
Linear Algebra: (0:36)
Real Analysis: (2:20)
Point Set Topology: (3:19)
Complex Analysis: (4:09)
Group Theory: (5:46)
Galois Theory: (6:54)
Differential Geometry: (7:23)
Algebraic Topology: (8:44)
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 the...
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 write proofs is very important before jumping into analysis, but these are always fun to look at even if you aren't an expert at proof writing. I hope you enjoy this video.
Here are the books.
Principles of Mathematical Analysis by Rudin https://amzn.to/3VicMKf
Advanced Calculus by Buck https://amzn.to/3EueMbI
Advanced Calculus by Fitzpatrick https://amzn.to/3VhmzQW
Understanding Analysis by Abbott https://amzn.to/3ACUDPl
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
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Advanced Calculus Course
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Calculus Integration Insanity
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Differential Equations Course
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College Algebra Course
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How to Write Proofs with Sets Course
https://www.udemy.com/course/how-to-write-proofs-in-set-theory-with-the-math-sorcerer/?referralCode=D503A7E3FB6916CF2D27
How to Write Proofs with Functions Course
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Trigonometry 2 Course
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Thank you:)
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 write proofs is very important before jumping into analysis, but these are always fun to look at even if you aren't an expert at proof writing. I hope you enjoy this video.
Here are the books.
Principles of Mathematical Analysis by Rudin https://amzn.to/3VicMKf
Advanced Calculus by Buck https://amzn.to/3EueMbI
Advanced Calculus by Fitzpatrick https://amzn.to/3VhmzQW
Understanding Analysis by Abbott https://amzn.to/3ACUDPl
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
Free Homework Help : https://mathsorcererforums.com/
My FaceBook Page: https://www.facebook.com/themathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join
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Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU
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Advanced Calculus Course
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Calculus 1 Course
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Calculus 2 Course
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Calculus 3 Course
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Calculus 1 Lectures with Assignments and a Final Exam
https://www.udemy.com/course/calculus-1-lectures-with-the-math-sorcerer/?referralCode=5D425153B63A8F506E30
Calculus Integration Insanity
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Differential Equations Course
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Differential Equations Lectures Course (Includes Assignments + Final Exam)
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College Algebra Course
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How to Write Proofs with Functions Course
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Thank you:)
Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before ta...
Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before taking Real Analysis. Enjoy!
#realanalysis
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Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before taking Real Analysis. Enjoy!
#realanalysis
►BECOME A CHANNEL MEMBER
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How do you study for Real Analysis? Can you pass real analysis? In this video I tell you exactly how I made it through my analysis classes in undergrad and grad...
How do you study for Real Analysis? Can you pass real analysis? In this video I tell you exactly how I made it through my analysis classes in undergrad and graduate school, and then moved on to become a professor of mathematics.
//Books
Rosenlicht (short and easy to follow) - https://amzn.to/3k9X2Zc
Rudin (gold standard, but a bit opaque) - https://amzn.to/3KeL0IC
Apostol (thorough, but long) - https://amzn.to/3LhEylx
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0:00 Introduction
1:20 The Best Books for Real Analysis
3:55 Chunking Real Analysis
5:30 Sketching Proofs
6:40 The key to success in Real Analysis
How do you study for Real Analysis? Can you pass real analysis? In this video I tell you exactly how I made it through my analysis classes in undergrad and graduate school, and then moved on to become a professor of mathematics.
//Books
Rosenlicht (short and easy to follow) - https://amzn.to/3k9X2Zc
Rudin (gold standard, but a bit opaque) - https://amzn.to/3KeL0IC
Apostol (thorough, but long) - https://amzn.to/3LhEylx
//Music Provided by Epidemic Sound
Late Nights - Daxten
Alice is on her way - Airae
Follow me wild horse - Cospe
Light Up - Ben Elson
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
https://www.epidemicsound.com/referral/644nao
//Stock Footage Provided By
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//Recording Equipment
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Canon T6i: https://amzn.to/3FUpkQh
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Yeti Nano Microphone: https://amzn.to/3I1mriA
SanDisc 256GB SD Card: https://amzn.to/3E3LOOr
Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN
Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc
Camera Power Adapter: https://amzn.to/3D3upUu
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 Introduction
1:20 The Best Books for Real Analysis
3:55 Chunking Real Analysis
5:30 Sketching Proofs
6:40 The key to success in Real Analysis
This is Understanding Analysis by Stephen Abbott. This is a wonderful book for beginners who want to learn undergraduate level real analysis/advanced calculus.
...
This is Understanding Analysis by Stephen Abbott. This is a wonderful book for beginners who want to learn undergraduate level real analysis/advanced calculus.
Here it is: https://amzn.to/3oGCk9b
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
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How to Write Proofs with Functions Course
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Thank you:)
This is Understanding Analysis by Stephen Abbott. This is a wonderful book for beginners who want to learn undergraduate level real analysis/advanced calculus.
Here it is: https://amzn.to/3oGCk9b
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
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00:00 Intro
2:41 What is real analysis?
5:30 How long did the book take me?
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00:00 Intro
2:41 What is real analysis?
5:30 How long did the book take me?
6:18 How to approach practice problems
8:08 Did I like the course?
8:42 Quick example
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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTu...
MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw
An introduction to set theory and useful proof writing techniques required for the course. We start to see the power of mathematical induction.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw
An introduction to set theory and useful proof writing techniques required for the course. We start to see the power of mathematical induction.
License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu
Support OCW at http://ow.ly/a1If50zVRlQ
We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topi...
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
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The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman
In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone ...
In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone who is taking an Undergraduate level course on Advanced Calculus/Real Analysis. The book is titled Real Analysis: A Long-Form Mathematics Textbook and it was written by Jay Cummings.
Here is the book: https://amzn.to/3VkaNoN
(this is my affiliate link)
If you enjoyed this video please consider liking, sharing, and subscribing.
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How to Write Proofs with Sets Course
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How to Write Proofs with Functions Course
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Thank you:)
In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone who is taking an Undergraduate level course on Advanced Calculus/Real Analysis. The book is titled Real Analysis: A Long-Form Mathematics Textbook and it was written by Jay Cummings.
Here is the book: https://amzn.to/3VkaNoN
(this is my affiliate link)
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
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Differential Equations Course
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The third in our popular series of filmed student lectures takes us to Integration. This is the opening lecture in the 1st Year course. Ben Green both links the course to the mathematics our students have already learnt at school and develops that knowledge, taking the students to the next, more rigorous, stage. Like all good lectures, it recaps and points forward.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
This video has a list of books, videos, and exercises that goes through the undergrad pure mathematics curriculum from start to finish.
---
REAL ANALYSIS
Book: “Understanding Analysis” by Stephen Abbott.
Videos: Lectures by Francis Su (https://www.youtube.com/playlist?list=PL0E754696F72137EC)
LINEAR ALGEBRA
Book: “Linear Algebra Done Right” by Sheldon Axler
Videos: Sheldon Axler’s Playlist
(https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw)
POINT SET TOPOLOGY
Online Notes with Problems: MAT327 Course Notes (http://www.math.toronto.edu/ivan/mat327/?resources)
COMPLEX ANALYSIS
Intro Book: “Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
More Technical Book: “Complex Analysis” by Serge Lang
Videos: Wesleyan University Playlist (https://www.youtube.com/playlist?list=PL_onPhFCkVQjdQTbG0eQk42eH0RaBoYJf)
GROUP THEORY
Book: “Topics in Algebra” by Herstein (Chapter 2)
Videos: Lectures by Benedict Gross (https://www.youtube.com/playlist?list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5)
GALOIS THEORY
Notes by Tom Leinster: https://www.maths.ed.ac.uk/~tl/gt/gt.pdf
DIFFERENTIAL GEOMETRY
Book: Introduction to Differentiable Manifolds and Riemannian Geometry by Boothby
ALGEBRAIC TOPOLOGY
Book: Algebraic Topology by Allen Hatcher (available for free on his website: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html)
Videos: Lectures by Pierre Albin (https://www.youtube.com/playlist?list=PL41FDABC6AA085E78)
Intro: (0:00)
Linear Algebra: (0:36)
Real Analysis: (2:20)
Point Set Topology: (3:19)
Complex Analysis: (4:09)
Group Theory: (5:46)
Galois Theory: (6:54)
Differential Geometry: (7:23)
Algebraic Topology: (8:44)
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 write proofs is very important before jumping into analysis, but these are always fun to look at even if you aren't an expert at proof writing. I hope you enjoy this video.
Here are the books.
Principles of Mathematical Analysis by Rudin https://amzn.to/3VicMKf
Advanced Calculus by Buck https://amzn.to/3EueMbI
Advanced Calculus by Fitzpatrick https://amzn.to/3VhmzQW
Understanding Analysis by Abbott https://amzn.to/3ACUDPl
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
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Physics https://amzn.to/3BhPCMp
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How to Write Proofs with Functions Course
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Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before taking Real Analysis. Enjoy!
#realanalysis
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
How do you study for Real Analysis? Can you pass real analysis? In this video I tell you exactly how I made it through my analysis classes in undergrad and graduate school, and then moved on to become a professor of mathematics.
//Books
Rosenlicht (short and easy to follow) - https://amzn.to/3k9X2Zc
Rudin (gold standard, but a bit opaque) - https://amzn.to/3KeL0IC
Apostol (thorough, but long) - https://amzn.to/3LhEylx
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0:00 Introduction
1:20 The Best Books for Real Analysis
3:55 Chunking Real Analysis
5:30 Sketching Proofs
6:40 The key to success in Real Analysis
This is Understanding Analysis by Stephen Abbott. This is a wonderful book for beginners who want to learn undergraduate level real analysis/advanced calculus.
Here it is: https://amzn.to/3oGCk9b
Useful Math Supplies https://amzn.to/3Y5TGcv
My Recording Gear https://amzn.to/3BFvcxp
(these are my affiliate links)
***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
Pre-algebra, Algebra, and Geometry https://amzn.to/3FdbwSn
College Algebra, Precalculus, and Trigonometry https://amzn.to/3UKjvfb
Probability and Statistics https://amzn.to/3FaaxCq
Discrete Mathematics https://amzn.to/3P6jPE4
Proof Writing https://amzn.to/3XXukxo
Calculus https://amzn.to/3iEH3F3
Differential Equations Books https://amzn.to/3Fac5wi
Partial Differential Equations Books https://amzn.to/3uyk1SV
Linear Algebra https://amzn.to/3VHiN3G
Abstract Algebra Books https://amzn.to/3FzLZEr
Real Analysis/Advanced Calculus https://amzn.to/3VIO4Ua
Complex Analysis https://amzn.to/3P6kbuo
Number Theory https://amzn.to/3UEm3vw
Graph Theory https://amzn.to/3BfRd5m
Topology https://amzn.to/3BiAGhe
Graduate Level Books https://amzn.to/3uv1eIg
Computer Science https://amzn.to/3Hh8kaU
Physics https://amzn.to/3BhPCMp
These are my affiliate links. As an Amazon Associate I earn from qualifying purchases.
If you enjoyed this video please consider liking, sharing, and subscribing.
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00:00 Intro
2:41 What is real analysis?
5:30 How long did the book take me?
6:18 How to approach practice problems
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8:42 Quick example
10:53 Advice for self teaching
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MIT 18.100A Real Analysis, Fall 2020
Instructor: Dr. Casey Rodriguez
View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw
An introduction to set theory and useful proof writing techniques required for the course. We start to see the power of mathematical induction.
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The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
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I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
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In this video I will show you a very interesting real analysis book. This book is excellent for anyone who wants to learn Real Analysis on their own, or anyone who is taking an Undergraduate level course on Advanced Calculus/Real Analysis. The book is titled Real Analysis: A Long-Form Mathematics Textbook and it was written by Jay Cummings.
Here is the book: https://amzn.to/3VkaNoN
(this is my affiliate link)
If you enjoyed this video please consider liking, sharing, and subscribing.
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These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.
Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).