History of Mathematics in 50 Minutes
54:22
GRCC Mathematics Professor John Dersch reviews many historical innovations in math.
MathHistory1a: Pythagoras theorem
48:55
Pythagoras' theorem is both the oldest and the most important non-trivial theorem in mathematics.
This is the first part of the first lecture of a course on the History of Mathematics, by N J Wildberger, the discoverer of Rational Trigonometry. We will follow John Stillwell's text Mathematics and its History (Springer, 3rd ed). Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. A few historical tidbits will be thrown in too...
In this first lecture (with two parts) we first give a very rough outline of world history from a mathematical point of view, position the work of the ancient Greeks as following from Egyptian and Babylonian influences, and introduce the most important theorem in all of mathematics: Pythagoras' theorem.
Two interesting related issues are the irrationality of the 'square root of two' (the Greeks saw this as a segment, or perhaps more precisely as the proportion or ratio between two segments, not as a number), and Pythagorean triples, which go back to the Babylonians. These are closely related to the important rational parametrization of a circle, essentially discovered by Euclid and Diophantus. This is a valuable and under-appreciated insight which high school students ought to explicitly see.
In fact young people learning mathematics should really see more of the history of the subject! The Greeks thought of mathematics differently than we do today, and all students can benefit from a closer appreciation of the difficulties which they saw, but which we today largely ignore.
This series has now been extended a few times--with more than 35 videos on the History of Mathematics.
My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .
LNU-MSU Faculty Lecture Series - Brief History of Mathematics
1:47:27
A very condensed brief history of mathematics from ancient times to present.
Too much Maths, too little History: The problem of Economics
1:37:11
This is a recording of the debate hosted by the LSE Economic History Department, in collaboration with the LSESU Economic History Society and the LSESU Economics Society.
Speakers:
Proposition Team - Lord Robert Skidelsky & Dr. Ha-Joon Chang
Opposition Team - Prof. Steve Pisckhe & Prof. Francesco Caselli
Chair - Professor James Foreman-Peck
The LSE is currently the only institution to have a separate EH department. We want to encourage students and academics alike to rethink the methodologies used to explain how our world works.
Do we use the theoretical and econometrical method to create models with assumptions to distil the complexities of human nature and produce measurable results? Or do we use the historical process of considering all factors to provide a more holistic explanation? More importantly, which method should be adopted to better understand increasingly complex economic phenomena in the future?
We are striving to provide our students breadth that exceeds their current theoretical studies. Hence, whilst we recognise the importance of economic history in allowing us to become closer to the truth and produce more intricate portrayal of events, the significance of models and mathematics remains to be emphasised.
Indeed, we wish to have this controversially named debate in order to both highlight the tension between the two disciplines and to produce a more nuanced overview in defence of the future of Economics.
ARVIND GUPTA - HINDI - MATHS THROUGH ACTIVITIES - Inspire lecture
40:03
LECTURE-DEMONSTRATION AT THE PANDIT RAVISHANKAR SHUKLA UNIVERSITY, RAIPUR, INSPIRE CAMP ON 28 FEB 2013 This work was supported by IUCAA and Tata Trust. This film was made by Ashok Rupner TATA Trust: Education is one of the key focus areas for Tata Trusts, aiming towards enabling access of quality education to the underprivileged population in India. To facilitate quality in teaching and learning of Science education through workshops, capacity building and resource creation, Tata Trusts have been supporting Muktangan Vigyan Shodhika (MVS), IUCAA's Children’s Science Centre, since inception. To know more about other initiatives of Tata Trusts, please visit tatatrusts.org
3. The Birth of Algebra
1:44:24
(October 15, 2012) Professor Keith Devlin looks at how algebra, one of the most foundational concepts in math, was discovered.
Originally presented in the Stanford Continuing Studies Program.
Stanford University:
Stanford Continuing Studies Program:
Stanford University Channel on YouTube:
2011 Hagey Lecture: Dr. Ian Hacking - How did mathematics become possible?
1:22:27
In the 2011 Hagey Lecture, Professor Ian Hacking explores how human beings developed the ability to do math.
Monday, October 3, 2011 at 8:00pm, Humanities Theatre, Hagey Hall
Drawing from recent cognitive science, the history of early mathematics, social studies of science, and what has been called the archaeology of mind—how fashioning artifacts has changed the human mind itself—the lecture aims less at building bridges between these different kinds of inquiry, than at highlighting how much we are learning right now, and how little we know.
Ian Hacking is regarded as a leading scholar in the history and philosophy of science, although his work has touched fields as diverse as statistical inference and the emergence of multiple personality disorder. His contributions have earned many awards, including the Killam Prize for Humanities and an appointment to the Order of Canada.
Waterloo's premier invitational public lecture series since 1970, the Hagey Lectures are co-sponsored by the Faculty Association and the University of Waterloo.
Gresham College & the History of Mathematics: Professor Tony Manns Heroes of Mathematics
1:16
From Christopher Wren and Robert Hooke, to John Barrow and Raymond Flood - Professor Tony Mann discusses the importance of Gresham College in the history of mathematics in Britain, and also some of his personal Gresham maths heroes.
Tony Mann is Visiting Professor of Computer Mathematics at Gresham College. Information on his ongoing series of free public lectures is available here:
More information on Professor Tony Mann can be found here:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,600 lectures free to access or download from the website.
Website:
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Vedic Mathematics: My Trip to India to Uncover the Truth - Alex Bellos
34:00
One day on YouTube, Alex Bellos saw a video of an amazing mathematical trick. He wanted to know more about this 'Vedic Mathematics', so he got on a plane to India. This is a lecture about his journey that touched on mathematics, mysticism, Indian history, nationalism and culture.
The transcript and downloadable versions of the full conference are available from the on the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website.
Intro to Math Analysis
1:19:40
This is the first lecture in a course titled Intro to Math Analysis. This is a test video, but with any luck, the full sequence of lectures will be published at some point.
S G Dani delivers History of Mathematics lecture - Diophantine Arithmetic
1:24:53
This is second in the series of Special lecture entitled History of Mathematics. Professor Srikrishna Gopalrao Dani narrates historically the developments of certain aspects of number theory-in particular Diophantine arithmetic and approximations. The History of Mathematics lectures were initiated by Vista Foundation Bangalore at the behest of Prof Ravi S Kulkarni a senior Mathematician working currently at Bhaskaracharya Pratishthan Pune.
Introduction to Higher Mathematics - Lecture 5: Set Theory
29:02
In this lecture we discuss the beginnings of set theory, a topic that runs throughout almost every area of mathematics.
MathHistory8: Projective geometry
1:9:42
Projective geometry began with the work of Pappus, but was developed primarily by Desargues, with an important contribution by Pascal. Projective geometry is the geometry of the straightedge, and it is the simplest and most fundamental geometry. We describe the important insights of the 19th century geometers that connected the subject to 3 dimensional space.
4. Calculus: One of the Most Successful Technologies
1:42:48
(October 22, 2012) Professor Keith Devlin discusses how calculus is truly one of the most useful discoveries of all time.
Originally presented in the Stanford Continuing Studies Program.
Stanford University:
Stanford Continuing Studies Program:
Stanford University Channel on YouTube:
MathHistory2a: Greek geometry
50:41
The ancient Greeks loved geometry and made great advances in this subject. Euclid's Elements was for 2000 years the main text in mathematics, giving a careful systematic treatment of both planar and three dimensional geometry, culminating in the five Platonic solids.
Apollonius made a thorough study of conics. Constructions played a key role, using straightedge and compass.
This is one of a series of lectures on the History of Mathematics by Assoc. Prof. N J Wildberger at UNSW.
MathHistory20: Group theory
58:54
Here we give an introduction to the historical development of group theory, hopefully accessible even to those who have not studied group theory before, showing how in the 19th century the subject evolved from its origins in number theory and algebra to embracing a good part of geometry.
Actually the historical approach is a very fine way of learning about the subject for the first time.
We discuss how group theory enters perhaps first with Euler's work on Fermat's little theorem and his generalization of it, involving arithmetic mod n. We mention Gauss' composition of quadratic forms, and then look at permutations, which played an important role in Lagrange's approach to the problem of solving polynomial equations, and was then taken up by Abel and Galois.
The example of the symmetric group is at the heart of the subject, and so we examine S_3. In the 19th century groups of transformations became to be intimately tied to symmetries of geometries, with the work of Klein and Lie. A nice example that ties together the algebraic and geometric sides of the subject is the symmetry groups of the Platonic solids.
If you are interested in supporting my production of high quality math videos, why not consider becoming a Patron of this channel? Here is the link to my Patreon page:
Leibniz | History of Philosophy ☆ Lecture
2:21:01
In this History of Modern Philosophy video lecture you will hear and learn about: Leibniz. This lecture was given by Professor John M. DePoe, at Marywood University.
Gottfried Wilhelm (von) Leibniz was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton.
This video was made by another YouTube user and made available for the use under the Creative Commons licence CC-BY. Source channel: John DePoe
MathHistory27: Sets, logic and computability
53:01
In this video we give a very quick overview of a highly controversial period in the development of modern mathematics: the rise of set theory, logic and computability in the late 19th and early 20th centuries.
Starting with the pioneering but contentious work of Georg Cantor in creating Set Theory arising from questions in harmonic analysis, we discuss Dedekind's construction of real numbers, ordinals and cardinals, and some of the paradoxes that this new way of thinking led to. We also explain how the Schools of Logicism, Intuitionism and Formalism all tried to steer a path around these paradoxes.
I should qualify this lecture by stating clearly that in fact I don't really ascribe to any of the theories presented here. My objections will be laid out at length in my MathFoundations series. In this video I am mostly overviewing--rather briefly to be sure!-- the standard thinking, even though I have very little sympathy with it.
But it is important to understand this historical period, since it impacts so heavily on the mathematics that we currently believe in, teach and apply to the world. We are part of a trajectory of human thought, and not necessarily on the pinnacle or high point of that trajectory--much as we would like to think so! In particular, there is much to be learnt by a study of the issues here that so captured the imagination of the late 19th century and early 20th century mathematical and philosophical thinkers.
My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .
MathHistory9: Calculus
1:00
Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes, who were interested in volume problems, and to a lesser extent in tangents. In the 17th century the subject was widely expanded and developed in an algebraic way using also the coordinate geometry of Descartes. This is one of the most important developments in the history of mathematics.
Calculus has two branches: the differential and integral calculus. The former arose from the study by Fermat of maxima and minima of functions via horizontal tangents.
The integral calculus computes areas and volumes beyond the techniques of Archimedes. It was developed independently by Newton and Leibnitz, but others contributed too. Newton's focus was on power series, for which differentiation and integration can be done term by term using a formula of Cavalieri, and which gave remarkable new formulas for pi and the circular functions. He had a dynamic view of the subject, motivated in large part by physics.
Leibnitz was more interested in closed forms, and introduced the notation which we use today. Both used infinitesimals, in the form of differentials.
A History of Mathematics in Non-Western Cultures
1:7:27
A History of Mathematics in Non-Western Cultures
Lecture-12- Highlights of Science in Ancient India – Part 1-IIT Kanpur
1:9:41
Exploring Indian Civilization by Michel Danino,IIT Kanpur
1. An overview of India’s early advances in geometry, mathematics and astronomy, from Vedic to historical times.
Maths Degree Lecture: mathematics of codes and code-breaking
50:19
What's it like to study Maths at University? Dr James Grime of Cambridge University discusses the fascinating history and mathematics of codes and code-breaking. The lecture includes a demonstration of a genuine World War II Enigma Machine. The lecture formed part of the University of Glamorgan's Annual Sixth Form Maths Lecture 2011.
Mathematics - Multivariable Calculus - Lecture 1
1:19:50
Multivariable Calculus
Instructor: Edward Frenkel
course website:
Lecture I - Beauty and Truth in Mathematics and Science
1:7:11
Robert May, Baron May of Oxford; Professor, Zoology, Oxford University and Imperial College
October 2, 2012
2012 Stanislaw Ulam Memorial Lectures
May explores the extent to which beauty has guided, and still guides, humanity's quest to understand how the world works, with a brief look at the interactions among beliefs, values, beauty, truth, and our expectations for tomorrow's world.
1. General Overview and the Development of Numbers
1:44:17
(October 1, 2012) Keith Devlin gives an overview of the history of mathematics. He discusses how it has evolved over time and explores many of its practical applications in the world.
Originally presented in the Stanford Continuing Studies Program.
Stanford University:
Stanford Continuing Studies Program:
Stanford University Channel on YouTube:
The Music of the Primes - Marcus du Sautoy
1:08
The Music of the Primes
Marcus du Sautoy, Oxford University
Thursday, May 8, 2008, at 6:00 pm
MIT, Compton Laboratories
Building 26, Room 26-100
Access via 60 Vassar Street
Marcus du Sautoy, author of the The Music of the Primes, will discuss the mystery of prime numbers, the history behind the Riemann hypothesis and the ongoing quest to solve it.
Why did Beckham choose the number 23 shirt? How is 17 the key to the evolutionary survival of a strange species of cicada? Prime numbers are the atoms of arithmetic -- the hydrogen and oxygen of the world of numbers. Despite their fundamental importance to mathematics, they represent one of the most tantalizing enigmas in the pursuit of human knowledge. In 1859, the German mathematician Bernhard Riemann put forward an idea -- a hypothesis -- that seemed to reveal a magical harmony at work in the numerical landscape. A million dollars now await the person who can unravel the mystery of the hidden music that might explain the cacophony of the primes.
Marcus du Sautoy is Professor of Mathematics at the University of Oxford and a Fellow of Wadham College. He is author of numerous academic articles and books on mathematics. He has been a visiting Professor at the École Normale Supérieure in Paris, the Max Planck Institute in Bonn, the Hebrew University in Jerusalem and the Australian National University in Canberra.
Marcus du Sautoy is author of the best-selling popular mathematics book The Music of the Primes published by Fourth Estate in 2003 and translated into 10 languages. It has won two major prizes in Italy and Germany for the best popular science book of the year. His new book Finding Moonshine: A Mathematician's Journey Through Symmetry is also published by Fourth Estate and was released in March 2008.
Our thanks to the MIT Mathematics Department for hosting this event.
Birmingham Popular Mathematics Lectures - the story of Pi
1:7:51
Robin Wilson, Emeritus Professor of Pure Mathematics at the Open University and Emeritus Professor of Geometry at Gresham College, London, relays the history of π, from the ancient Egyptians and Mesopotamians, via Archimedes, China and the Middle Ages, to the Indiana court case and the advances of the modern computer age.
James Clerk Maxwell: The Greatest Victorian Mathematical Physicists - Professor Raymond Flood
52:32
James Clerk Maxwell (1831-1879) was one of the most important mathematical physicists of all time, after only Newton and Einstein. Within a relatively short lifetime he made enormous contributions to science which this lecture will survey. Foremost among these was the formulation of the theory of electromagnetism with light, electricity and magnetism all shown to be manifestations of the electromagnetic field. He also made major contributions to the theory of colour vision and optics, the kinetic theory of gases and thermodynamics, and the understanding of the dynamics and stability of Saturn's rings.
This talk was a part of the conference on '19th Century Mathematical Physics', held jointly by Gresham College and the British Society of the History of Mathematics. The transcript and downloadable versions of all of the lectures are available from the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There is currently nearly 1,500 lectures free to access or download from the website.
Website:
Twitter:
Facebook:
Eulers Exponentials - Professor Raymond Flood
50:57
A thorough examination of the life and work of one of histories greatest mathematicians, the Shakespeare of Numbers, Leonhard Euler:
Leonhard Euler was the most prolific mathematician of all time. He introduced the symbols e for the exponential number f for a function and i for √-1. He discovered what many mathematicians consider to be the most beautiful expression in mathematics, e ix = cosx + i sinx: a relation connecting the exponential and trigonometric functions. The exponential function and its inverse the logarithm function appear throughout mathematics and its applications, in physics, engineering, mathematical biology, chemistry and economics.
The transcript and downloadable versions of the lecture are available from the Gresham College Website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,500 lectures free to access or download from the website.
Website:
Twitter:
Facebook:
A Tribute to Euler - William Dunham
55:08
A Tribute to Euler
William Dunham
Truman Koehler Professor of Mathematics, Muhlenberg College
Tuesday, October 14, 2008, at 6:00 PM
Harvard University Science Center, Hall D
The fall 2008 Clay Public Lecture will be held at Harvard on October 14, in association with the Harvard Mathematics Department. Known for his writings on the history of mathematics, Professor William Dunham will examine the genius of one of the world's most prolific mathematicians in his talk A Tribute to Euler in Hall D of the Harvard Science Center at 6 pm.
Among history's greatest mathematicians is Leonhard Euler (1707-1783), the Swiss genius who produced an astonishing 25,000 pages of pure and applied mathematics of the very highest quality.
In this talk, we sketch Euler's life and describe a few of his contributions to number theory, algebra, and other branches of mathematics. Then we examine a particular Eulerian theorem: his simple but beautiful proof that there are as many ways to decompose a whole number as the sum of distinct summands as there are ways to decompose it as the sum of (not necessarily distinct) odd summands.
Condorcet, in his Eulogy to Euler, wrote that All mathematicians now alive are his disciples. It should be clear to those who attend the Clay Public Lecture that these words are as true today as when they were first set down, over two centuries ago.
William Dunham, who received his B.S. (1969) from the University of Pittsburgh and his M.S. (1970) and Ph.D. (1974) from Ohio State, is the Truman Koehler Professor of Mathematics at Muhlenberg College. In the fall term of 2008 he is visiting at Harvard University and teaching a course on the work of Leonhard Euler.
Over the years, he has directed NEH seminars on the history of mathematics and has spoken on historical topics at dozens of U.S. colleges and universities, as well as at the Smithsonian Institution, the Swiss Embassy in Washington, and on NPR's Talk of the Nation: Science Friday.
In the 1990s, Dunham wrote three books on mathematics and its history: Journey Through Genuis: The Great Theorems of Mathematics (1990), The Mathematical Universe (1994), and Euler: The Master of Us All (1999). In the present millennium, he has written The Calculus Gallery: Masterpieces from Newton to Lebesgue (2005) and edited The Genius of Euler: Reflections on His Life and Work (2007). His expository writing has been recognized by the Mathematical Association of America with the George Pólya Award in 1992, the Trevor Evans Award in 1997, the Lester R. Ford Award in 2006, and the Beckenbach Prize in 2008. The Association of American Publishers designated The Mathematical Universe as the Best Mathematics Book of 1994.
Our thanks to the Harvard Mathematics Department for hosting this event.
The Queen of Mathematics - Professor Raymond Flood
1:20
Carl Friedrich Gauss one of the greatest mathematicians, is said to have claimed: Mathematics is the queen of the sciences and number theory is the queen of mathematics. The properties of primes play a crucial part in number theory. An intriguing question is how they are distributed among the other integers. The 19th century saw progress in answering this question with the proof of the Prime Number Theorem although it also saw Bernhard Riemann posing what many think to be the greatest unsolved problem in mathematics - the Rieman Hypothesis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently nearly 1,500 lectures free to access or download from the website.
Website:
Twitter:
Facebook:
MathHistory12: Non-Euclidean geometry
50:52
The development of non-Euclidean geometry is often presented as a high point of 19th century mathematics. The real story is more complicated, tinged with sadness, confusion and orthodoxy, that is reflected even the geometry studied today. The important insights of Gauss, Lobachevsky and Bolyai, along with later work of Beltrami, were the end result of a long and circuitous study of Euclid's parallel postulate. But an honest assessment must reveal that in fact non-Euclidean geometry had been well studied from two thousand years ago, since the geometry of the sphere had been a main concern for all astronomers.
This lecture gives a somewhat radical and new interpretation of the history, suggesting that there is in fact a much better way of thinking about this subject, as perceived already by Beltrami and Klein, but largely abandoned in the 20th century. This involves a three dimensional linear algebra with an unusual inner product, looked at in a projective fashion. This predates and anticipates the great work of Einstein on relativity and its space-time interpretation by Minkowski.
For those interested, a fuller account of this improved approach is found in my Universal Hyperbolic Geometry (UnivHypGeom) series of YouTube videos.
Lecture 1: Functions | Prof. Pervez Hoodbhoy
24:28
Lecture 1: FUNCTIONS
Different kinds of numbers.
What is a function?
Sums and products of functions.
Composite functions (function of a function)
Inverse function.
Mathematics, Measurement and Money - Professor Norman Biggs
54:26
An overview of Mathematics, Measurement and Money and their evolution over time
THE JOINT LONDON MATHEMATICAL SOCIETY/ GRESHAM COLLEGE ANNUAL LECTURE
Throughout its brief history, mathematics has been closely linked with measurement and money. In the ancient settlements the rules of arithmetic and geometry were used to solve problems about the allocation of food and resources. When life became more complex, the use of coined money led to computational problems that required good algorithms for their solution.
Nowadays we rely on mathematics for security, and the links between information and money have become blurred. Can mathematics keep us safe?
The transcript and downloadable versions of the lecture are available from the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,900 lectures free to access or download from the website.
Website:
Twitter:
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X-Math@LSU Summer 2009: History Of Knot Theory, Lecture by Dan Silver
51:29
History of Knot Theory;
Lecture by Dan Silver (University of South Alabama)
For details see:
A Mathematicians view on symmetry p2
1:8:00
This is second part of the History of Mathematics Lecture series-Inaugural talks. Speaker:Ravi Kulkarni of Bhaskaracharya Pratishthan PUNE
MathHistory16: Differential Geometry
51:32
Differential geometry arises from applying calculus and analytic geometry to curves and surfaces. This video begins with a discussion of planar curves and the work of C. Huygens on involutes and evolutes, and the related notions of curvature and osculating circle. We discuss involutes of the catenary (yielding the tractrix), cycloid and parabola. The evolute of the parabola is a semi-cubical parabola. For space curves we describe the tangent line, osculating plane, principle normal and binormal.
Surfaces were studied by Euler, who investigated curvatures of planar sections and by Gauss, who realized that the product of Euler's two principal curvatures gave a new notion of curvature intrinsic to a surface. Curvature was ultimately extended by Riemann to higher dimensions, and plays today a major role in modern physics, due to the work of Einstein.
If you like this topic, and want to learn more, make sure you don't miss Wildberger's exciting new course on Differential Geometry! See the Playlist DiffGeom, at this channel.
My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .
Mathematical History: Triangular Relationships - Professor Patricia Fara
48:49
And first, the fair PARABOLA behold,
Her timid arms with virgin blush unfold!...
Mathematical poetry may seem an unlikely form of satire, but 'The Loves of the Triangles' (1798) was not only a clever parody of Erasmus Darwin (Charles' grandfather) but also a powerful political commentary expressing contemporary fears of revolution and evolution.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website.
History of Mathematics
7:05
WEBSITE:
An animated movie on the development of numbers throughout history.
Speed , Distance and Time - Anuj Garg Coaching
40:11
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MathHistory6a: Polynomial equations
52:41
We now move to the Golden age of European mathematics: the period 1500-1900, in this course on the History of Mathematics. We discuss hurdles that the Europeans faced before this time and how they emerged, with the help of Arab algebra and translations of Greek works, to harness the Hindu-Arabic number system and a host of novel symbols including Vieta's new use of letters to represent unknowns to tackle new problems.
Quadratic equations had been solved by almost all earlier mathematical civilizations; cubic equations was a natural step, taken by Tartaglia and Cardano and others. Tartaglia also discovered a formula for the volume of a tetrahedron, and Vieta a trigonometric way of solving cubics.
My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .
A mathematicians view on symmetry
54:37
This is first of the History of Mathematics Lecture series organized by Vista Foundation's Centre for advanced study Bangalore. Speaker: prof Ravi S Kulkarni of Bhaskaracharya Pratishthana PUNE.
The Map of Mathematics
11:06
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.
If you would like to buy a poster of this map, they are available here:
I have also made a version available for educational use which you can find here:
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.
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.
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics:
Earliest human counting:
First use of zero:
First use of negative numbers:
Renaissance science:
History of complex numbers:
Proof that pi is irrational:
and
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:
Atomic Adventure:
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Ghosts of Departed Quantities: Calculus and its Limits - Professor Raymond Flood
56:31
In 1734 Bishop Berkeley published a witty and effective attack on the foundations of the calculus as developed by Newton and Leibniz. But it took nearly 90 years for the calculus to be given a rigorous foundation through the work of the prolific mathematician, Augustin-Louis Cauchy, who formalised the concept of a limit and created the specialism now called analysis.
The transcript and downloadable versions of the lecture are available from the Gresham College website:
Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There is currently over 1,300 lectures free to access or download from the website.
Website:
Twitter:
Facebook:
Prof. Jean Dieudonné: The Historical Development of Algebraic Geometry
1:4:38
The Historical Development of Algebraic Geometry presented by Prof. Jean Dieudonné on Mar. 3, 1972
(Video starts off bad and gets better as lecture continues)
Great Mathematicians, Great Mathematics: An Introduction by Professor Raymond Flood
3:48
Gresham Professor of Geometry, Professor Raymond Flood, introduces us to his 2014-15 lecture series on the lives and work of the greatest Mathematicians in history. From Fermat to Euler, Fourier to Cantor, Professor Flood will examine the biography of each, placing their work in it historical context. Then, through examples and applications, he explains the importance of their work to modern mathematics. Raymond Flood is Gresham Professor of Geometry at Gresham College. Information on her ongoing series of free public lectures is available here: More information on Professor Flood can be found here: Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,600 lectures free to access or download from the website. Website: Twitter: Facebook:
Senior Lectures: Ralph Abraham - Complex Dynamical Systems
19:35
2010 lecture by Ralph Abraham to Ross School Seniors on the history of mathematics leading to the development of Complex Dynamical Systems Theory and the impact that Chaos Theory had on this 'new' branch of mathematics.
ncert lectures mathematics class 9 chapter 4 SA 2
7:12
ncert lectures mathematics class 9 chapter 4 SA 2 Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4 (ii) x – y = 2 (iii) y = 3x (iv) 3 = 2x + y
Basic Math: Lesson 1 - Numbers
38:44
This lesson consists of providing you with a Self-Tutorial on all about the classification and sets of numbers. Learn what are natural numbers, integers, rational numbers and more. I also explain how to use your graphing calculator to input all types of numbers (integers, fractions, square roots, etc.).
Notes are here:
MathHistory28: Computability and problems with Set theory
47:05
We look at the difficulties and controversy surrounding Cantor's Set theory at the turn of the 20th century, and the Formalist approach to resolving these difficulties. This program of Hilbert was seriously disrupted by Godel's conclusions about Inconsistency of formal systems. Nevertheless, it went on to support the Zermelo-Fraenkel axiomatic approach to sets which we have a quick look at.
Then we introduce Alan Turing's ideas of computability via Turing machines and some of the consequences.
The lecture closes with a review of historical positions on the contentious idea of completed infinite sets, quoting illustrious mathematicians from Aristotle to A. Robinson, along with G. Cantor himself.
In summary, it appears that this is not a closed chapter in the History of Mathematics. For those interested in a more in depth discussion of these and other interesting issues, see my MathFoundations series of YouTube videos--also at this channel.
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