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The Queen of the Sciences: A History of Mathematics

Embark on a supreme intellectual adventure with an award-winning Professor of Mathematics.
Queen of the Sciences: A History of Mathematics is rated 4.7 out of 5 by 73.
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Rated 5 out of 5 by from The series of Mathematics' lectures was excellent Thank you Dr Bressoud for a most excellent mathematic series of lectures. I prefer ancient mathematics because of historical value rather than the more complicated modern mathematics such as Topology. It seems to me that the ancients such as Archimedes had the first notions of calculus by considering volumes of smaller size, towards the infinite. Thank you so much Professor and I intend to view your lectures on an ongoing basis.
Date published: 2024-05-10
Rated 2 out of 5 by from Alas, what could have been a great course The course had the potential to be excellent, but it was unfortunately hampered by poor graphics, inadequate diagrams, and lengthy verbal explanations of complex concepts. A lack of visual aids, such as a whiteboard or well-drawn diagrams, made it difficult to follow the material. While I persevered through Chapters 16 and 17, the focus on geometry exposed the limitations of the teaching format even further. If the video presentation is this challenging, I can only imagine how frustrating the audio version would be. It's clear that the instructor possesses a deep understanding of the subject. I enrolled in this course with high hopes of exploring the historical evolution of mathematics. While I wouldn't say I learned nothing, it fell far short of my expectations. Ultimately, the lack of clear explanations and visual aids prevents me from giving a higher rating. This course could have been truly engaging and informative with just a few improvements to the clarity of the explanations and the use of visual tools.
Date published: 2024-03-27
Rated 5 out of 5 by from Excellent overview I have listened to a number of math classes offered by the Great Courses, so I sampled this one out of curiosity. It was a pleasant surprise. Professor Bressoud’s take on the history of math and the personalities involved makes a very interesting experience. While the goal is not to teach you how to do math, there is enough information about the broad outlines of various topics to improve your perspective on how it all fits together. I had not seen math from this point of view. The instructor has a very buttoned-down style of presentation, which (remarkably) turns out to be quite effective at conveying information and even enthusiasm. One impression which will stay with me is the brevity of the lives of so many mathematicians in the hazardous times they were born into. Galois, Abel, Ramanujan, etc made their contributions at precociously young ages. And then of course one realizes that quite sophisticated math research has been going on for thousands (!) of years. Archimedes starting from Euclid’s area of the triangle to cleverly find the area of the circle is one of my all-time favorites.
Date published: 2023-11-04
Rated 5 out of 5 by from Amazing course! I find this course enlightning, engaging and vast knowledge grab for any history, science history and math enthusitast. I got a admit that I was not fan of university math while at the university, just took them to amass the credits necessary to finish the degree program. After viewing this course, wish we had a history course like this to keep us grounded and knowledgeable. This professor obviously one of the best teachers I've seen in Wondrium. Effortless delivery in a class-room type course is a great talent. Thanks for this course!
Date published: 2023-10-19
Rated 5 out of 5 by from The big picture in math While I've studied math before and many of the mathematicians were familiar, my emphasis was always on how to do things - like work out the shape of a soap bubble. I took for granted modern arithmetic not realizing that was a long slow battle to even have the number representations and systems, though Mesopotamia and ancient Greece were surprising. I found I was able to wrap my knowledge of mathematics in a more harmonious package by how it was discovered and how hard the gains actually were. Math has been in the back of my mind when it wasn't in the front. Without this course I don't think I would have ever seen it connected and relived its origins, let alone in under 12 hrs, I completed the course in a week of spare time! I listened at 1.5x though often pausing as I furiously made notes. On a second pass, which I always need for fluency, I would add mathematicians' lives and interests into the timeline in the provided notes and attempt to commit it to memory. Also I would make a comparison to art genres as Sharon Latchaw Hirsh presented in her "How to Look at and Understand Great Art". For that reason, I would mention Leonardo. Also left as an exercise for the reader were possibly the Kalman filter and antiaircraft applications, calculus of variations might be explicitly mentioned. But I wouldn't want anything changed or taken out. So I bet we could justify another 6 lectures or 12? Math appreciation for the layman (or nonspecialist) of higher math and current research, and some of the glossed over material. It's a wonderful course!
Date published: 2023-09-30
Rated 5 out of 5 by from The title is very appropriate. This course is much more than I expected. Professor Bressoud did an excellent job in explaining each chapter. Also, he always looked into the camera when he had too, unlike other speakers.
Date published: 2023-05-06
Rated 5 out of 5 by from I found this a terrific series of lectures! I have read a few histories of math and histories of parts of it. I am not a mathematician. I have studied it throughout my life as I have studied other provinces of the life of the mind. Bressoud gives the grand narrative of its development, details about some key figures, and a few words about the ideas. No blackboard work. If you know something about the ideas, his words are very effective. He is an attractive person.
Date published: 2022-06-23
Rated 5 out of 5 by from Enthusiastic, earnest, friendly professor Helps me begin to understand academic work from decades ago in my life, as well as appreciate how it fit into the discipline of math overall
Date published: 2022-04-06
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Overview

For at least 4,000 years of recorded history, humans have engaged in the study of mathematics. Our progress in this field is a gripping narrative that describes a never-ending search for hidden patterns in numbers, a philosopher's quest for the ultimate meaning of mathematical relationships, and a chronicle of amazing progress. Embark on a supreme intellectual adventure with The Queen of the Sciences: A History of Mathematics, 24 illuminating lectures taught by award-winning Professor of Mathematics David M. Bressoud.

About

David M. Bressoud

The stories of mathematics reveal it to be a creative endeavor done by real people who struggled to discover the underlying patterns of nature on which we have built our modern world.

INSTITUTION

Macalester College

Dr. David M. Bressoud is the DeWitt Wallace Professor of Mathematics in the Department of Mathematics and Computer Science at Macalester College. He earned his bachelor's degree in Mathematics from Swarthmore College and his master's degree and Ph.D. in Mathematics from Temple University. Professor Bressoud is experienced in teaching mathematics to students of all levels. As a Peace Corps volunteer before earning his Ph.D., he taught mathematics and science to intermediate school students in the West Indies, and he taught Advanced Placement Calculus at State College Area High School in Pennsylvania. A former Fulbright fellow and Sloan Foundation fellow, Professor Bressoud has served as Visiting Professor at the Institute for Advanced Study and the Mathematical Association of America's Pólya Lecturer and has received the Mathematical Association of America's Allegheny Mountain Section Distinguished Teaching Award. He is president of the Mathematical Association of America for the 2009-2011 term. He is the author of more than 50 research articles; 15 articles on mathematics education and related issues; and seven books, including four textbooks that draw on the history of mathematics, and Proof and Confirmation: The Story of the Alternating Sign Matrix Conjecture, which won the MAA Beckenbach Book Prize.

By This Professor

What Is Mathematics?

01: What Is Mathematics?

You explore the peculiar nature of mathematics. Why is it that abstractions that arose in one context can lead to unexpected insights in another? This lecture closes with a look at the major conceptual advances that are the focus of this course.

32 min
Babylonian and Egyptian Mathematics

02: Babylonian and Egyptian Mathematics

Egyptian and Mesopotamian mathematics were well developed by the time of the earliest records from the 2nd millennium B.C. Both knew how to find areas and volumes. The Babylonians solved quadratic equations using geometric methods and knew the Pythagorean theorem.

30 min
Greek Mathematics—Thales to Euclid

03: Greek Mathematics—Thales to Euclid

This lecture surveys more than 300 years of Greek mathematics, from Thales and Pythagoras to Euclid. Euclid's "Elements" covers much of the mathematical knowledge of the time and is considered the most important book of mathematics ever written.

30 min
Greek Mathematics—Archimedes to Hypatia

04: Greek Mathematics—Archimedes to Hypatia

Foremost among Greek mathematicians was Archimedes, who developed methods equivalent to the modern technique of integration. Hypatia was the first woman known to have made important contributions to mathematics and was one of the last scholars of the famous Museion at Alexandria.

31 min
Astronomy and the Origins of Trigonometry

05: Astronomy and the Origins of Trigonometry

The origins of trigonometry lie in astronomy, especially in finding the length of the chord that connects the endpoints of an arc of a circle. Hipparchus discovered a solution to this problem, that was later refined by Ptolemy who authored the great astronomical work the "Almagest."

31 min
Indian Mathematics—Trigonometry Blossoms

06: Indian Mathematics—Trigonometry Blossoms

You journey through the Gupta Empire and the great period of Indian mathematics that lasted from A.D. 320 to 1200. Along the way, you explore the significant advances that occurred in trigonometry and other mathematical fields.

31 min
Chinese Mathematics—Advances in Computation

07: Chinese Mathematics—Advances in Computation

At least as early as the 3rd century B.C.E., Chinese civil servants had to solve problems in surveying and collecting taxes.

30 min
Islamic Mathematics—The Creation of Algebra

08: Islamic Mathematics—The Creation of Algebra

Algebra was perfected here in the 9th century by the great mathematician Abu Jafar al-Kwarizmi, whose name would become the word "algorithm."

31 min
Italian Algebraists Solve the Cubic

09: Italian Algebraists Solve the Cubic

Mathematics from the Islamic world gradually spread into Europe in the 13th century, starting with Leonardo of Pisa, also known as Fibonacci. Italian mathematicians began to make original contributions in the 16th century when they discovered how to solve the general cubic and quartic equations.

31 min
Napier and the Natural Logarithm

10: Napier and the Natural Logarithm

Working at the turn of the 17th century, John Napier found a way to facilitate calculation for astronomers by inventing logarithms. He also discovered the number now designated by the letter "e."

31 min
Galileo and the Mathematics of Motion

11: Galileo and the Mathematics of Motion

In the early 17th century, Galileo Galilei made important innovations in the study of motion, establishing the pattern of relying on mathematical models to explore physical phenomena. René Descartes and Christiaan Huygens would build directly on his insights.

30 min
Fermat, Descartes, and Analytic Geometry

12: Fermat, Descartes, and Analytic Geometry

A lawyer for whom mathematics was an avocation, Pierre de Fermat was instrumental in the origins of calculus. In 1637, both Fermat and René Descartes published explanations of analytic geometry.

31 min
Newton—Modeling the Universe

13: Newton—Modeling the Universe

Isaac Newton famously said, "If I have seen further, it is by standing on the shoulders of giants." You learn who those giants were and explore Newton's invention of calculus to explain the motions of the heavens in "Principia Mathematica," published in 1687.

29 min
Leibniz and the Emergence of Calculus

14: Leibniz and the Emergence of Calculus

Independently of Newton, Gottfried Wilhelm Leibniz discovered the techniques of calculus in the 1670s, developing the notational system still used today.

31 min
Euler—Calculus Proves Its Promise

15: Euler—Calculus Proves Its Promise

Leonard Euler dominated 18th-century mathematics so thoroughly that his contemporaries believed he had solved all important problems.

30 min
Geometry—From Alhambra to Escher

16: Geometry—From Alhambra to Escher

You look at the influence of geometry on art, exploring the intriguing types of symmetry in Moorish tiling patterns. You also examine the geometrical experiments of M. C. Escher and August Möbius.

31 min
Gauss—Invention of Differential Geometry

17: Gauss—Invention of Differential Geometry

You explore Carl Friedrich Gauss and his interest in geometry on various kinds of surfaces, including his work on the parallel postulate, which laid the foundations for non-Euclidean geometry.

31 min
Algebra Becomes the Science of Symmetry

18: Algebra Becomes the Science of Symmetry

Algebra underwent a fundamental change in the 19th century, becoming a tool for studying transformations. One of the most tragic stories in mathematics involves Evariste Galois, who invented a set of transformations before dying at age 20 in a duel.

30 min
Modern Analysis—Fourier to Carleson

19: Modern Analysis—Fourier to Carleson

By 1800, calculus was well established as a powerful tool for solving practical problems, but its logical underpinnings were shaky. You explore the creative mathematics that addressed this problem in work from Joseph Fourier in the 19th century to Lennart Carleson in the 20th.

30 min
Riemann Sets New Directions for Analysis

20: Riemann Sets New Directions for Analysis

Bernhard Riemann left two famous legacies: the Riemann hypothesis, which deals with the distribution of prime numbers and is the most important open problem in mathematics today, and Riemann's new system of geometry, which Einstein used to develop his general theory of relativity.

31 min
Sylvester and Ramanujan—Different Worlds

21: Sylvester and Ramanujan—Different Worlds

This lecture explores the contrasting careers of James Joseph Sylvester, who was instrumental in developing an American mathematical tradition, and Srinivasa Ramanujan, a poor college dropout from India who produced a rich range of new mathematics during his short life.

30 min
Fermat's Last Theorem—The Final Triumph

22: Fermat's Last Theorem—The Final Triumph

Pierre de Fermat's enigmatic note regarding a proof that he didn't have space to write down sparked the most celebrated search in mathematics, lasting more than 350 years. This lecture follows the route to a proof, finally achieved in the 1990s.

31 min
Mathematics—The Ultimate Physical Reality

23: Mathematics—The Ultimate Physical Reality

Mathematics is the key to realms outside our intuition. You begin with Maxwell's equations and continue through general relativity, quantum mechanics, and string theory to see how mathematics enables us to work with physical realities for which our experience fails us.

31 min
Problems and Prospects for the 21st Century

24: Problems and Prospects for the 21st Century

This last lecture introduces some of the most promising and important questions in the field and examines mathematical challenges from other disciplines, especially genetics.

33 min