Zero to Infinity: A History of Numbers

Course No. 1499
Professor Edward B. Burger, Ph.D.
Southwestern University
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Course No. 1499
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Course Overview

Numbers surround us. They mark our days, light our nights, foretell our weather, and keep us on course. They drive commerce and sustain civilization. But what are they? Whether you struggled through algebra or you majored in mathematics, you will find Professor Edward B. Burger's approach accessible and stimulating. If you think math is just problems and formulas, prepare to be amazed.

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24 lectures
 |  Average 30 minutes each
  • 1
    The Ever-Evolving Notion of Number
    While numbers are precision personified, the exact definition of "number" is elusive, because it's still evolving. The course will trace progress in understanding and using numbers while also exploring discoveries that have advanced our grasp of number. We will meet the great thinkers who made these discoveries—from old friends Pythagoras and Euclid to the more modern but equally brilliant Euler, Gauss, and Cantor. x
  • 2
    The Dawn of Numbers
    One of the earliest questions was "How many?" Humans have been answering this question for thousands of years—since Sumerian shepherds used pebbles to keep track of their sheep, Mesopotamian merchants kept their accounts on clay tablets, and Darius of Persia used a knotted cord as a calendar. x
  • 3
    Speaking the Language of Numbers
    As numbers became useful to count and record as well as calculate and predict, many societies, including the Sumerians, Egyptians, Mayans, and Chinese, invented sophisticated numeral systems; arithmetic developed. Negative numbers, Arabic numerals, multiplication, and division made number an area for abstract, imaginative study as well as for everyday use. x
  • 4
    The Dramatic Digits—The Power of Zero
    When calculation became more important, zero—a crucial breakthrough—was born. Unwieldy additive number systems, like Babylonian nails and dovetails, or Roman numerals, gave way to compact place-based systems. These systems, which include the modern base-10 system we use today, made modern mathematics possible. x
  • 5
    The Magical and Spiritual Allure of Numbers
    As numbers developed from tools into a branch of learning, they gained power and mystery. Mesopotamians used numbers to name their gods, for example, while Pythagoreans believed that numbers were divine gifts. Humans have invoked the power of numbers for millennia to ward off bad luck, to attract good luck, and to entertain the curious—uses that have drawn some to explore numbers' more serious and subtle properties. x
  • 6
    Nature's Numbers—Patterns without People
    Those who studied them found numbers captivating and soon realized that numerical structure, pattern, and beauty existed long before our ancestors named the numbers. In this lecture, our studies of pattern and structure in nature lead us to Fibonacci numbers and to connect them in turn to the golden ratio studied by the Pythagoreans centuries earlier. x
  • 7
    Numbers of Prime Importance
    Now we study prime numbers, the building blocks of all natural (counting) numbers larger than 1. This area of inquiry dates to ancient Greece, where, using one of the most elegant arguments in all of mathematics, Euclid proved that there are infinitely many primes. Some of the great questions about primes still remain unanswered; the study of primes is an active area of research known as analytic number theory. x
  • 8
    Challenging the Rationality of Numbers
    Babylonians and Egyptians used rational numbers, better known as fractions, perhaps as early as 2000 B.C. Pythagoreans believed rational and natural numbers made it possible to measure all possible lengths. When the Pythagoreans encountered lengths not measurable in this way, irrational numbers were born, and the world of number expanded. x
  • 9
    Walk the (Number) Line
    We have learned about natural numbers, integers, rational numbers, and irrationals. In this lecture, we'll encounter real numbers, an extended notion of number. We'll learn what distinguishes rational numbers within real numbers, and we'll also prove that the endless decimal 0.9999... exactly equals 1. x
  • 10
    The Commonplace Chaos among Real Numbers
    Rational and irrational numbers have a defining difference that leads us to an intuitive and correct conclusion, and to a new understanding about how common rationals and irrationals really are. Examining random base-10 real numbers introduces us to "normal" numbers and shows that "almost all" real numbers are normal and "almost all" real numbers are, in fact, irrational. x
  • 11
    A Beautiful Dusting of Zeroes and Twos
    In base-3, real numbers reveal an even deeper and more amazing structure, and we can detect and visualize a famous, and famously vexing, collection of real numbers—the Cantor Set first described by German mathematician Georg Cantor in 1883. x
  • 12
    An Intuitive Sojourn into Arithmetic
    We begin with a historical overview of addition, subtraction, multiplication, division, and exponentiation, in the course of which we'll prove why a negative number times a negative number equals a positive number. We'll revisit Euclid's Five Common Notions (having learned in Lecture 11 that one of these notions is not always true), and we'll see what happens when we raise a number to a fractional or irrational power. x
  • 13
    The Story of pi
    Pi is one of the most famous numbers in history. The Babylonians had approximated it by 1800 B.C., and computers have calculated it to the trillions of digits, but we'll see that major questions about this amazing number remain unanswered. x
  • 14
    The Story of Euler's e
    Compared to pi, e is a newcomer, but it quickly became another important number in mathematics and science. Now known as Euler's number, it is fundamental to understanding growth. This lecture traces the evolution of e. x
  • 15
    Transcendental Numbers
    Pi and e take us into the mysterious world of transcendental numbers, where we'll learn the difference between algebraic numbers, known since the Babylonians, and the new—and teeming—realm of transcendentals. x
  • 16
    An Algebraic Approach to Numbers
    This part of the course invites us to take two views of number, the algebraic and the analytical. The algebraic perspective takes us to imaginary numbers, while the analytical perspective challenges our sense of what number even means. x
  • 17
    The Five Most Important Numbers
    Looking at complex numbers geometrically shows a way to connect the five most important numbers in mathematics: 0, 1, p, e, and i, through the most beautiful equation in mathematics, Euler's identity. x
  • 18
    An Analytic Approach to Numbers
    We'll explore real numbers from another perspective: the analytical approach, which uses the distance between numbers to discover and fill in holes on a rational number line. This exploration leads to a new kind of absolute value based on prime numbers. x
  • 19
    A New Breed of Numbers
    Pythagoreans found irrational numbers not only counterintuitive but threatening to their world-view. In this lecture, we'll get acquainted with—and use—some numbers that we may find equally bizarre: p-adic numbers. We'll learn a new way of looking at number, and about a lens through which all triangles become isosceles. x
  • 20
    The Notion of Transfinite Numbers
    Although it seems that we've looked at all possible worlds of number, we soon find that these worlds open onto a universe of number—and further still. In this lecture, we'll learn not only how humans arrived at the notion of infinity but how to compare infinities. x
  • 21
    Collections Too Infinite to Count
    Now that we are comfortable thinking about the infinite, we'll look more closely at various collections of numbers, thereby discovering that infinity comes in at least two sizes. x
  • 22
    In and Out—The Road to a Third Infinity
    If infinity comes in two sizes, does it come in three? We'll use set theory to understand how it might. Then we'll apply this insight to infinite sets as well, a process that leads us to a third kind of infinity. x
  • 23
    Infinity—What We Know and What We Don't
    If there are several sizes of infinity, are there infinitely many sizes of it? Is there a largest infinity? And is there a size of infinity between the infinity of natural numbers and real numbers? We'll answer two of these questions and learn why the answer to the other is neither provable nor disprovable mathematically. x
  • 24
    The Endless Frontier of Number
    Now that we've traversed the universe of number, we can look back and understand how the idea of number has changed and evolved. In this lecture, we'll get a sense of how mathematicians expand the frontiers of number, and we'll look at a couple of questions occupying today's number theorists—the Riemann Hypothesis and prime factorization. x

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Your professor

Edward B. Burger

About Your Professor

Edward B. Burger, Ph.D.
Southwestern University
Dr. Edward B. Burger is President of Southwestern University in Georgetown, Texas. Previously, he was Francis Christopher Oakley Third Century Professor of Mathematics at Williams College. He graduated summa cum laude from Connecticut College, where he earned a B.A. with distinction in Mathematics. He earned his Ph.D. in Mathematics from The University of Texas at Austin. Professor Burger is the recipient of many teaching...
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Zero to Infinity: A History of Numbers is rated 4.5 out of 5 by 48.
Rated 4 out of 5 by from
Date published: 2015-04-26
Rated 4 out of 5 by from Speaker Quality I have the same complaint with this course as I do with his other course. His "pause" or filler words are too often and too many. Instead of "a," "um," and "you know;" he gives us "now," and "well" with both words over used until they are meaningless. He knows his topic and gave me new information and concepts. I feel that he is used to a longer lecture period and isn't sure what fits in a half hour. He needs some retakes and more practice for the half hour sessions.
Date published: 2014-12-06
Rated 5 out of 5 by from Making mathematics fun to learn Let's get one thing straight: I've never enjoyed math. I purchased this course because I was interested in the history of zero. But the entire course was so interesting that zero became just one of the many fascinating topics. Fibonacci numbers was the most entertaining lecture topic but I was amazed to find that I could actually understand - and enjoyed - the concept of multiple infinities. Don't be intimidated by this course if you think you're not a "math" person. Professor Burger's explanations are clear and his enjoyment of the topics makes this course easy to watch. You do not need a background in mathematics, just an open mind ready to learn that math really can be fascinating.
Date published: 2014-02-21
Rated 5 out of 5 by from Great Blend of History and Math Professor Burger offers a fun and stimulating exploration of numbers beginning with the ancient need of Sumerian shepherds to track their flocks. He traces a roughly chronological history of numbers through time, to include the Babylonians, Egyptians, and Chinese, right up to the innovative Pythagoras himself. The story of the Pythagoreans and their reaction to the discovery of irrational numbers is startling. The course continues through Euclid, the Mayans, Brahmagupta, Fibonacci, Cardano, Euler, Gauss, Cantor and many more historical figures key to the expansion of knowledge in mathematics. It sounds as if the life and works of Georg Cantor, along with the startling responses of the scientific community to his brilliant ideas, could fill a fascinating 12 to 24 lecture course of its own Professor Burger provides excellent order to his lecture series allowing the learner to build and review their math skills so that more advanced material is easier to digest when presented. The math is really not all that advanced - and when he does present some more involved math it is often not really critical to the broad historical understanding of the material (so you can either take the math part or leave it). The mathematical content overlaps somewhat with that of the Teaching Company course, Joy of Mathematics, presented by Professor Benjamin. Both courses cover concepts regarding primes, Fibonacci numbers, Pi, imaginary numbers, the number e, infinity, and more. The two courses are quite complementary; with Professor Burger’s course focusing more closely on the history and Professor Benjamin’s more on the mathematical ideas. The last six lectures are fantastic and introduce some mathematical concepts you may not have encountered before. I certainly had little knowledge of p-adic numbers, Cantor sets, different sizes of infinity, and the Continuum Hypothesis despite taking many a university level math course in my college days. This course will be great fun for anyone with a mathematical bent and some advanced high school level math experience. Professor Burger nicely blends the history and the mathematics to provide new perspectives on the historical development of the idea of number.
Date published: 2013-11-22
Rated 3 out of 5 by from overwhelmed with numbers I admit it, I'm not a numbers' person and that's why I listened to this course. I found the history of the development of numbers and historical use to be fascinating. Then, Dr. Binger 'promised' to not have much math, and proceeded to have formula after formula. Maybe, it's just not my thing, but I had to stop watching because I was overwhelmed with formulas and numbers. He is very enthusiastic. Unfortunately, it was not contagious--and I didn't catch the bug.
Date published: 2013-06-23
Rated 4 out of 5 by from Historical Intro & Human Perspective to Math This course certainly challenged my notion of "number" from the transcendentals as not algebraic numbers (still seems odd to define something by what is not) to the still confusing p-adic numbers that will probably always seem counter-intuitive. The way math is taught in school give a sense that mathematical proofs are accepted as true, but one of my favorite parts was Cantor's story of his defense of multiple infinities in reaction to a highly opposed mathematical community. When quoting mathematicians, he does read from the sources. There is some brief calculus, geometry, and algebra 2 concepts, but he explains them well enough that almost no prior knowledge is needed to understand the overall concepts (the specifics aren't necessarily the focus, rather its the journey that's important). He does briefly mention various cultures in comparing discoveries like Mesopotamia, Egypt, India, and Italy. While some lectures seemed a bit random, for the most part there was some order to the lectures. I will consider getting his "Intro to Number Theory" course.
Date published: 2012-11-03
Rated 5 out of 5 by from A GEM OF A COURSE ~ FOR ALL! Recommended enthusiastically! And the really good news is that to enjoy & benefit from this course, you do not need to have any advanced knowledge of maths. A little algebra will be helpful but even that isn't necessary, as Dr Edward Burger presents his lectures in clear step-by-step procedure. A wonderfully refreshing course with a bright, energetic professor who understands perfectly well how to communicate, how to get his points across in a most appealing way, maintaining a healthy pace. He uses straightforward language, is friendly, never condescending ~ and he sprinkles in a handy dash of humour (he worked briefly as a joke-writer for Jay Leno!). The blending of history, nature, language and mathematics in this course is fascinating, as the development of numbering systems and numbers is revealed. The onscreen graphics are essential, an integral part of the course, serving to emphasise as well as to demonstrate. The in-studio demonstrations are memorable & amusing. Exercises are set in the handbook, to assist in testing your understanding, if you so desire. Rational and irrational , transcendental, prime numbers, Fibonacci, pi, e, and much more are explained as the leading players in the world of numbers are introduced like characters in a drama. We'll probably be seeing more of Dr Burger -- I certainly hope so.
Date published: 2012-08-04
Rated 5 out of 5 by from Best Math Course So Far I haven't done a lot of math courses but so far this is my favorite. The reason is that Burger takes you further into intelligible no-gloss no-cheat real proofs of real math ideas than any other (even a bit better than Burger and Starbird's general intro, which was superb in its own way).
Date published: 2012-04-29
Rated 4 out of 5 by from A different look at the number theory My high school professor was a boring pedant. Professor Burger was much more interesting. I sensed that feeling of mystique associated with transcendental numbers and infinities. This course made me think about failures of reductionism and the origins of individuality in the humankind. Professor Burger injected that sense of life into the ancient field of math and made it fresh and interesting for me all over again.
Date published: 2012-03-27
Rated 4 out of 5 by from Startled The counterintuitive mathematical concepts present in this series are truly startling on a number of levels, and are genuine mind openers. With this type of complexity to express, the lecturer did a fantastic job of making the material easy to digest. His metaphor for the field of mathematics is so apt I've used it to characterize mathematics to others; an excellent course.
Date published: 2011-05-15
Rated 5 out of 5 by from Excellent Overview of Number Theory I bought this course as part of a set thinking that I would enjoy learning more about the history of numbers and how that history fits into modern mathematical theory. Not being a mathematician I wondered if this course would be too simplified or too complex. I found it just about right! The presenter does a very good job of taking his time not to overwhelm and to explain complex subjects. While he uses mathematics it is not so complicated to take away from what he is trying to get across. His explanation of the history of numbers relating to our world today is interesting and useful. For example, why stocks are quoted in 1/8 of a point or why a non metric ruler is dividing in 1/2, 1/4,1/8 and so on. Why is time measured in 60 minutes, 60 seconds, etc.? Why are longitude and latitude similarly measured? Where did our numbers come from and when did zero and infinity come into mathematical thinking and why? All of these he answers in a straightforward and understandable manner. I found his explanation of the Fibonacci numbers quite good and one of the best I have heard. If I can find fault it is to focus on items like prime numbers, real numbers, rational and irrational numbers and even Fibonacci numbers etc. without putting in context of why they are useful and important. We all learned about prime numbers, etc. but I remain somewhat mystified as to why they are important to know -- other than on SAT tests of course! Or to pass a college math class. The manner of presentation is very good and he has good speaking voice which makes it easy to follow him as he moves through a subject I knew little about.. Now, thanks to this course, I know a great deal more. If interested in this subject can recommend this course for your consideration.
Date published: 2011-03-15
Rated 5 out of 5 by from Surprisingly deep content I have taken at least forty other teaching company courses and can’t think of one I didn’t love ... but I found this one to be special. If you experienced Prof. Burger in the “Joy of Thinking” course and found him to be a little too bubbly for your taste (I did), in this course he has toned his presentation down, but by doing this it has gained intensity. As I watched the last course and thought about all that was presented, I realized that Prof. Burger had taken me on a wonderful journey through number, which surprised me, because I didn’t realize that there was a journey to be made. And even though a course like this, by its very nature, can only provide a sketch of such an intricate topic, Prof. Burger, in his love and understanding, was skillfully able to provide a depth and clarity that, at least for me, painted a wonder picture.
Date published: 2011-02-21
Rated 5 out of 5 by from Mathematical wonder and elegance "Dr. Burger is a wonderful teacher. His enthusiasm and energy for the subject is contagious. He explains things clearly and brings out mathematical magic into his courses on number theory. Sometimes the material can be a bit of a stretch, but stops short of frustrating, and is an intriguing challenge. I recaptured my joy of mathematics which I left behind decades ago. Dr. Burger takes math to its artistic edge. I highly recommend his teachings."
Date published: 2011-02-12
Rated 5 out of 5 by from Great course Wonderfully full and clearly presented. Props like 10-sided dice and stuffed rabbits, good graphics, and repetition of concrete examples make it easy to follow proofs. You can see how knowledge of number and math progressed logically from sheep counting to the Continuum Hypothesis. Burger's comments on the value of failure and surprise and his descriptions of how an academic discipline moves forward were an important part. He obviously loves math, respects the work of our mathematical forefathers, and has limitless intellectual curiosity. Must be why he gets teaching awards.
Date published: 2010-11-20
Rated 5 out of 5 by from Excellent beyond words I am a foreign language major. I have feared math all my life. I took a leap of faith when I purchased this course. I now sit in awe after each lesson admiring the beauty of what has been taught and the "simple complexity" with which it is presented. You don't have to be a math genius to follow this course. You just need to let the excellent instructor guide you on a journey you will not forget. Too bad I am not given the ability to give this course six stars. I have purchased over ten other courses and this is the first time I feel compelled to write a review.
Date published: 2010-09-13
Rated 4 out of 5 by from Great Information This course will expand your knowledge of human history as it relates to numbers. Professor Berger clearly loves his subject and knows how to walk you through the widely and not so widely known areas regarding number and number theory. Great course to watch with someone else as there is plenty to talk about. You will see the world differently.
Date published: 2010-03-01
Rated 3 out of 5 by from Some interesting material but not gripping Prof. Burger is an enthusiastic and articulate presenter, but the content in this course was not very satisfying to me. He covers a lot of history and facts about numbers and mathematical concepts, but I don't find that the material sticks when presented in 30 minute lectures.
Date published: 2010-02-05
Rated 4 out of 5 by from I Looked Forward to Every Lecture Number Theory is a fascinating topic, and this course is an engaging introduction. It must be difficult to present mathematical ideas without really exploring the underlying mathematics, but Professor Burger does a very credible job. One caution is that each lecture was really just an introduction into the topic being covered, and in that sense, it was hard to sink my teeth into the true mathematics being discussed.
Date published: 2009-08-29
Rated 5 out of 5 by from Engaging and Fun Of the twenty-plus sci-math courses I have from TTC, this was definitely one of the most enjoyable and educational. Prof. Burger clearly enjoys this topic, and his enthusiasm comes across in the lectures. For your first pass, don't bother to take notes - just sit back and enjoy. Note-taking, should you wish, can always come later. If you're trying to decide between Prof. Burger's "Introduction to Number Theory" and this course, I'd have to recommend this one unless you're very well versed in the behavior (and misbehavior) of numbers. This course is very easy to follow, and will let you decide if you want to tackle tougher stuff in the other course. This is not to imply this course is easy throughout. As the course progresses, Prof. Burger moves to concepts and theorems that become less intuitive and more complex. But, Prof. Burger progresses slowly, explains every step and includes plenty of examples. You may not get a concept entirely in the first pass, so repeating lectures may be necessary. Now, this course isn't all math. It mixes in history very well, as well as some interesting stories of the main players, so you can gain a perspective of how all this theory evolved over the centuries. These stories - some comical, some tragic - add the human dimension to the long development of number theory. And, they're nice (and often welcome) breaks from the equations. You don't need anything much beyond arithmetic as far as math skills go. Some algebra and basic trigonometry are used, but proficiency isn't at all necessary. Where used, Prof. Burger leads you through this math gently. This may even be good family viewing. Even kids with nothing more than a knowledge of arithmetic up to and including fractions - and assuming an appetite for numbers - will thoroughly enjoy this course, and they'll learn a lot, even if they don't understand all of it. Excellent course.
Date published: 2009-08-10
Rated 4 out of 5 by from Much Better than Zero But Well Short of Infinite! There is much of value in this course but it falls short of its full potential. In general the lectures are clearly presented, the content quite comprehensive historically, the graphics are good and very helpful and Burger is enthusiastic and does a reasonable job in conveying this enthusiasm. For all the complexity of many of the ideas, however, Burger is primarily concerned with assisting his audience to understand the basic mathematical reasoning. While this is valuable and important, it means that the lectures sometimes become a bit too ponderous in explaining simple ideas rather than reflecting more deeply on their import. A more profound course would go deeper into the philosophical import of the mathematical concepts. This is perhaps a bit unfair on some of Burger's treatments but in general he is better on 'numbers' rather than 'number'. Notably, many of the big philosophical debates about mathematics start in the 20th century in the wake of Cantor, Frege, Russell and Godel, and it is revealing that Burger essentially (except for a very brief and narrow excursus at the end) stops at Cantor rather than explore some of these deeper ideas. Knowing the right balance for these courses is obviously difficult., I think this one needed a bit more depth. Three and a half stars - but I will err given our choices towards 4 stars.
Date published: 2009-08-02
Rated 4 out of 5 by from You thought you knew numbers? Zero to Infinity: A History of Numbers examines a slender but critical thread in the history of mathematics. Mathematics was never entirely about numbers, of course, but without them there would be little left. But surely we all know what a number is? No, we don't. And we haven't. It took a long time to get zero accepted as a number; longer perhaps to get one accepted as a number in some mathematical traditions! Our expanding notion of numbers has given us mathematical tools of great import. Combining real and imaginary numbers, for instance, allowed us to reveals that circular and exponential functions are two faces of the same thing, with great benefits to the study of electricity and magnetism (and much more). I have a very dusty engineering degree, so a fair amount of this course's content was familiar to me. Nevertheless, it was a pleasure to see my knowledge as part of a bigger picture. It was good to see names attached to ideas and achievments I already knew. And the material that was new to me gave me the chance to stretch myself. A word on the presentation: the overall course structure is very good, but I found the presentation a little rough. It may just be a matter of taste. It did not stand in the way of learning or enjoying the content.
Date published: 2009-08-01
Rated 5 out of 5 by from Surprised I Loved It My mother picked up this course for herself and one day I decided to borrow it on a whim. Thank goodness. The breadth and life and charm I found in this course was a pleasant shock. My favorite, unmissible take away was the lecture on number in nature, how it corresponds to the Fibonacci sequence. That blew me away. It took me a couple lectures to get into the professor since I watched this on DVD and normally choose Audio when purchasing myself, but I quickly came around to realizing how much this guy loved what he was talking about and by the fourth lecture no longer had any issue.
Date published: 2009-02-10
Rated 4 out of 5 by from Very Good with Slight Presentation Issues DVD: I'm writing the kind fo review I hate to read, but I have to be honest. I rate the course content 5 stars. Prof. Burger does a great job selecting his materials. And I can say I recommend this course. However, and this can easily be just my bias, Prof. Burger's presentation style strikes me as condescending, and that's one thing that can make me fail to complete a course. His style for me brings the course value down from the 5 stars it should have been to 4 stars (due to my 3-star rating of his presentation). No doubt Prof. Burger is effective with many students who do not perceive what I perceive in his style. But I've seen too many science and math lecturers over the years who somehow think it necessary to speak down to the "masses" because so few of them are up to the task of math and science. And for me that is simply not acceptable. I'm sure Prof. Burger would be surprised at this review. He may not even be conscious of the arrogance that comes across. Teachers who inwardly hold themselves as knowers of THE truth, like any fundamentalist, come across with this subtle kind of arrogance and condescension. They must let it go to become truly great.
Date published: 2009-01-27
Rated 4 out of 5 by from A Mathematical Odyssey of Theory and Biography This course breaks new ground in the Teaching Company repertoire, for all the following reasons. Edward Burger has really opened up a niche for himself, as I can see the potential for many more such courses from him in the future. Edward and his colleague Michael Starbird have really been the icons of TTC mathematics courses, nearly ten in total now. They both contrast greatly with the other recent mathematics course from Arthur Benjamin called Joy of Mathematics. The latter is packed with so much information in each single lecture that it can get overwhelming very quickly. I dreaded knowing I would become exhausted by just having to keep up with Arthur's lighting speed delivery. Edward approaches this course from the opposite end of the spectrum. No pressure, no intimidation, only a fostering of the interest we all must have had to begin viewing such a course anyway. Only later on does he delve into topics that really get beyond the comprehension level for a first time viewer. But that is acceptable, since it would be quite boring without such a challenge, and any course that requires repeat viewings is good for the purchaser. It also appeals to a wider range of audience, young and old, uninitiated and experienced. I liked the graphical support in this course, which is so important for mathematics courses in general. The blackboard is still the best way to convey the language of number, so the ever increasing need for an accessible power point presentation has taken over in that respect. Though the accessibility of the lecturer remains the most importance aspect in any course, and Edward Burger is one of their best. Just one new course every few years and there will be quite a library of courses from Edward built up over time. He emphasizes in his last lecture of the course, that there is no real point in deciding whether this course is historical or mathematical. Both are required in their own respects to form the integrated whole. The narratives on Georg Cantor's life, including his bipolarity, really do add to the types of insights involved in his work. I think of other such scientists like Newton, Faraday, Boltzmannnn, or Kurt Godel himself. Their mental illness is so much a part of their complete story, that it would be very inappropriate to leave it out. Edward realizes this in dealing with Cantor, and really develops an intriguing historical perspective in his presentation. The emphasis on historical elements in this course, could form a significant core for his future Teaching Company engagements. This type of perspective may even be a true model for other courses as well.
Date published: 2009-01-12
Rated 4 out of 5 by from Fun math, interesting history We sometimes take certain number concepts for granted such as zero, decimals, and 'number' as an abstract concept (as opposed to a pile of pebbles). It is easy to mistakenly assume that people down through history have understood these concepts. Dr. Burger enthusiastically walks the class through the evolution of the concept of 'number' showing us how concepts we take for granted developed. The lectures covering infinity and the various levels of infinity were especially fun and interesting. Dr. Burger is able to communicate complex concepts with down-to-earth language and examples.
Date published: 2009-01-11
Rated 5 out of 5 by from Outstanding A terrific course - if you like math, take it; if you don't, you will by the time you're done. Fascinating material, clearly explained, enthusiastic and articulate professor. Of importance - does not talk down to students. Yes, many topics are challenging, and some may require re-viewing, but definitely more than worth it.
Date published: 2008-12-20
Rated 5 out of 5 by from Mathematics in Human History I would describe this course as "mathematics in human history". We travel through world cultures, observing how they coped with the concept of quantity for practical or non practical purposes. We are presented both with a history of (global) mathematical truths and with a history of (local) concerns about how to compute and compare quantities.
Date published: 2008-12-03
Rated 4 out of 5 by from Prof. Burger's enthusiasm was infectious. An excellent job of encompassing a vast subject in a reasonably sized course. Not my cup of tea (I'm an engineer) but interesting- approaching engrossing.
Date published: 2008-10-17
Rated 1 out of 5 by from To much time telling us what he was going to tell us.
Date published: 2008-10-17
Rated 5 out of 5 by from Some of the lectures will have to be listened to again since the first viewing wasn't sufficient to get all the information (for me anyway).
Date published: 2008-10-17
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