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In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate mathematics students, and for this reason I am looking for:

  1. Material rich in pictures, animations, interactive applets perhaps, which may attract the attention of those young students, and useful for conferences and other activities.

  2. Pedagogical material: showing the power of mathematics perhaps without having studied the topic rigorously.

  3. Material dealing with advanced mathematics: the real challenge is to show the importance of advanced mathematics, because basic mathematics examples are abundant and overused.

Of course, besides material, any idea or suggestion is welcomed.

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  • $\begingroup$ How young are undergraduate students where you are? And given that they have chosen to study math, should one not expect them to already have a good idea of why they are interested in it? $\endgroup$ – Tobias Kildetoft Dec 18 '14 at 13:20
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    $\begingroup$ They range from eighteen to twenty-three years (more or less). They are interested in mathematics because they are beautiful, but nevertheless it is sometimes hard for them to study, and an extra motivation would be very helpful. $\endgroup$ – Jjm Dec 18 '14 at 13:26
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    $\begingroup$ Great idea! Specially helpful are the pdfs in this AMS site: ams.org/samplings/mathmoments/browsemoments?cat=all. They are ready to be used. $\endgroup$ – Jjm Dec 18 '14 at 15:07
  • $\begingroup$ @Jjm, thanks, I've added a link in my answer. $\endgroup$ – lhf Dec 18 '14 at 17:35
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There is another good source for mathematics outside mathematics world: Feature Column from the AMS. One may try the following categories:

  • History of Mathematics
  • Math and Nature
  • Math and Technology
  • Math and the Arts
  • Math and the Sciences
  • Miscellaneous
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  • $\begingroup$ Why did you put it as three answers? You can edit in your first answer itself.. $\endgroup$ – supremum Dec 20 '14 at 6:51
  • $\begingroup$ Yes, it is true, but as it is intended to make a big list of sources, I thought it would be better to present different sources in different answers. $\endgroup$ – user63660 Dec 20 '14 at 10:33
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    $\begingroup$ To make separation within an answer you can use ---. $\endgroup$ – supremum Dec 20 '14 at 11:15
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Here is an extremely good source I have recently found: Panorama

And in general, all the page Mathigon is outstanding well done.


Another very useful source: Math in Real Life Series

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In my opinion, there are two hits in the history of advanced mathematics in everyday world which must be highly enlighted:

  1. Google's Pagerank Algorithm, based on the properties of linear algebra eigenanalysis.
  2. RSA algorith, based on number theory.

For the first item, here is a link explaining the system, but I hope somebody comes up with better documents, something in the spirit of MathMoments, for undergraduate mathematicians, with lots of pictures and so on.

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There are many books which will generate enthusiasm for mathematics in a layman reader. Some of them are listed below:


1) One Two Three ... Infinity: Facts and Speculations of Science : George Gamow

Book by theoretical physicist George Gamow in $1947$, exploring some fundamental concepts in mathematics and science, but written at a level understandable by middle school students up through "intelligent layman" adults.


2) Fractals, Music, Hypercards and More ..., Mathematical Recreations from SCIENTIFIC AMERICAN Magazine : Martin Gardner


3)Time Travel and Other Mathematical Bewilderments : Martin Gardner


4)The Universe in a Handkerchief : Martin Gardner


5)Men of Mathematics: E T Bell

Book on the history of mathematics written in $1937$ by the mathematician E. T. Bell. After a brief chapter on three ancient mathematicians, the remainder of the book is devoted to the lives of about forty mathematicians who worked in the seventeenth, eighteenth and nineteenth centuries. The emphasis is on mainstream mathematics following on from the work.

Men of Mathematics has inspired many young people, including the young John Forbes Nash Jr. and Freeman Dyson, to become mathematicians.


6)The Man Who Knew Infinity: A Life of the Genius Ramanujan : Robert Kanigel

Biography book of the Indian mathematician Srinivasa Ramanujan written in $1991$ by Robert Kanigel. The book gives a detailed account of his upbringing in India, his mathematical achievements and his mathematical collaboration with English mathematician G. H. Hardy. The book also reviews the life of Hardy and the academic culture of Cambridge University during early twentieth century.


7)A Beautiful Mind : Sylvia Nasar

Biography of Nobel Prize-winning economist and mathematician John Forbes Nash, Jr. by Sylvia Nasar. The book inspired a film by the same name, which was produced in 2001, directed by Ron Howard and starring Russell Crowe and Jennifer Connelly.


8)A Passion for Mathematics : Clifford A Pickover


9)Strange Brains and Genius : Clifford A Pickover


10)Surfing Through Hyperspace,Understanding Higher Universes in Six Easy Lessons: Clifford A Pickover


11)The Pattern Book, Fractals, Art and Nature : Clifford A pickover(editor)


12)The Mobius Strip : Clifford A Pickover


13)The Stars of Heaven, This book is dedicated to the triple alpha process and the number 7.6549: the reasons we are alive today,and smiling,on Earth : Clifford A Pickover


14)The Road to Reality: A Complete Guide to the Laws of the Universe: Roger Penrose

Book on modern physics by the British mathematical physicist Roger Penrose, published in $2004$.

It covers the basics of the Standard Model of particle physics, discussing general relativity and quantum mechanics, and discusses the possible unification of these two theories.

The book is just over $1100$ pages, of which the first $383$ are dedicated to mathematics—Penrose's goal is to acquaint inquisitive readers with the mathematical tools needed to understand the remainder of the book in depth.


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I would recommend the numberphile youtube channel: https://www.youtube.com/user/numberphile He gives short, really good introductions to cool areas of math, some of which stand on their own and others that can be used as a starting point for a class.

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