August Site of the Month is about applications of advanced mathematics: mathoverflow
The site is a thread of MathOverflow, a site for professional mathematicians.
This thread, however, simply collects all the applications of different areas of research mathematics.
Scroll down and enjoy.
The August book of the month is actually a group of books, all “The Story of Phi” particular numbers. These books include a social history as well as the mathematical history.
e: The story of a number by Eli Maor, first published in 1993 and republished in 1998 by Princeton University Press.
An Imaginary Tale: The story of √-1 by Paul Nahin, first published in 1998 and republished in 2007 by Princeton University Press.
A History of π by Petr Beckmann, first published in 1970, republished in 1976 by St Martin’s Griffin.
Zero: The biography of a dangerous idea by Charles Seife, published in paperback in 2000 by Penguin.
The Golden Ratio: The story of phi, the world’s most astonishing number by Mario Livio, first published in 2002, in paperback in 2003 by Random House.
The Site of the Month for July is MathWorld from Wolfram. An encyclopedic collection of mathematical items, searchable by topic or alphabetical index. It is “a free resource from Wolfram Research built with Mathematica” and was created (and continues to be nurtured by) Eric Weisstein with help from the global mathematics community.
The July Book of the Month is in German: 4000 Jahre Algebra (4000 Years of Algebra) by Alten, Naini, Eick, Folkerts, Schlosser, Schlote, Wesemüller-Koch, & Wußing. First published in 2003 and republished by Springer-Verlag in 2014 (also available as an e-book), this is one in a series reviewing mathematics from a historical and social standpoint. It traces the development of algebra as part of our culture, linking early ways of calculating up to computer algebra to historical events.
June’s Book of the Month is Fantasia Mathematica, a collection of mathematical stories, poems, and humour compiled by Clifton Fadiman, and first published by Simon & Schuster in 1958. Authors include Aldous Huxley, H.G. Wells, and Arthur C. Clarke. It was republished in softback in 1997 by Copernicus (Springer-Verlag). A companion volume called The Mathematical Magpie was published in 1962.
Originating author is Timo Leuders.
Introduction
There are some questions that accompany the development of mathematics through cultures and ages. One of these questions is how to find an unknown quantity 
of which one knows some relations such as – in today’s algebraic notation:
![\[x^2 =x+5\]](http://blog.kleinproject.org/wp-content/ql-cache/quicklatex.com-806ecb0da5a22f568776b02af0cb3552_l3.png "Rendered by QuickLaTeX.com")
Finding solutions to such quadratic equations are essentially known since Babylonian
times and are core content school mathematics:
![\[x^2-x-5=0 \, \Rightarrow \, x=\frac{1}{2}+\frac{1}{2} \sqrt{21} \, \vee \, x=\frac{1}{2}-\frac{1}{2} \sqrt{21}\]](http://blog.kleinproject.org/wp-content/ql-cache/quicklatex.com-e2f05ff82f42e031131cae247ab865e5_l3.png "Rendered by QuickLaTeX.com")
But how about 
, which looks only slightly different? Are there also straightforward ways to calculate the solutions? Do the solutions also look symmetric in a similar way?
June’s Site of the Month is: Mathematical Impressions
A series of video presentations of mathematical phenomena, and discussion of their properties.
These videos by geometer George Hart are part of the Simons Foundation scientific outreach. George Hart’s work can be seen in other places (e.g. the American Mathematical Society website).
May’s Site of the Month is the On-Line Encyclopaedia of Integer Sequences.
The wiki-page is available in over 50 languages.
This site of over a quarter of a million sequences allows you to enter the first integers of any sequence and search for information on that sequence. It has links to famous, puzzle, classic and “hot” sequences, and is very fully referenced. There is a movie of the first 1000 terms of 1000 sequences. The site also invites you to contribute your own sequence.
May’s Book of the Month is Metamagical Themas by Douglas Hofstadter. First published in 1985 by Basic Books, available in hardback and paperback. Also available in French under the title Ma Thémagie (InterEditions, 1988).
Our second ever Book of the Month was Martin Gardner’s Mathematical Puzzles and Diversions — that author’s collected columns from Scientific American. Hofstadter followed Gardner writing this column, and the current month’s book is also a collection of those columns. Hofstadter also wrote Gödel, Escher, Bach which is another featured Book of the Month.
April’s Site of the Month is: TEDEd Lessons Worth Sharing
TEDEd Lessons are short (~4mins) video clips, and the ones on mathematics include several riddles, plus unusual uses of mathematics. There are also some conventional clips such as “The Secrets of Pascals Triangle” (which does acknowledge prior appearances in other cultures) and “The Complex Geometry of Islamic Design”. If you have an idea for a mathematical TEDEd Lesson then you can get assistance making the animated video.
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: A Biography of the World’s Most Famous Equation