Perth, Western Australia As part of Perth's role as the capital of Western Australia, the state's Parliament and Supreme Court are located within the city, as well as Government House, the residence of the Governor of Western Australia. Perth became known worldwide as the "City of Light" when city residents lit their house lights and streetlights as American astronaut John Glenn passed overhead while orbiting the earth on Friendship 7 in 1962.[10][11] The city repeated the act as Glenn passed overhead on the Space Shuttle in 1998.[12][13] Perth came 9th in the Economist Intelligence Unit's August 2012 list of the world's most liveable cities,[14] and was classified by the Globalization and World Cities Research Network in 2010 as a world city.[15] History[edit] Indigenous history[edit] The area where Perth now stands was called Boorloo by the Aborigines living there in 1827 at the time of their first contact with Europeans. Early European sightings[edit] Swan River Colony[edit] Federation and beyond[edit]
Theorem of the Day The Whole Jolly Lot (now enriched with The list is presented here in reverse chronological order, so that new additions will appear at the top. This is not the order in which the theorem of the day is picked which is more designed to mix up the different areas of mathematics and the level of abstractness or technicality involved. The way that the list of theorems is indexed is described here. Every theorem number is linked to its entry in the delightful 'Prime Curios!' All files are pdf , mostly between 100 and 300 Kbytes in size. A QED following a theorem indicates that the description includes a proof of the theorem. 211 Willans' Formula QED 210 The Basel Problem QED 209 The Erdős Discrepancy Conjecture QED ( a Theorem under construction!) 208 Toricelli's Trumpet QED 207 The Eratosthenes-Legendre Sieve QED 206 Euler's Formula QED 205 The Classification of the Semiregular Tilings 204 Singmaster's Binomial Multiplicity Bound QED ( 203 Euler's Continued Fraction Correspondence 191 L'Hospital's Rule
Principia Mathematica ✸54.43: "From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2." —Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version). (The proof is actually completed in Volume II, 1st edition, page 86, accompanied by the comment, "The above proposition is occasionally useful." Τhey go on to say "It is used at least three times, in ✸113.66 and ✸120.123.472.") The title page of the shortened Principia Mathematica to ✸56 I can remember Bertrand Russell telling me of a horrible dream. Hardy, G. He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one Littlewood, J. The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. PM has long been known for its typographical complexity.
Quantum Aspects of Life Quantum Aspects of Life is a 2008 science text, with a foreword by Sir Roger Penrose, which explores the open question of the role of quantum mechanics at molecular scales of relevance to biology. The book adopts a debate-like style and contains chapters written by various world-experts; giving rise to a mix of both sceptical and sympathetic viewpoints. The book addresses questions of quantum physics, biophysics, nanoscience, quantum chemistry, mathematical biology, complexity theory, and philosophy that are inspired by the 1944 seminal book What Is Life? by Erwin Schrödinger. Contents[edit] Foreword by Sir Roger Penrose Section 1: Emergence and Complexity Chapter 1: "A Quantum Origin of Life?" Section 2: Quantum Mechanisms in Biology Chapter 3: "Quantum Coherence and the Search for the First Replicator" by Jim Al-Khalili and Johnjoe McFaddenChapter 4: "Ultrafast Quantum Dynamics in Photosynthesis" by Alexandra Olaya-Castro, Francesca Fassioli Olsen, Chiu Fan Lee, and Neil F. See also[edit]
Gödel, Escher, Bach Gödel, Escher, Bach: An Eternal Golden Braid (pronounced [ˈɡøːdəl ˈɛʃɐ ˈbax]), also known as GEB, is a 1979 book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll".[1] By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, GEB expounds concepts fundamental to mathematics, symmetry, and intelligence. In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. Structure[edit] GEB takes the form of an interweaving of various narratives. One dialogue in the book is written in the form of a crab canon, in which every line before the midpoint corresponds to an identical line past the midpoint. Themes[edit] Puzzles[edit] The book is filled with puzzles. Impact[edit] Translation[edit]
Hammack Home This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Part I: Fundamentals Part II: How to Prove Conditional Statements Part III: More on Proof Part IV: Relations, Functions and Cardinality Thanks to readers around the world who wrote to report mistakes and typos! Instructors: Click here for my page for VCU's MATH 300, a course based on this book. I will always offer the book for free on my web page, and for the lowest possible price through on-demand publishing.
The Notation in Principia Mathematica 1. Why Learn the Symbolism in Principia Mathematica? Principia Mathematica [PM] was written jointly by Alfred North Whitehead and Bertrand Russell over several years, and published in three volumes, which appeared between 1910 and 1913. This entry is intended to assist the student of PM in reading the symbolic portion of the work. 2. Below the reader will find, in the order in which they are introduced in PM, the following symbols, which are briefly described. 3. An immediate obstacle to reading PM is the unfamiliar use of dots for punctuation, instead of the more common parentheses and brackets. The use of dots. 3.1 Some Basic Examples Consider the following series of extended examples, in which we examine propositions in PM and then discuss how to translate them step by step into modern notation. Example 1 ⊢:p∨p.⊃.pPp This is the second assertion of “star” 1. ⊢[p∨p.⊃.p] So the brackets “[” and “]” represent the colon in ∗1·2. ⊢(p∨p)⊃p Example 2 p.q.=. (p&q)=df[∼(∼p∨∼q)] p&q=df∼(∼p∨∼q) ⊢:∼p.∨.
The Emperor's New Mind The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics is a 1989 book by mathematical physicist Sir Roger Penrose. Penrose argues that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The collapse of the quantum wavefunction is seen as playing an important role in brain function. The majority of the book is spent reviewing, for the scientifically minded layreader, a plethora of interrelated subjects such as Newtonian physics, special and general relativity, the philosophy and limitations of mathematics, quantum physics, cosmology, and the nature of time. Penrose states that his ideas on the nature of consciousness are speculative, and his thesis is considered erroneous by experts in the fields of philosophy, computer science, and robotics.[1][2][3] See also[edit]
Principe de relativité Un article de Wikipédia, l'encyclopédie libre. Le principe de relativité[1] affirme que les lois physiques s'expriment de manière identique dans tous les référentiels inertiels. D'une théorie à l'autre (physique classique, relativité restreinte ou générale), la formulation du principe a évolué et s'accompagne d'autres hypothèses sur l'espace et le temps, sur les vitesses, etc. Certaines de ces hypothèses étaient implicites ou « évidentes » en physique classique, car conformes à toutes les expériences, et elles sont devenues explicites et plus discutées à partir du moment où la relativité restreinte a été formulée. Exemples en physique classique[modifier | modifier le code] Première situation Supposons que dans un train roulant à vitesse constante (sans les accélérations, petites ou grandes, perceptibles dans le cas d'un train réel), un voyageur se tient debout, immobile par rapport à ce train, et tient un objet dans la main. Deuxième situation Conclusion Propriété : soit ( ), alors ( ) et ( ) et
Cantor and Cohen: Infinite investigators part I June 2008 This is one half of a two-part article telling a story of two mathematical problems and two men: Georg Cantor, who discovered the strange world that these problems inhabit, and Paul Cohen (who died last year), who eventually solved them. The first of these problems — the axiom of choice — is the subject of this article, while the other article explores what is known as the continuum hypothesis. Each article is self-contained, so you don't have to read both to get the picture. Cantor: The infinite match-maker Georg Cantor was a German logician who, in the late 19th century, achieved a feat which scientists, philosophers, and theologians had previously only dreamed about: a detailed analysis of infinity. Georg Cantor Cantor's discovery was that there is not just one infinity, but a never-ending hierarchy, each infinitely bigger than the last. Suppose you have two collections of objects. Sets and politics Paradoxes and axioms But others were more receptive to Cantor's ideas. , written