How to Become a Pure Mathematician (or Statistician) Nick's Mathematical Puzzles Welcome to my selection of mathematical puzzles. What's new? See puzzle 160. The math puzzles presented here are selected for the deceptive simplicity of their statement, or the elegance of their solution. They range over geometry, probability, number theory, algebra, calculus, trigonometry, and logic. Explaining how an answer is arrived at is more important than the answer itself. Each puzzle is assigned a level of difficulty of between one and four stars, with four being the most difficult. The source for each problem is given at the bottom of the solution page. I welcome feedback of any kind. Some brief biographical information. Nick Back to top
ShareBookFree.com – Free eBooks Download Visualizing Basic Algebra Last weekend, I shared some interesting properties of numbers with my kids. The great thing about explaining something to a non-expert is that you have to actually understand the topic. (This is why making teaching universities and research universities the same actually makes sense.) This is why I thought “why are far away things smaller?” Some of the interesting properties of numbers are: that (n + 1)×(n-1)=n2-1: that the perfect squares (0,1,4,9,…) go up by successive odd numbers (1,3,5,…); and that the area of a triangular number (1+2+…+n) has a closed form. Multiplication and division are grounded in visuospatial concepts, which is why these number theoretical results are easy to understand. Properties of Addition Addition is associative: and commutative: Multiplication is Commutative The commutative law is that a×b=b×a. Or, in the case of three factors, volume preserving: Distributive Law Associativity Difference of Squares The perfect squares are 0, 1, 4, 9, 16, …. ! Triangle Numbers
Mysterious number 6174 March 2006 Anyone can uncover the mystery The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special. Kaprekar's operation In 1949 the mathematician D. It is a simple operation, but Kaprekar discovered it led to a surprising result. When we reach 6174 the operation repeats itself, returning 6174 every time. We reached 6174 again! A very mysterious number... When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. Only 6174? The digits of any four digit number can be arranged into a maximum number by putting the digits in descending order, and a minimum number by putting them in ascending order. 9 ≥ a ≥ b ≥ c ≥ d ≥ 0 and a, b, c, d are not all the same digit, the maximum number is abcd and the minimum is dcba. which gives the relations for those numbers where a>b>c>d. For three digit numbers the same phenomenon occurs. and
Free eBooks at Planet eBook - 80+ Classic Novels and Literature s Introduction to Complex Systems by David Kirshbaum I. Introduction: Complex Systems Theory : Basic Definition II. III. I. A Complex System is any system which involves a number of elements, arranged in structure(s) which can exist on many scales. Previously, when studying a subject, researchers tended to use a reductionist approach which attempted to summarize the dynamics, processes, and change that occurred in terms of lowest common denominators and the simplest, yet most widely provable and applicable elegant explanations. But since the advent of powerful computers which can handle huge amounts of data, researchers can now study the complexity of factors involved in a subject and see what insights that complexity yields without simplification or reduction. Scientists are finding that complexity itself is often characterized by a number of important characteristics: (II.1) Self-Organization(II.2) Non-Linearity(II.3) Order/Chaos Dynamic(II.4) Emergent Properties. (II.1) Self-Organization Examples (II.2) Non-Linearity
100 Incredible Open Lectures for Math Geeks While many math geeks out there may have been teased for their love of numbers, it’s math that makes the world go round, defining everything from the economy to how the universe itself operates. You can indulge your love of mathematics in these great lectures and lecture series, which are a great diversion for those diligently working toward traditional or online master’s degree programs in mathematics. Some are meant to review the basics and others will keep you on the cutting edge of what renowned researchers are doing in the field, but all will help you expand your knowledge and spend a few hours enjoying a topic you love. Basic Math These lectures cover some pretty basic mathematical issues that can be a great review or help younger math lovers get a handle on a subject. Such lectures are an excellent resource for students who are completing online degrees in applied mathematics with the intention of entering careers as mathematics educators in middle schools and high schools. Algebra
Vulgata Clementina Epistola B. Joannis Apostoli Prima 11 Quod fuit ab initio, quod audivimus, quod vidimus oculis nostris, quod perspeximus, et manus nostræ contrectaverunt de verbo vitæ : 2 et vita manifestata est, et vidimus, et testamur, et annuntiamus vobis vitam æternam, quæ erat apud Patrem, et apparuit nobis : 3 quod vidimus et audivimus, annuntiamus vobis, ut et vos societatem habeatis nobiscum, et societas nostra sit cum Patre, et cum Filio ejus Jesu Christo. 4 Et hæc scribimus vobis ut gaudeatis, et gaudium vestrum sit plenum. 21 Filioli mei, hæc scribo vobis, ut non peccetis. Sed et si quis peccaverit, advocatum habemus apud Patrem, Jesum Christum justum : 2 et ipse est propitiatio pro peccatis nostris : non pro nostris autem tantum, sed etiam pro totius mundi. 12 Scribo vobis, filioli, quoniam remittuntur vobis peccata propter nomen ejus. 13 Scribo vobis, patres, quoniam cognovistis eum, qui ab initio est. 31 Videte qualem caritatem dedit nobis Pater, ut filii Dei nominemur et simus.
Dave's short course in trigonometry Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Ptolemy’s sum and difference formulas Ptolemy’s theorem The sum formula for sines The other sum and difference formulas Summary of trigonometric formulas Formulas for arcs and sectors of circles Formulas for right triangles Formulas for oblique triangles Formulas for areas of triangles Summary of trigonometric identities More important identities Less important identities Truly obscure identities About the Java applet.
Fibonacci Number The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation with . The Fibonacci numbers for , 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials Fibonacci numbers are implemented in the Wolfram Language as Fibonacci[n]. The Fibonacci numbers are also a Lucas sequence , and are companions to the Lucas numbers (which satisfy the same recurrence equation). The above cartoon (Amend 2005) shows an unconventional sports application of the Fibonacci numbers (left two panels). A scrambled version 13, 3, 2, 21, 1, 1, 8, 5 (OEIS A117540) of the first eight Fibonacci numbers appear as one of the clues left by murdered museum curator Jacque Saunière in D. The plot above shows the first 511 terms of the Fibonacci sequence represented in binary, revealing an interesting pattern of hollow and filled triangles (Pegg 2003). ends in zeros. The Fibonacci numbers give the number of pairs of rabbits is given by .
Epitome de Caesaribus Inhalt und Quellen[Bearbeiten] Die panegyrische Biographie Theodosius’ des Großen im 48. Kapitel hat der Autor möglicherweise als Zeitgenosse selbst verfasst. Er brachte es als Nichtchrist fertig, diesen christlichen Kaiser ausführlich zu preisen, ohne dessen Religionszugehörigkeit und Religionspolitik mit einem Wort zu erwähnen. Rezeption[Bearbeiten] Textausgaben[Bearbeiten] Franz Pichlmayr (Hrsg): Sexti Aurelii Victoris Liber de Caesaribus. Literatur[Bearbeiten] Jörg A. Weblinks[Bearbeiten] A Gentle Introduction To Learning Calculus I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). Calculus is similarly enlightening. They are. Unfortunately, calculus can epitomize what’s wrong with math education. It really shouldn’t be this way. Math, art, and ideas I’ve learned something from school: Math isn’t the hard part of math; motivation is. Teachers focused more on publishing/perishing than teachingSelf-fulfilling prophecies that math is difficult, boring, unpopular or “not your subject”Textbooks and curriculums more concerned with profits and test results than insight ‘A Mathematician’s Lament’ [pdf] is an excellent essay on this issue that resonated with many people: Poetry is similar. Feisty, are we? Yowza!