Algebra

Interactive Mathematic Miscellany and Puzzles

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What Is Arithmetic?
What Is Algebra?
Arithmetic: Articles and Problems

  1. 17 rooks on an 8×8 chessboard
  2. 3-Colors Tower of Hanoi [Java]
  3. 3 glass puzzle [JavaScript]
  4. 3-Term Arithmetic Progression
  5. 4x4 coloring problem
  6. A 49th Degree Challenge
  7. A Clique of Acquaintances
  8. About numbers
  9. Absolute Value
  10. Achieve the Equilibrium [Flash]
  11. Addition
  12. Addition and Subtraction Formulas for Sine and Cosine III
  13. Affirmative Action Problem [Java]
  14. Algebraic Structure of Complex Numbers
  15. All Integers Are Equal to 1
  16. All Powers of x are Constant
  17. Almost every integer has the digit 3 in it
  18. Almost Integers - Gaussian Integers
  19. Ambassadors at a Round Table [Java]
  20. An Inequality for Grade 8
  21. An Inequality With an Infinite Series
  22. Arithmetic-Geometric Means Inequality
  23. A simple integral
  24. Another simple integral
  25. Averages, Arithmetic and Harmonic Means [Java]
  26. Averages in a sequence
  27. The Ballot Lemma [Java]
  28. Banzhaf Power Index Calculator [Java]
  29. Barcode Encoding
  30. Barcode Magic [Java]
  31. Base Converter [JavaScript]
  32. Bayes' Theorem
  33. Beatty Sequences
  34. Bilateral Diagrams [Java]
  35. Binomial Distribution [Java]
  36. Binomial Theorem
  37. Bisector of an imaginary angle may be real
  38. Byzantine Basketball
  39. Calculation of the Digits of pi by the Spigot Algorithm [Java]
  40. Cantor-Bernstein-Schroeder theorem
  41. Cardinal Numbers
  42. Cartesian Coordinate System [Java]
  43. Cavalieri's Principle [Java]
  44. Chinese Remainder Theorem
  45. Clifford Algebras
  46. Clubs in a Vector Space
  47. Collatz Conjecture [Java]
  48. Coloring a Graph [Java]
  49. Combinatorial Proofs
  50. Committee Chairs
  51. Comparing complex numbers
  52. Completing a Square and Quadratic Formula
  53. Complex Numbers: A Dynamic Tool [Java]
  54. Complex number to a complex power may be real
  55. Constructible Numbers
  56. Construction of Pascal's Triangle [Java]
  57. Continued fractions
  58. Countability of Rational Numbers
  59. Counting Chips On a Circle [Java]
  60. Counting Squares in a Square [Java]
  61. Counting Triangles [Java]
  62. Counting Triangles II [Java]
  63. Covering A Chessboard With Domino
  64. Cubic Formula [JavaScript]
  65. Cubics and Bézout's Theorem
  66. Derivatives without Limits
  67. Descartes' Rule of Signs
  68. Diagonal Argument
  69. Distance between the Orthocenter and Circumcenter
  70. Distance Between Strings [Java]
  71. Distance From a Point to a Straight Line [Java]
  72. Dividing Loot Fairly
  73. Divisibility and Modulo Arithmetic at IMO 2007
  74. Dollars in Pockets
  75. Dot Patterns and Sierpinski Gasket [Java]
  76. Dots and fractions [Java]
  77. Ducci Sequences [Java]
  78. EAN-13 Encoding [Java]
  79. Eigenvectors by Inspection
  80. Equations of the Staight Line [Java]
  81. Equivalence Relations
  82. Euclid's Algorithm
  83. Euclid's Algorithm: An Interactive Illustration [Java]
  84. Euler’s formula for e
  85. Euler's Function and Congruence Theorem
  86. Evolution of Algebraic Symbolism
  87. Extension of Euclid's Algorithm
  88. Factorial Products
  89. Factorials and division
  90. Fair Division: Method of Sealed Bids II [Java]
  91. Falsity implies anything
  92. Farey Series
  93. Fermat's Little Theorem
  94. Fibonacci's Quickies
  95. First Geometric Interpretation of Complex Numbers [Java]
  96. Five Methods of Apportionment [Java]
  97. Five Lattice Points [Java]
  98. Fleury's Algorithm and Euler's Paths and Cycles [Java]
  99. Flipping Items Simultaneously [Java]
  100. Flipping Items Simultaneously II [Java]
  101. Flipping pancakes [Java]
  102. Floor Function
  103. Formal Systems - an Example
  104. Formula for Primes
  105. Four Hinged Squares: using complex numbers
  106. Four Pegs That Form a Square
  107. Four Voting Methods [Java]
  108. Function
  109. Function in the Plane That Vanishes
  110. Fundamental Theorem of Algebra
  111. Gasoline Stations on a Circular Trek
  112. GCD(M, N) × LCM(M, N) = M × N [Java]
  113. Generalization That Solves the Problem
  114. Generating Functions
  115. Geometric Construction of Roots of Quadratic Equation [Java]
  116. Gödel's Incompleteness Theorem
  117. Graph and Roots of a Third Degree Polynomial [Java]
  118. Graph and Roots of Quadratic Polynomial [Java]
  119. Graph of a Polynomial [Java]
  120. Graph of a Polynomial Defined by Its Roots [Java]
  121. Group multiplication of permutations [Java]
  122. Finding Hamilton Paths and Circuits [Java]
  123. Getting a Scout out of Desert [Java]
  124. Harmonic Serires And Its Parts
  125. Horner's Method [Java]
  126. How to Ask an Embarrassing Question
  127. How to define a permutation? [Java]
  128. However You Solve It ... A Wonderful Equation
  129. Hyperintegers and Hyperreal Numbers
  130. Implementation of Base Conversion
  131. Importance of the Absolute Value
  132. Inclusion-Exclusion Principle
  133. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
  134. Inequality (1 + 1-3)(1 + 2-3)(1 + 2-3)...(1 + n-3) < 3
  135. Inequality 1 + 2-2 + 3-2 + 4-2 + ... + n-2 < 2.
  136. Inequality from Math Magazine 2009
  137. Infinite Discent for x4 + y4 = z4
  138. Infinitesimals. Non-standard Analysis
  139. Infinitude of Primes
  140. Infinity As a Limit
  141. Inflection Points of Fourth Degree Polynomials [Java]
  142. Integer Iterations on a Circle [Java]
  143. Integer Iterations on a Circle III [Java]
  144. Integer roots of integers are irrational
  145. Integers and Rectangles [Java]
  146. Integers and Rectangles: a Proof by Induction [Java]
  147. Integers and Rectangles: Two Simple Proofs [Java]
  148. Interest Calculations [Java]
  149. ISBN Encoding [Java]
  150. Irrational number to an irrational power may be rational
  151. Is 0.999... = 1?
  152. It's All About Powers of 10
  153. Joachimsthal's Notations
  154. Jumping Isn't Everything [Java]
  155. Kaprekar's Iterations and Numbers [Java]
  156. Lagrange's identity, Proof
  157. Lagrange interpolation
  158. Langford and Skolem Sequences [Java]
  159. Latin Squares [Java]
  160. Legendre's Formula
  161. Leibniz and Pascal Triangles [Java]
  162. Less than, Equal to, Greater Than Symbols
  163. Lewis Carroll's Game of Logic [Java]
  164. Light Bulbs in a Circle [Java]
  165. Lights Out [Java]
  166. Linear functions
  167. Linear Programming
  168. Linear System with Parameter
  169. Listing All Combinations [Java]
  170. Listing all permutations [Java]
  171. Listing All Permutations: Johnson-Trotter Method [Java]
  172. Logistic Model applet [Java]
  173. Long Runs of Composite Numbers
  174. Long Up Short Down
  175. Looking your best
  176. Loop or Halt [Java]
  177. Lucas' Theorem
  178. Lucky Numbers [Java]
  179. Marriage Theorem
  180. Marriage Problem, simulation [Java]
  181. Math Lotto
  182. Mathematical Induction
  183. Mathematical Proof
  184. Mathematicians Doze Off
  185. Matrix Groups
  186. Maximum Volume of a Cut Off Box [Java]
  187. Means [Java]
  188. Mediant Fractions
  189. Method of Markers II [Java]
  190. Minesweeper Theorem
  191. Mini Lights Out [Java]
  192. Minimax Principle [Java]
  193. Minimax Theorem [Java]
  194. Minumum Spanning Trees and Kruskal's Algorithm [Java]
  195. Modular Arithmetic [Java]
  196. Monotone Convergence Theorem
  197. Monotone Number Sequences [Java]
  198. Multiplication
  199. Napoleon's Relatives [Java]
  200. Nested Radicals
  201. Nested Subsets
  202. Newton's Method [Java]
  203. Nine Squares [Java]
  204. Number 8 Is Interesting
  205. Number sequences and Pigeonhole [Java]
  206. Number System With Base 36
  207. On the Games of Hex and Y
  208. One Dimensional Ants
  209. One Trigonometric Formula and Its Consequences
  210. Order. Well-ordered sets.
  211. Ordinal Numbers
  212. Outline Mathematics
  213. p-adic Expansions
  214. p-adic Numbers
  215. Parity counting [Java]
  216. Parrondo Paradox Via Simpson Paradox [Java]
  217. Party Acquaintances [Java]
  218. Patterns in Pascal's Triangle
  219. Peano axioms
  220. Pennies in Boxes [Java]
  221. Percent
  222. Permutations
  223. Pigeonhole Principle
  224. Place Value [Java]
  225. Probability of Divisibility
  226. Problem 1 from the IMO 2009
  227. Problem A1, 69th Putnam Competition
  228. Problem A2, 69th Putnam Competition
  229. Problem of Divisibility by 5n
  230. Product of Diagonals in Regular N-gon
  231. Product Of Four Consecutive Integers
  232. Product of Simple Fractions [Java]
  233. Product of permutations [Java]
  234. Proizvolov's Identity [Java]
  235. Proofs Without Words [Java]
  236. Property of an
  237. Property of the Powers of 2 [Java]
  238. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
  239. Pythagorean Triples [Java]
  240. Quasigroups and block designs from triangular grid [Java]
  241. Rabbits Reproduce; Integers Don't
  242. Ramsey's Theorem
  243. Random Walks [Java]
  244. Recombining Permutations [Java]
  245. Rectangle on a Chessboard [Java]
  246. Reflection Lemma [Java]
  247. Riemann Sphere and Möbius Transformation
  248. Riemann Sums - Function Integration [Java]
  249. Right Replacement [Java]
  250. Rolle's and Mean Value Theorems [Java]
  251. Round Robin Tournament
  252. Russell's Paradox
  253. Scheduling and Critical Path Algorithm [Java]
  254. Scrub Tile Puzzle [Java]
  255. Self-descriptive Strings [Java]
  256. Self-reference
  257. Seven Terms Periodic Sequence
  258. Shapley-Shubik Power Index [Java]
  259. Shapley-Shubik Power Index Calculator [Java]
  260. Shifting Digits and a Point of View
  261. Ship-Dock Theorem
  262. Sierpinski Gasket and Tower of Hanoi
  263. Sierpinski's Gasket and Dihedral Symmetry [Java]
  264. Sieve of Squares [Java]
  265. Σ2-n = Σn·2-n
  266. Signs and Sums in a Sequence [Java]
  267. Signs in a Matrix [Java]
  268. Simple Cellular Automaton [Java]
  269. Simple Graph Practice [Java]
  270. Simpson Paradox [Java]
  271. Sine of a Sum Formula, Proof Without Words
  272. Single formula to express any integer with digits 0-9 each used just once
  273. Six Balls, Two Weighings
  274. Size of a Class: Two Viewpoints
  275. Slider Puzzles [Java]
  276. Solitaire in Two Colors [Java]
  277. Solve xx3 = 3
  278. Soriteses
  279. Sorting Algorithms
  280. Sperner's Theorem
  281. Splitting piles
  282. Square root of 2 is irrational
  283. Steinhaus' Problem [Java]
  284. Step into the Elliptic Realm
  285. Stern-Brocot Tree
  286. Straight Tromino on a Chessboard [Java]
  287. Structure of Hyperreal Numbers
  288. Subtraction Game [Java]
  289. Sums of Power Series
  290. Sums Of Successive Squares
  291. Sum without Adding
  292. Sums and Products [Java]
  293. Sums of powers of digits [Java]
  294. Superposition Principle
  295. Surreal Numbers
  296. Taking Games Seriously [Java]
  297. The ass and the mule [Java]
  298. The Local-Global Principle
  299. The Size is in the Eyes of the Beholder
  300. Tool for Constructing Orthogonal Latin Squares [Java]
  301. Three Dimensional Cross
  302. Tower of Hanoi, the Hard Way [Java]
  303. Transpositions
  304. Traveling Salesman Problem [Java]
  305. Treatise on Arithmetical Triangle
  306. Triangular numbers that are also square
  307. Trilateral Diagrams [Java]
  308. Trinary Tree(s) underlying Primitive Pythagorean Triples
  309. Twenty five boys and twenty five girls around a table.
  310. Two Circles and a Limit [Java]
  311. Two Colors in Two Rows [Java]
  312. Two Men of Tibet [Java]
  313. Uncountability of the Reals - via a Game
  314. Universal Coloring [Java]
  315. Universal Product Code [Java]
  316. Unproperty of the Powers of 2
  317. USA 1975 Problem 3
  318. Venn Diagrams
  319. Ways To Count
  320. Weierstrass Product Inequality
  321. What, how, and the Web [Java]
  322. What Is Algorithm?
  323. What Is Infinity?
  324. What Is Limit?
  325. What is so natural about “natural logarithms”?
  326. What Is Space Completion?
  327. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
  328. Where To Start? [Java]
  329. Why 17?
  330. Wilson's Theorem
  331. Word Problems [Java]
  332. Yet Another Puzzle with Hats
  333. Zeros and Nines [Java]

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