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Outline of algebra

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377: 258:– states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a 556: 448: 551: 331: 255: 390: 441: 525: 520: 515: 510: 505: 500: 495: 490: 485: 480: 475: 468: 457: 307: 434: 186: 182: 92: 313: 196: 163: 65: 46: 202: 88: 42: 376: 337: 222: 162:
is an equation involving only algebraic expressions in the unknowns. These are further classified by
355: 349: 325: 192: 104: 96: 382: 361: 277: 243: 159: 121: 100: 77: 402: 561: 212: 141: 85: 546: 420: 295: 289: 226: 131: 17: 406: 271: 170: 126: 283: 259: 136: 58: 540: 73: 416: 343: 116: 38: 409:, 17 October 2007 (available for MP3 and MP4 download, as well as a text file). 372: 301: 206: 176: 69: 179:– equation in which a polynomial is set equal to another polynomial. 319: 265: 216: 153: 54: 50: 304:– an algebraic expression consisting of variables and coefficients 230: 81: 33: 426: 316:– mapping that associates a single output value with each input value 61: 80:. In addition to working directly with numbers, algebra also covers 412: 352:– algebraic structure with addition, multiplication and division 430: 95:, but their precise definitions lead to structures such as 364:– algebraic structure with addition and multiplication 358:– algebraic structure with a single binary operation 322:– ordered list of elements either finite or infinite 286:– an algebraic equation with a degree of three 298:– an algebraic equation with a degree of five 292:– an algebraic equation with a degree of four 280:– an algebraic equation with a degree of two 274:– an algebraic equation with a degree of one 442: 346:– basic algebraic structure of linear algebra 8: 195:– equation in which the unknowns are 449: 435: 427: 268:– equality of two mathematical expressions 91:. Addition and multiplication are general 173:– algebraic equation of degree one. 27:Overview of and topical guide to algebra 262:with an imaginary part equal to zero. 7: 415:Example problems and solutions from 229:of interest of the unknowns are the 340:– two dimensional array of numbers 25: 557:Outlines of mathematics and logic 53:. Algebra studies the effects of 375: 225:– equation where the only 526:Technology and applied sciences 37:is one of the main branches of 405:, lecture by Robin Wilson, at 256:Fundamental theorem of algebra 199:rather than simple quantities. 1: 501:Natural and physical sciences 391:Table of mathematical symbols 310:– a comparison between values 185:– equation involving a 18:List of basic algebra topics 521:Society and social sciences 516:Religion and belief systems 334:– element of a vector space 215:– equation involving 205:– equation involving 578: 151: 552:Mathematics-related lists 464: 328:– finite set of equations 250:General algebra concepts 189:of one of its variables. 41:, covering the study of 511:Philosophy and thinking 403:'4000 Years of Algebra' 187:transcendental function 183:Transcendental equation 76:and determining their 496:Mathematics and logic 203:Differential equation 481:Geography and places 476:Culture and the arts 326:Systems of equations 223:Diophantine equation 413:ExampleProblems.com 193:Functional equation 177:Polynomial equation 148:Algebraic equations 72:, along with their 491:History and events 486:Health and fitness 458:Knowledge outlines 383:Mathematics portal 278:Quadratic equation 244:History of algebra 160:algebraic equation 122:Elementary algebra 534: 533: 469:General reference 213:Integral equation 142:Universal algebra 84:, variables, and 16:(Redirected from 569: 451: 444: 437: 428: 385: 380: 379: 296:Quintic equation 290:Quartic equation 132:Abstract algebra 21: 577: 576: 572: 571: 570: 568: 567: 566: 537: 536: 535: 530: 506:People and self 460: 455: 407:Gresham College 399: 381: 374: 371: 272:Linear equation 252: 240: 171:Linear equation 156: 150: 127:Boolean algebra 113: 28: 23: 22: 15: 12: 11: 5: 575: 573: 565: 564: 559: 554: 549: 539: 538: 532: 531: 529: 528: 523: 518: 513: 508: 503: 498: 493: 488: 483: 478: 472: 471: 465: 462: 461: 456: 454: 453: 446: 439: 431: 425: 424: 410: 398: 397:External links 395: 394: 393: 387: 386: 370: 367: 366: 365: 359: 353: 347: 341: 335: 329: 323: 317: 311: 305: 299: 293: 287: 284:Cubic equation 281: 275: 269: 263: 260:complex number 251: 248: 247: 246: 239: 236: 235: 234: 220: 210: 200: 190: 180: 174: 149: 146: 145: 144: 139: 137:Linear algebra 134: 129: 124: 119: 112: 109: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 574: 563: 560: 558: 555: 553: 550: 548: 545: 544: 542: 527: 524: 522: 519: 517: 514: 512: 509: 507: 504: 502: 499: 497: 494: 492: 489: 487: 484: 482: 479: 477: 474: 473: 470: 467: 466: 463: 459: 452: 447: 445: 440: 438: 433: 432: 429: 422: 418: 414: 411: 408: 404: 401: 400: 396: 392: 389: 388: 384: 378: 373: 368: 363: 360: 357: 354: 351: 348: 345: 342: 339: 336: 333: 330: 327: 324: 321: 318: 315: 312: 309: 306: 303: 300: 297: 294: 291: 288: 285: 282: 279: 276: 273: 270: 267: 264: 261: 257: 254: 253: 249: 245: 242: 241: 237: 232: 228: 224: 221: 218: 214: 211: 208: 204: 201: 198: 194: 191: 188: 184: 181: 178: 175: 172: 169: 168: 167: 165: 161: 155: 147: 143: 140: 138: 135: 133: 130: 128: 125: 123: 120: 118: 115: 114: 110: 108: 106: 102: 98: 94: 90: 87: 83: 79: 75: 74:factorization 71: 67: 63: 60: 56: 52: 48: 44: 40: 36: 35: 30: 19: 344:Vector space 308:Inequalities 157: 32: 31: 29: 207:derivatives 117:Pre-algebra 70:polynomials 59:multiplying 39:mathematics 541:Categories 302:Polynomial 152:See also: 93:operations 320:Sequences 314:Functions 266:Equations 227:solutions 217:integrals 197:functions 66:variables 43:structure 562:Outlines 423:algebra. 421:abstract 369:See also 154:Equation 111:Branches 89:elements 51:quantity 47:relation 547:Algebra 332:Vectors 238:History 231:integer 82:symbols 62:numbers 34:Algebra 356:Groups 338:Matrix 164:degree 105:fields 103:, and 97:groups 68:, and 55:adding 417:basic 362:Rings 350:Field 233:ones. 101:rings 78:roots 419:and 57:and 49:and 158:An 86:set 543:: 166:. 107:. 99:, 64:, 45:, 450:e 443:t 436:v 219:. 209:. 20:)

Index

List of basic algebra topics
Algebra
mathematics
structure
relation
quantity
adding
multiplying
numbers
variables
polynomials
factorization
roots
symbols
set
elements
operations
groups
rings
fields
Pre-algebra
Elementary algebra
Boolean algebra
Abstract algebra
Linear algebra
Universal algebra
Equation
algebraic equation
degree
Linear equation

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