Opiskelupolut 2023
Opiskelupolut
Juuri 11 Lukuteoria ja todistaminen
Opiskelupolut
1.1 Jaollisuus ja jakoyhtälö (1 h)
|
AS 5-6 |
101 102 103 104 105 114 |
|
AS 7-8 |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 |
|
AS 9-10 |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 |
1.2 Alkuluvut (2 h)
|
AS 5-6 |
121 122 123 124 125 126 127 |
|
AS 7-8 |
121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 137 138 |
|
AS 9-10 |
121 122 123 124 125 126 127 128 129 130 131 133 134 136 137 138 139 140 143 145 146 147 |
1.3 Eukleideen algoritmi ja kokonaislukuyhtälöt (2 h)
|
AS 5-6 |
149 150 151 152 153 154 155 |
|
AS 7-8 |
149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 166 |
|
AS 9-10 |
149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 165 167 169 170 172 174 175 |
2.1 Kongruenssi (1 h)
|
AS 5-6 |
201 202 203 204 205 |
|
AS 7-8 |
201 202 203 204 205 206 207 208 209 210 211 212 213 |
|
AS 9-10 |
201 202 203 204 205 206 207 208 209 210 211 213 214 216 217 220 221 |
2.2 Jaollisuustarkasteluja kongruenssin avulla (2 h)
|
AS 5-6 |
223 224 225 226 227 228 229 |
|
AS 7-8 |
223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 240 241 |
|
AS 9-10 |
223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 243 246 248 249 |
3.1 Looginen päättely ja konnektiivit (2 h)
|
AS 5-6 |
301 302 303 304 305 306 307 |
|
AS 7-8 |
301 302 303 304 305 306 307 308 309 310 311 312 313 315 316 319 |
|
AS 9-10 |
301 302 303 304 305 306 307 308 309 310 311 312 313 315 316 319 320 322 323 324 326 327 |
3.2 Totuustaulut (1 h)
|
AS 5-6 |
328 329 330 331 332 |
|
AS 7-8 |
328 329 330 331 332 333 334 335 336 337 338 339 341 |
|
AS 9-10 |
328 329 330 331 332 333 334 335 336 337 338 339 340 341 344 345 |
4.1 Väitteen todistaminen oikeaksi ja vääräksi (1 h)
|
AS 5-6 |
401 402 403 404 405 |
|
AS 7-8 |
401 402 403 404 405 406 407 408 409 410 411 412 413 |
|
AS 9-10 |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 |
4.2 Suora ja epäsuora todistus (2 h)
|
AS 5-6 |
421 422 423 424 425
|
|
AS 7-8 |
421 422 423 424 425 426 427 428 429 430 431 432 |
|
AS 9-10 |
421 422 423 424 425 426 427 428 429 430 431 432 434 435 436 437 |
4.3 Rekursiivinen lukujono ja induktioperiaate (1 h)
|
AS 5-6 |
441 442 443 444 |
|
AS 7-8 |
441 442 443 444 445 446 447 448 450 451 452 |
|
AS 9-10 |
441 442 443 444 445 446 447 448 450 451 452 453 454 455 |
4.4 Induktiotodistus (1-2 h)
|
AS 5-6 |
460 461 462 463 464 |
|
AS 7-8 |
460 461 462 463 464 465 466 467 468 469 470 |
|
AS 9-10 |
460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 477 478 |