Opiskelupolut 2023
Opiskelupolut 2023
Juuri 11 Lukuteoria ja todistaminen
Opiskelupolut
1.1 Looginen päättely ja konnektiivit "ja", "tai" ja "ei" (1 h)
|
AS 5-6 |
101 102 103 104 105 106 107 108 109 |
|
AS 7-8 |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 116 118 121 |
|
AS 9-10 |
101 102 103 104 105 106 107 108 109 110 111 112 113 114 116 118 121 124 126 128 |
1.2 Implikaatio ja ekvivalenssi (1 h)
|
AS 5-6 |
130 131 132 133 134 135 136 |
|
AS 7-8 |
130 131 132 133 134 135 136 137 138 140 141 142 144 146 |
|
AS 9-10 |
130 131 132 133 134 135 136 137 138 140 141 142 144 146 147 148 |
2.1 Jaollisuus ja jakoyhtälö (1 h)
|
AS 5-6 |
201 202 203 204 205 206 207 221 (tarkista myös oma henkkari) |
|
AS 7-8 |
201 202 203 204 205 206 207 208 209 211 212 213 214 216 217 218 221 (tarkista myös oma henkkari) |
|
AS 9-10 |
201 202 203 204 205 206 207 208 209 211 212 213 214 216 217 218 221 (tarkista myös oma henkkari) 223 225 226 |
2.2 Alkuluvut (2 h)
|
AS 5-6 |
229 230 231 232 233 234 235 236 237 |
|
AS 7-8 |
229 230 231 232 233 234 235 236 237 238 240 241 244 246 248 249 251 253 |
|
AS 9-10 |
229 230 231 232 233 234 235 236 237 238 240 241 244 246 248 249 251 253 254 255 256 257 259 |
2. Eukleideen algoritmi ja kokonaislukuyhtälöt (2 h)
|
AS 5-6 |
261 262 263 264 265 266 267 |
|
AS 7-8 |
261 262 263 264 265 266 267 268 270 271 272 274 275 |
|
AS 9-10 |
261 262 263 264 265 266 267 268 270 271 272 274 275 277 278 279 280 |
3.1 Kongruenssi (1 h)
|
AS 5-6 |
301 302 303 304 305 306 307 |
|
AS 7-8 |
301 302 303 304 305 306 307 308 309 310 312 313 314 315 316 318 |
|
AS 9-10 |
301 302 303 304 305 306 307 308 309 310 312 313 314 315 316 318 319 320 321 |
3.2 Jaollisuustarkasteluja kongruenssin avulla (2 h)
|
AS 5-6 |
323 324 325 326 327 328 329 330 |
|
AS 7-8 |
323 324 325 326 327 328 329 330 331 333 334 335 336 339 |
|
AS 9-10 |
323 324 325 326 327 328 329 330 331 333 334 335 336 339 342 343 344 346 347 |
4.1 Algoritmi (1 h)
|
AS 5-6 |
401 402 403 404 405 406 |
|
AS 7-8 |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 416 |
|
AS 9-10 |
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 |
4.2 Ohjelmoinnin perusteita (2 h)
|
AS 5-6 |
420 421 422 423 424 |
|
AS 7-8 |
420 421 422 423 424 425 426 427 428 429 430 431 432 |
|
AS 9-10 |
420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 |
4.3 Valinta (1 h)
|
AS 5-6 |
436 437 438 439 440 441 |
|
AS 7-8 |
436 437 438 439 440 441 442 443 445 446 447 449 |
|
AS 9-10 |
436 437 438 439 440 441 442 443 445 446 447 449 451 |
4.4 Toisto (2 h)
|
AS 5-6 |
453 454 455 456 457 458 459 460 |
|
AS 7-8 |
453 454 455 456 457 458 459 460 461 462 463 464 466 468 469 471 |
|
AS 9-10 |
453 454 455 456 457 458 459 460 461 462 463 464 466 469 471 473 474 476 |
4.5 Harjoitustyö: lajitteluelgoritmi tai yhtälön numeerinen ratkaisu (1 h)