Erinevus lehekülje "ITC8190 Mathematics for Computer Science" redaktsioonide vahel
| 109. rida: | 109. rida: | ||
Topics to prepare for exam: | Topics to prepare for exam: | ||
| − | 1. Equivalence and order relations on sets. | + | 1. Equivalence and order relations on sets, set partitions. |
| − | 2. Greatest common divisor, Euclidean algorithm, Bezout identity, extended Euclidean algorithm. | + | 2. Greatest common divisor, Euclidean algorithm, |
| + | Bezout identity, extended Euclidean algorithm. | ||
3. Euler phi function, Euler theorem, Fermat little theorem. | 3. Euler phi function, Euler theorem, Fermat little theorem. | ||
4. Congruences, solutions to ax = c (mod n). Congruence classes. | 4. Congruences, solutions to ax = c (mod n). Congruence classes. | ||
| − | 5. Modular | + | 5. Modular inverse. Invertibility of elements modulo n. |
6. Chinese Remainder Theorem. | 6. Chinese Remainder Theorem. | ||
7. Mathematical induction. | 7. Mathematical induction. | ||
| − | 8. Probability Theory: event algebra, event independence, probability of events, event composition, | + | 8. Probability Theory: event algebra, event independence, |
| − | the chain rule, Bayes' theorem, conditional and joint probabilities. | + | probability of events, event composition, |
| − | 9. Group Theory: group axioms, subgroups, group order, cyclic groups and group generators, | + | the chain rule, Bayes' theorem, conditional and |
| − | + | joint probabilities. | |
| + | 9. Group Theory: group axioms, subgroups, group order, | ||
| + | cyclic groups and group generators, order of element | ||
| + | in a group, group structure, Cayley tables, Lagrange theorem. | ||
=== Grades === | === Grades === | ||
Redaktsioon: 15. detsember 2018, kell 15:05
Course information
Code: ITC8190 Mathematics for Computer Science
ECTS: 6
Assessment form: examination
Instructor: Aleksandr Lenin, email: aleksandr dot lenin at ttu dot ee
Consultations: slots agreed with instructor via email
Schedule
Lecture: Tue 12:00 - 13:30 @SOC-218
Exercise: Wed 12:00 - 13:30 @ICT-637
Announcements
06.09.2018 Math test results are available here.
11.09.2018 In connection with quite sudden change in the timetable, the IVCM13 group students are advised that the practice session will take place on Wednesday, September 11th 12:00 - 13:30 @ICT-637 (in accordance with the old timetable).
17.09.2018 The deadline for the first home assignment has been extended by 1 week. The submissions will be due September 25th.
02.10.2018 The test covering the fundamentals of this course will take place on October 16 during the practice session. The topics covered by the test will include binary relations on sets, mappings/functions and their properties, equivalence relations and orders.
14.11.2018 The second homework covering number theory and counting has been posted. Solutions due November 28th to email address ahto dot truu at ttu dot ee.
22.11.2018 Examination dates are as follows
- 19.12.2018 14:00 EIK-219 Available places: 16
- 07.01.2019 12:00 ICT-A1 Available places: 20
- 11.01.2019 12:00 ICT-A1 Available places: 20
Every student is eligible for two examination attempts, the student can register to up to two examination dates. Registration in ÕIS is compulsory. The students who have not registered will not be admitted. Please make sure to keep your ID with you.
Lectures
Week 1: Introduction to the course
Week 2: Sets and Set Operations
Week 3: Binary Relations on Sets
Week 4: Mappings
- Lecture
- Exercises and Solution
- Group Work. Deadline October 23rd.
Week 5: Equivalence Relations on Sets
Week 6: Order Relations on Sets
Week 7: Recap & Test
Week 8: Elementary Number Theory
Week 9: Congruences
Week 10: Counting: Basic Methods
Week 11: Counting: Solving Recurrences
Week 12: Mathematical Induction
Week 13: Elementary Probability Theory
Week 14: Group Theory
Week 15: Group Isomorphisms
Week 16: Recap and Preparation for Exam
Topics to prepare for exam:
1. Equivalence and order relations on sets, set partitions.
2. Greatest common divisor, Euclidean algorithm,
Bezout identity, extended Euclidean algorithm.
3. Euler phi function, Euler theorem, Fermat little theorem.
4. Congruences, solutions to ax = c (mod n). Congruence classes.
5. Modular inverse. Invertibility of elements modulo n.
6. Chinese Remainder Theorem.
7. Mathematical induction.
8. Probability Theory: event algebra, event independence,
probability of events, event composition,
the chain rule, Bayes' theorem, conditional and
joint probabilities.
9. Group Theory: group axioms, subgroups, group order,
cyclic groups and group generators, order of element
in a group, group structure, Cayley tables, Lagrange theorem.
Grades
| Student Code | HW01 (max 10p) | Group Work | Test 1 | HW02 (max 10p) |
|---|---|---|---|---|
| 182497IVCM | 9.5 | 10 | 6 | 8.4 |
| 182504IVCM | 9.5 | 10 | 5.5 | 7.9 |
| 182505IVCM | 9.5 | 10 | 9.5 | 8.2 |
| 182506IVCM | 10 | 10 | 9.5 | 9.3 |
| 182510IVCM | 10 | 10 | 6.5 | 8.8 |
| 182513IVCM | 9.5 | 10 | 7.5 | 8.7 |
| 182514IVCM | 9 | 10 | 6 | 7.8 |
| 182515IVCM | 9 | 10 | 4.5 | 7.9 |
| 182516IVCM | 8.5 | 10 | 5.5 | 6.7 |
| 182519IVCM | 9 | 10 | 4.5 | 7.7 |
| 184505IVCM | 1 | 10 | 8 | 8.3 |
| 184518IVCM | 0 | 10 | 0.5 | 6.4 |
| 184561IVCM | 9.5 | 10 | 8 | 8.2 |
| 184662IVCM | 8 | 10 | 1 | -- |
| 184664IVCM | 9 | 10 | 2.5 | 7.7 |
| 184677IVCM | 10 | 10 | 6 | 7.8 |
| 184683IVCM | 10 | 10 | 8.5 | 7.7 |
| 184690IVCM | 9 | 10 | 8 | 6.4 |
| 186358IVCM | 9.5 | 10 | 9 | 7.7 |