Math4 Discrete MathematicsLaajuus (3 cr)
Code: TZLM4300
Credits
3 op
Teaching language
- Finnish
- English
Responsible person
- Harri Varpanen
Objective
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Assessment criteria, satisfactory (1)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Assessment criteria, good (3)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Assessment criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
TTV23S2Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Weeks 35 - 50, Dynamo, Lutakko
Learning materials and recommended literature
Hammack: Book of Proof (concentrating in chapter 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Contact teaching 2 hours / week
Weekly exercises
Two midterms
Student workload
Teaching & midterms about 30h
Exercise work about 51h
Further information for students
The grade 0-5 is determined from the number of exercises done, along with the points from the midterms. The details are negotiated during the first week on the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV23S3Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV23S5Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV23SMTieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2024 - 22.08.2024
Timing
26.08.2024 - 18.12.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Ida Arhosalo
Groups
-
TTV23S1Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Weeks 35 - 50, Dynamo, Lutakko
Learning materials and recommended literature
Hammack: Book of Proof (concentrating in chapter 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Contact teaching 2 hours / week
Weekly exercises
Two midterms
Student workload
Teaching & midterms about 30h
Exercise work about 51h
Further information for students
The grade 0-5 is determined from the number of exercises done, along with the points from the midterms. The details are negotiated during the first week on the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22S1Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22S2Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22S3Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22S4Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22S5Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22SMTieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV22SM2Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2023 - 24.08.2023
Timing
28.08.2023 - 19.12.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
20 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC22S1Bachelor's Degree Programme in Information and Communications Technology
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Weeks 35 - 51, Dynamo, Lutakko
Learning materials and recommended literature
Hammack: Book of Proof (concentrating in chapter 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Contact teaching 2 hours / week
Weekly exercises
Two midterms
Student workload
Teaching & midterms about 30h
Exercise work about 51h
Further information for students
The grade 0-5 is determined from the number of exercises done, along with the points from the midterms. The details are negotiated during the first week on the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TIC21S1Bachelor's Degree Programme in Information and Communications Technology
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Weeks 35 - 51, Dynamo, Lutakko
Learning materials and recommended literature
Hammack: Book of Proof (concentrating in chapter 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Contact teaching 2 hours / week
Weekly exercises
Two midterms
Student workload
Teaching & midterms about 30h
Exercise work about 51h
Further information for students
The grade 0-5 is determined from the number of exercises done, along with the points from the midterms. The details are negotiated during the first week on the course.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Virtual portion
1 op
Mode of delivery
67 % Face-to-face, 33 % Online learning
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV21S1Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV21S2Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV21S3Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV21S5Tieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.
Enrollment
01.08.2022 - 25.08.2022
Timing
29.08.2022 - 16.12.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Lutakko Campus
Teaching languages
- Finnish
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Information and Communications Technology
Teachers
- Harri Varpanen
Groups
-
TTV21SMTieto- ja viestintätekniikka (AMK)
Objectives
Objective
In the Discrete Mathematics course you learn basics in mathematics and how they can be applied specifically in the field of ICT. In particular, you learn to think logically and mathematically. You learn to use mathematical language, algorithmic thinking and several ways to solve mathematical problems. You see natural applications of discrete mathematics e.g. in the fields of computer science, data networks and business. You need knowledge of discrete mathematics in your further mathematics courses.
Competences
EUR-ACE Knowledge and Understanding
- knowledge and understanding of natural scientific and mathematical principles in ICT
- knowledge and understanding of the own specialization field in engineering sciences at a level that enables achieving the other program outcomes including an understanding of requirements in your own field.
Learning outcome
You are able to calculate basics of enumerating and apply the enumerating techniques to simple practical problems. You know basic terms and markings related to divisibility and graphs. You are able to use computer to assist you with your work. You are able to formulate simple problems of discrete mathematics in mathematical language and solve them. You understand the basics of logic and set theory.
Content
Combinatorics, number theory, graph theory, set theory, and logic. Introduction to some mathematical software.
- enumerating lists
- product rule, factorials
- enumerating subsets
- binomial coefficient, Pascal's triangle
- sieve principle
- divisibility, congruence, greatest common divisor
- directed and undirected graphs
- graph adjacency matrix
- enumerating paths in a graph
- matrix multiplication
- sets and operations with sets
•joukko-operaatioiden yhteys logiikkaan = connections between set theory and logic
•loogiset operaatiot = logical operators (parempi kuin operations)
•esimerkkejä ja havainnollistuksia matemaattisilla ohjelmistoilla = some examples using mathematical software
Time and location
Toteutus on viikoilla 35 - 51 Lutakon kampuksen Dynamolla
Learning materials and recommended literature
Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf
Teaching methods
Kontaktiopetus 2 h / viikko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta
Student workload
Kontaktiopetus ja kokeet noin 30h
Itsenäinen työskentely noin 51h
Further information for students
Arvosana 0-5 määräytyy tehtyjen harjoitusten lukumäärästä ja välikoemenestyksestä.
Tarkemmat käytännöt sovitaan aloitusviikolla.
Evaluation scale
0-5
Evaluation criteria, satisfactory (1-2)
Sufficient 1:
You know the most important concepts. You are able to manually solve with a model basic tasks related to combinatorics, divisibiliy and logic as well as simple problems of discrete mathematics with a computer. You understand basics of logic and set theory.
Satisfactory 2:
You understand the most important concepts. You are able to solve typical problems both manually and using a computer. You understand basic principles of logic and set theory. Use of markings and terms is still hesitant.
Evaluation criteria, good (3-4)
Good 3:
You know and understand most concepts. You express yourself in language of mathematics in rudimentary manner. You apply problem solving techniques and software to simple problems. You know the markings of logic and set theory and understand their basic principles.
Very good 4:
You have a clear overall picture of the most central topics of the course. You express yourself clearly in language of mathematics. You are able to apply problem solving techniques and software to typical problems.
Evaluation criteria, excellent (5)
Excellent 5:
You have a clear overview picture of the topics of the entire course. You express yourself in mathematical language clearly and fluently. You apply problem solving techniques and software to problems you encounter independently and effortlessly.