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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
  • TTV23S2
    Tieto- 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
  • TTV23S3
    Tieto- 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.

Opintojaksolla on 80% läsnäolovelvoite. Läsnäoloa seurataan.

Opiskelijapalaute on annettava.

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
  • TTV23S5
    Tieto- 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.

Opintojaksolla on 80% läsnäolovelvoite. Läsnäoloa seurataan.

Opiskelijapalaute on annettava.

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

Virtual portion

3 op

Mode of delivery

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
  • TTV23SM
    Tieto- 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

Learning materials and recommended literature

Hammack: Book of Proof (keskittyen lukuun 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

Teaching methods

Etäopetus 2 h / vko
Itsenäisiä laskuharjoituksia
Kaksi välikoetta

Student workload

Etäopetus 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.

Opiskelijapalaute on annettava.

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
  • English
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Harri Varpanen
Groups
  • TIC23S1
    Bachelor'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 at Dynamo

Learning materials and recommended literature

Hammack: Book of Proof (emphasis on chapter 3 - counting)
https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

Teaching methods

Classes 2 hrs / week
Exercises (12 sets, i.e. one each week)
Two midterms

Student workload

Classes and exams appx. 30h
Exercises and self-study appx. 51h

Further information for students

The grade 0-5 is determined by the exercises and the midterms.
More precise information is given during the first week of the course.

The course has an 80% attendance requirement. Attendance is monitored.

The student feedback has to be given.

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
  • TTV23S1
    Tieto- 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
  • TTV22S1
    Tieto- 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
  • TTV22S2
    Tieto- 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
  • TTV22S3
    Tieto- 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
  • TTV22S4
    Tieto- 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
  • TTV22S5
    Tieto- 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
  • TTV22SM
    Tieto- 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
  • TTV22SM2
    Tieto- 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
  • TIC22S1
    Bachelor'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
  • TIC21S1
    Bachelor'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
  • TTV21S1
    Tieto- 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
  • TTV21S2
    Tieto- 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
  • TTV21S3
    Tieto- 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
  • TTV21S5
    Tieto- 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
  • TTV21SM
    Tieto- 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.