Topics in Applied Mathematics (5 cr)

Evaluation scale

H-5

Content scheduling

Spring semester 2025, according to the schedule.
Part 1, weeks 3-9
Part 2, weeks 10-18

Objective

After completing the course the student can
- apply logical rules and notation
- compute and apply permutations and combinations
- apply the concepts and properties of divisibility and congruence
- process arithmetic and geometric sequences and sums
- calculate the sum of a converging infinite geometric series
- form Taylor polynomials and utilize them in numerical computation
- determine coefficients for Fourier-series expansions using mathematical computation tools

Content

- Fundamentals of logic
- Basics od number theory with applications
- Basics of combinatorics with applications
- Sequences and series
- Taylor series
- Fourier series

Materials

All course materials will be published in Itslearning.
We use MATLAB, for which TUAS has a campus licence. You can download it to your own device for free or use MATLAB Online version.
Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part (Part 2).

Teaching methods

Part 1, Logic, combinatorics and number theory:
lectures, homework, self-study, exam

Part 2, Sequences and series:
lectures, MATLAB exercises, homework sessions, self-study, exam

Exam schedules

The midterm exam for Part 1 is on 24.2.2025, first retake on 6.3.2025.
The midterm exam for Part 2 is on 8.4.2025, first retake on 22.4.2025.
The final retake exam for both parts is on 29.4.2025.
Exact times in the schedule.

Note. Homework and exercises must be submitted in time, there is no way to complement or "retake" them later.

Student workload

Part 1:
Intro 1h
Lectures 9*2h
Exam 2h
Self-study (homework, preparing for exams etc.) ~46h.

Part 2:
Lectures 5*2h
Homework sessions 5*2h (Mandatory attendance)
Exam 2h
Self-study (homework, installing and learning Matlab, preparing for exams etc.) ~46h.

Evaluation methods and criteria

Achieve at least 40% of the points in both Midterm exams or retakes.
Submit at least 25% of the MATLAB exercises in Part 2 is mandatory to pass the course.
A minimum of 80% attendance is mandatory for Part 2 homework sessions during weeks 10-14.

Additional points from homework will improve your grade.

Failed (0)

Less than 40% of the points in one or both of the Midterm exams or retakes.
Less than 25% of the MATLAB exercises submitted.
More than 20% (unauthorized) non-attendance from Part 2 homework sessions.

Student has not demonstrated achieving the learning objectives of the course. They recognize and can use only few of the concepts of the course topics, and show no skills to apply them.

The course will also be failed if any academic misconduct is detected in the student's performance.

Assessment criteria, satisfactory (1-2)

Student has demonstrated having achieved the learning objectives of the course on satisfactory level. They recognize and can to some extent use most of the concepts of the course topics.

Assessment criteria, good (3-4)

Student has demonstrated having achieved the learning objectives of the course well.
They recognize and can use most of the concepts of the course topics, and are able to apply them on various study and work contexts.

Assessment criteria, excellent (5)

Student has demonstrated having achieved the learning objectives of the course on excellent level. They master the concepts of the course topics, and are able to fluently apply them on study and work contexts.

Qualifications

Previous mathematics courses of ICT engineering curriculum (or equivalent skills):
Introduction to Engineering Mathematics
Calculus

Further information

Itslearning and email

Homework sessions in Part 2 of the course are mandatory to help students learn MATLAB independently and confidently.