Topics in Applied Mathematics (5 cr)

Evaluation scale

H-5

Content scheduling

Fall 2022, according to the schedule.

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

Lecture notes, homework and MATLAB exercises will be published in Itslearning.

Teaching methods

Part 1, Sequences and series:
lectures, MATLAB exercises, self-study, exercises/homework

Part 2, Logic, combinatorics and number theory:
lectures and demonstrations, self-study, homework

Exam schedules

Midterm exam, part 1 on week 41, Midterm exam, part 2 on week 49, retakes on week 50. Exact dates and times in the schedule.

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

Student workload

Lessons 49 h
Exams + preparing for them 26 h
Self-study (homework, Matlab etc.) 60 h so approx. 5 h per week.

Evaluation methods and criteria

Submit in time at least 25 % of the homework/exercises for both modules.

Active participation in MATLAB exercises.

Achieve at least 6/15 points in both Midterm exams or retakes.

Failed (0)

Less than 25 % of homework exercises submitted in time.
More than 20 % (unauthorized) non-attendance from MATLAB exercises
Less than 6/15 points in one or both of the Midterm exams or retakes.

Student has not achieved 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.

Assessment criteria, satisfactory (1-2)

Student has 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 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 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

We will use MATLAB, for which TUAS has a campus licence. You'll need to download it to your laptops.

Taking the self-study course MATLAB Basics for ICT is highly recommended prior to the start of Sequences and Series part (by week 43).