Introduction to Mathematical Sciences (5 cr)

Evaluation scale

H-5

Content scheduling

PART 1:
1 Basic arithmetic operations
2 Fractions
3 Powers
4 Roots
5 Polynomials, simplifying rational expressions
6 Polynomial equations of 1. and 2. degree
7 Simultaneous linear equations

PART 2:
8 Variable and function, graphs of functions
9 Lines and parabolas
10 Basics of geometry
11 Basics of trigonometry
12 Percentages
13 Quantity and unit
14 Basics of physics

Objective

Student obtains the skills and knowledge required for basic courses of mathematical sciences within polytechnical studies.

Content

• Real numbers
• Basic arithmetic operations and the order of operations
• Fractions
• Powers, roots and rational exponents
• Polynomials and polynomial equations of 1. and 2. degree
• Simplifying rational expressions
• Percentages
• Simultaneous linear equations
• Lines and parabolas
• Concepts of variable and function
• Graphs of functions and interpretation of graphs
• Basics of geometry and trigonometry
• International system of units, unit conversions
• Calculations involving quantities and units
• Field-specific content

Materials

Course material shared by the teacher through Itslearning.
ViLLE-exercises at ville.utu.fi
Function calculator (Casio fx-82EX or similar).

Teaching methods

Lectures, self-study, homework, homework sessions, exams

Exam schedules

The exam part 1 on 6.3.2025. The first retake on 14.3.2025.
The exam part 2 on 23.4.2025. The first retake on 29.4.2025
The final retake in 5.5.2025 where student can do both Part 1 and 2, or just one of the other
Exact times in the schedule.

Student workload

Lectures 13*2h = 26h
Homework sessions 11*2h = 22h
Exams 4h
Self-study (homework, exercises, preparing for exams etc.) ~86 h

Evaluation methods and criteria

To pass the course, you must
- submit at least 40 % of the ViLLE exercises
- achieve at least 5/14 points in both midterm exams.

Failed (0)

The student has not demonstrated that they have achieved the objectives of the course. The student recognizes and can use only a few concepts related to the course's subject matter and is unable to apply what they have learned.

A failing grade follows if:
- The student has not submitted enough ViLLE assignments (less than 40%).
- The student has not passed one or both of the midterm exams (minimum 5/14 points on each exam).

The course will also be failed if any academic misconduct is detected in the student's performance. The first detected instance of misconduct or an attempt at misconduct will result in the rejection of the individual exam or assignment. The second detected instance will lead to the failure of the entire course.

Assessment criteria, satisfactory (1-2)

The student has demonstrated that they have satisfactorily achieved the objectives of the course. The student recognizes and can somewhat utilize the concepts related to the course's subject matter.

Assessment criteria, good (3-4)

The student has demonstrated that they have achieved the objectives of the course well, although there is still room for improvement in certain areas of knowledge and skills. The student can effectively use the concepts related to the course's subject matter and apply what they have learned in both academic and professional situations.

Assessment criteria, excellent (5)

The student has demonstrated that they have excellently achieved the objectives of the course. The student has a strong command of the concepts related to the course's subject matter and can analyze related issues fluently and with well-founded reasoning. The student is well-equipped to apply what they have learned in both academic and professional situations.

Further information

Itslearning and email