Introduction to Mathematical Sciences (5 cr)

Evaluation scale

H-5

Content scheduling

Opening lecture in week 36. Teaching weekly in weeks 36-50. More detailed schedule on the course's Itslearning pages.

Mathematical skills learned in the course are basic skills needed in vocational studies and in working life. Contents:
- Number representations and number sets
- Basic calculations and order of calculations
- Calculating with fractions and handling fractional expressions
- Quantities and the SI system
- Processing of units in calculations and unit conversions
- Powers and powers of ten (also negative and root = fractional powers)
- Processing of polynomials (Simplification of expressions, also fractional expressions)
- Function values and reading the graph of the function
- 1st degree functions and 1st degree function graph
- 1st degree equations and inequalities (also ratios),
- Percentage calculation
- 2nd degree functions and the graph of a 2nd degree function
- 2nd degree equations and inequalities
- A pair of linear equations
- Right triangle trigonometry
- Basics about the geometry of other bodies

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

The course follows the books on the Openstax website:
- Elementary Algebra 2e https://openstax.org/details/books/elementary-algebra-2e
- Intermediate Algebra 2e https://openstax.org/details/books/intermediate-algebra-2e
- Prealgebra 2e https://openstax.org/details/books/prealgebra-2e
Electronic and online material, educational videos in the Itslearning learning system and linked there

Teaching methods

Learning-by-doing, task-based, independent study, calculation workshops

The course provides the prerequisites for studying the mathematics and physics courses included in the engineering education through diverse teaching, guided calculation exercises, electronic Ville exercises, independent practice and group work.

Exam schedules

The course is divided into midterm test and final exams. If the course is completed with test and exam, you must attend both of them. Otherwise, in connection with the last exam, the student must take a course exam covering all areas of the course.
The test will be held around week 41 and the final exam at week 48.

Pedagogic approaches and sustainable development

learning-by-doing, supporting learning, the course provides mathematical skills for sustainable selection of everyday activities

Completion alternatives

Independent study and a successfully completed exam. This method of completion must be agreed with the teacher and must be based on a strong mathematical background. The mathematical background is assessed based on the score of the entry level test and the opportunity to take a course exam is offered at the beginning of the semester.

Student workload

5 credits = 135 h of student work, divided on average
- Joint calculation workshops 50 h
- Independent study with the help of calculation handouts and guide videos, about 4 hours/handout = 43 hours
- training in Ville-platform
- Rehearsals for the exams 16 h
- Test and exam 1+3=4 h

Evaluation methods and criteria

The course is evaluated numerically from 0 to 5.

The assessment is based on course points, which are collected as follows:
- Presence and active participation in lectures and counting exercises (20 meetings) 0.5p x 20 = 10p
- From weekly calculation exercises max 1p/multiplier = maximum 1p x 12 = 12p
- For independent ViLLE tasks exceeding the required 40%, 1% = 0.1p x 60% = 6p (max)
- Two partial exams or one course exam, max 100 points as follows:
* Partial exam 1 tests the basics and its weight is 30 points
* Partial exam 2 tests more extensive, more in-depth content and its weight is 70 points

Receiving course points from weekly calculation exercises requires them to be returned to ItsLearning in electronic form and self-assessment of your own performance by the deadline. Points are awarded in proportion to the number of calculated tasks.

Qualified performance (number 1) is required
- at least 50% attendance of meetings
- at least 40% of the maximum score for independent ViLLE tasks
- at least 40 credits in total

Other grades are determined by points on a linear scale:

Failed (0)

The student is missing one of the required pass conditions:
- The student has not received at least 40% of the maximum score for ViLLE assignments.
- Student has not achieved at least 40% = 40 course points total

Assessment criteria, satisfactory (1-2)

The student has received at least 40% of the maximum points for ViLLE assignments and course points as follows:
Course points 40-51 = 1
Course points 52-63 = 2

Competence corresponding to level 1-2: The student can solve 1st and 2nd degree polynomial equations and their applications. The student masters right-angled triangle trigonometry.

Assessment criteria, good (3-4)

The student has received at least 40% of the maximum points for ViLLE assignments and course points as follows:
Course points 64-75 = 3
Course points 76-87 = 4

Competence corresponding to level 3-4: In addition to the competence of level 1-2, the student masters one of the following topics:
- handling of units and unit conversions
- refining various powers and expressions
- graphs of functions and related calculations
- solving a pair of equations
- basics of vector calculus

Assessment criteria, excellent (5)

The student has received at least 40% of the maximum points for the ViLLE assignments.
The student has received at least 88 course points in total.

Competence corresponding to level 5: In addition to level 1-2 competence, the student also masters the basics of handling units and unit conversions, refining various powers and expressions, examining and calculating graphs of functions, solving pairs of equations and vector calculations.

Further information

The teacher sends the most important announcements of the course by e-mail. Contact the teacher by email (aaro.mustonen@turkuamk.fi). Information related to lessons in itslearning. Announcements related to the course in Itslearning on the Course Overview page.

The amount of AvoinAMK study places 3.