Mathematics

Subject	Mathematics
Semester	1st semester (autumn)
Type	Required
ECTS	9 ECTS
Study programme:	Business studies
Primary language:	Slovene

Introduction
How is it possible to enjoy studying mathematics, Business Studies, or work and life at large?  How to make these experiences optimal? The psychology of optimal experience, flow, was studied by M. Csíkszentmihályi, and pedagogical and educational methods that develop grit leading to flow were studied by A. L. Duckworth. Is it possible to develop mathematical formulations of this psychological research? This will be one of the challenges used to illustrate mathematical concepts and at the same time combine classical mathematical course with the reflection of our attitude to mathematics and knowledge in general.
The course will be presented in Slovenian language according to the course design of the Business Studies curriculum. The mandatory course consists of ten modules, listed under section Syllabus. The modules will be delivered in the context of course theses developed by students featuring mathematical models. These models will aid students to strengthen their mathematics competencies as well as to develop competencies of applying the mathematics to problems they will study in other courses of the curriculum or they will meet in their future workplace.
 
Preconditions
Any student attending the course must have desire for knowledge and time to devote to realizing this desire. They must develop a suitable level of responsibility for either studying regularly and following the development of competencies leading to fulfillment of their course obligations within the course process organized and led by mentor, or have the passion and responsibility to independently acquire the knowledge, skills, and competencies given and required by the course, with a significantly greater engagement. Attending the first lecture is mandatory; there, we present the process of acquiring competencies and fulfilling requirements, as well as about any adaptations to the process adjusting to individual circumstances, which do not hinder the level of knowledge acquired. In the case that a student cannot attend the first lecture, no responsibility or liability of the lecturer for student’s success is assumed, until the student shows initiative and arranges for his participation in the learning process to be verified by the mentor.

Goals
1.Affirm the existing knowledge of mathematics and upgrade it with concepts, required for understanding of models of business processes, financial instruments, and other models in economics and society.
2.Train the student in logical and analytical thinking process and in applying this process to abstract mathematical contexts as well as real world problem solving.
3.Support mathematical skills with basic technologies helping its application (such as Excel,  SageMath, R Studio, other free software) and teach him to independently discover the applications of these tools when developing mathematical models.
4.Develop mathematical (logical, analytical, algebraic) formalization of simpler professional problems and using mathematical tools for finding mathematical answers to related professional questions as well as interpreting the mathematical answers.
5.Prepare a course paper/thesis showing fulfillment of the above goals.

Competencies

• Understanding of basic analytical concepts (vector, matrix, function, limit, derivative, integral).
• Using Excel or a similar program to collect data and perform basic modeling techniques.
• Using R or similar programs for basic optimization or data management processes (linear program, scenario simulations).
• Using SageMath or similar programs for symbolic computation (limits, derivatives, integrals).
• Using online or library resources for independent acquisition of advanced topics related to these technologies.

Syllabus
1.Mathematics as a language describing reality. Sets, maps.
2.Mathematics as a language describing relationships. Logic, numbers, functions.
3.Mathematics as a language describing processes. Vectors, matrices.
4.Matrix computations. Euclidean spaces. Linear dependence and matrix rank. Systems of linear equations and Gaussian algorithm.
5.Linear programming: problem formulation and graphic solving.
6.Sequences. Limit of a sequence. Series. Interest rate computations.
7.Continuity of functions. Properties of continuous functions. Overview of elementary functions.
8.Derivative and differential. Extrema. Analysis of functions.
9.Indeterminate integral. Determinate integral and relation to indeterminate integral. Area and average value. Irregular integral.
10. Presentation of course papers.

Teaching and learning activities

• Lectures and other frontal forms of teaching.
• Student seminar.
• Independent and individual work of students.

Teaching methods

• Explanations
• Discussions
• Case studies
• Exercise solving
• Reading and composing professional texts explaining mathematical models.

Evaluation system
Key element of the evaluation of the acquired knowledge, skills, and content understanding is a course paper/thesis which demonstrates student’s ability to recognize mathematical concepts in Business Studies curriculum, their formalizations and using of mathematical tools for answering questions asked at other courses. The course paper/thesis could yield 75 of 100 possible points of the final course score.
The other 25/100 points are acquired through a written exam, which can be delivered in four examination opportunities. The first examination opportunity is offered through a short exercise prior to each lecture examining understanding of the previous lecture. Each brings up to 10 points, together 90 points. The final score is divided by 3, hence 75 points need to be collected for full score. For a passing grade, at least 42 (14 after the division) points need to be acquired.
The other three examination opportunity are standard written exams of 5 exercises each valuing 5 points, together 25 points. One exam is in June, another in September and another in February. At least 13 points need to be reached for a passing grade.
The final grade of the exam is computed by integer dividing the total number of points by 10 and increasing by 1, i. e. by a standard 10-level scale.
The points assigned to a course paper are valid for another semester after the semester in which the course paper was prepared. If the course obligations are not fulfilled in this time, a new paper needs to be prepared to fulfil course obligations.
The final course paper needs to be submitted onto a described online folder at least three weeks prior to the exam the candidate wants to attend or at least a week after the last lecture in the semester in which the course work was prepared. Course work not submitted in due time will not be evaluated.

Teaching and learning material

• Žerovnik, Janez. 2020. Matematika 1. Ljubljana: Univerza v Ljubljani, Fakulteta za strojništvo.
• Indihar, Stane et al. 2006. Matematika za ekonomiste, 1. del. Maribor: Univerza v Mariboru, Ekonomsko poslovna fakulteta.
   

Office hours

• Before and after the lectures
• By arrangement