Mathematics I
Code: 102097Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Accounting and Finances | FB | 1 |
| Business and Information Technology | FB | 1 |
Contact lecturer
- Name :
- Antoine Robert Christian Zerbini
- Email :
- antoine.zerbini@uab.cat
Teaching staff
- Maria Beatriz Quiros Blasco
- Mónica Berrocal Tijeras
- Carlos Cardo Olmo
Group languages
You can consult this information at the end of the document.
Prerequisites
Entry level pre-requisites have not been established. However, enrolment in the course requires the student to have achieved a knowledge of mathematics at secondary/high school level. It is strongly recommended that those students who do not meet those standards, or those with difficulties in mathematics (in particular those who have not studied higher levels maths in high school) to enrol in the preparation programme organised by the Faculty and/or other preparatory courses in order to achieve the minimal tools required to pass the course satisfactorily.
Objectives
The objective of the Mathematics I course is to bring all the students to a certain level of mathematics that will allow them to acquire and consolidate theknowledge and skills necessary to understand and correctly manipulate basic mathematical concepts and carry out the analysis of a real variable. In addition, the student must be capable of applying such knowledge to simple models and problems as they pertain to an economics and business context.
The skills and knowledge acquired in Mathematics I, together with Mathematics II, will afford the student the necessary tools to study more advanced subjects.
For this reason, the objectives that are intended to be achieved are the following:
1. To familiarise the student with the formulation and mathematical reasoning.
2. To introduce the role of mathematical models in economics and business.
3. To identify and to know how to handle the main families of functions.
4. To work with derivatives and solve limits of functions in one variable.
5. To understand and to know how to determine the basic properties that exhibit the functions of one variable.
6. To represent functions of one variable graphically.
7. To solve optimisation problems with one variable.
8. To determine and to calculate anti-derivatives using the basic integration techniques.
Learning outcomes
Accounting and Finances
- CM10 (Use mathematical language and basic demonstration methods for problems in the field of business and economics.) Use mathematical language and basic demonstration methods for problems in the field of business and economics.
- CM11 (Analyse the properties and notions of limits, derivatives and integrals using the graph of a function that describes economic and business behaviours.) Analyse the properties and notions of limits, derivatives and integrals using the graph of a function that describes economic and business behaviours.
- CM12 (Describe basic differential calculus results in one and several real variables to determine optimal solution. ) Describe basic differential calculus results in one and several real variables to determine optimal solution.
- CM13 (Solve linear equation systems that represent problems in the field of business and economics.) Solve linear equation systems that represent problems in the field of business and economics.
- CM14 (Analytically solve optimisation problems in the field of business and economics.) Analytically solve optimisation problems in the field of business and economics.
- KM07 (Describe the analytical tools required, both qualitative and quantitative, for problem-solving and decision-making at the different functional levels of the company. ) Describe the analytical tools required, both qualitative and quantitative, for problem-solving and decision-making at the different functional levels of the company.
- SM06 (Use mathematical and algorithmic tools to solve problems in the business-economic sphere with deterministic components.) Use mathematical and algorithmic tools to solve problems in the business-economic sphere with deterministic components.
- SM07 (Apply methods to convert data into relevant information for business control and decision making and to share these decisions within and outside the organisation.) Apply methods to convert data into relevant information for business control and decision making and to share these decisions within and outside the organisation.
Business and Information Technology
- CM09 (Analyse the properties and notions of limits, derivatives and integrals using the graph of a function that describes economic and business behaviours.) Analyse the properties and notions of limits, derivatives and integrals using the graph of a function that describes economic and business behaviours.
- CM10 (Refer to the operation of the most common mathematical programming algorithms for the resolution of optimization problems.) Refer to the operation of the most common mathematical programming algorithms for the resolution of optimization problems.
- CM11 (Solve linear equation systems that represent problems in the field of business and economics.) Solve linear equation systems that represent problems in the field of business and economics.
- CM12 (Analytically solve optimisation problems in the field of business and economics.) Analytically solve optimisation problems in the field of business and economics.
- CM18 (Use mathematical language and basic demonstration methods for problems in the field of business and economics.) Use mathematical language and basic demonstration methods for problems in the field of business and economics.
- CM21 (Describe basic differential calculus results in one and several real variables to determine optimal solution.) Describe basic differential calculus results in one and several real variables to determine optimal solution.
- KM12 (Describe the analytical tools required, both qualitative and quantitative, for problem-solving and decision-making at the different functional levels of the company.) Describe the analytical tools required, both qualitative and quantitative, for problem-solving and decision-making at the different functional levels of the company.
- KM19 (Define the mathematical and algorithmic principles applicable to solving business and technological problems.) Define the mathematical and algorithmic principles applicable to solving business and technological problems.
- SM05 (Use mathematical and algorithmic tools to solve problems in the business-economic sphere with deterministic components.) Use mathematical and algorithmic tools to solve problems in the business-economic sphere with deterministic components.
- SM06 (Apply methods to convert data into relevant information for business control and decision making and to share these decisions within and outside the organisation.) Apply methods to convert data into relevant information for business control and decision making and to share these decisions within and outside the organisation.
Contents
PART I. INTRODUCTION
Topic 1. BASIC CONCEPTS
1.1. Basics: variables, constants, parameters, equations and identities
1.2. Sets. Basic operations and properties between sets
1.3. The real number: concept and absolute value
1.4. The real line: distance, inequalities, inequalities and intervals
Topic 2. BASICS OF ALGEBRA AND BASIC OPERATIONS
2.1. Growth rates
2.2. The use of logarithms. Applications to the economy
2.3. Calculation with fractions, powers and roots
2.4. Simplification of mathematical expressions
PART II. STUDY AND REPRESENTATION OF FUNCTIONS
Topic 3. FUNCTIONS
3.1. Real functions of a variable; domain and image
3.2. Type of functions and properties
3.3. Operations with functions
Topic 4. CONTINUITY
4.1. Limits and indeterminations. The sandwich theorem.
4.2. Study of the continuity of a function
Topic 5. DIFFERENTIATION
5.1. The concept of derivative. Economic and geometric interpretation
5.2. The derived function. Differentiation rules
Topic 6. STUDY AND REPRESENTATION OF FUNCTIONS
6.1. Differentiable functions
6.2. Basic study of functions; cutting points and symmetries
6.3. Monotony of functions. Increase, decrease and local
stationary points
6.4. Curvature of functions. Concavity, convexity, maximum, minimum and points of inflection
6.5. Asymptotes
6.6. Graphical representation of functions
PART III. OPTIMISATION WITH A VARIABLE
Topic 7. OPTIMISATION WITH RESPECT TO ONE VARIABLE
7.1. Optimisation issues. Local extrema and optimum solutions
7.2. Optimisation over closed intervals. The Intermediate Value and Weierstrass theorem
PART IV. PRINCIPLES OF INTEGRATION
Topic 8. INTRODUCTION TO INTEGRATION
8.1. The concept of integral
8.2. Anti-derivatives and calculation of integrals
8.3. Definite integrals
Topic 9. CALCULATION OF INTERGALS
9.1. Integration by substitution
9.2. Integration by parts
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Follow-up of homework | 3 | 0.12 | |
| Study | 90 | 3.6 | |
| Problem sets resolution | 17 | 0.68 | |
| Tutorships | 3.5 | 0.14 | |
| Theory lectures | 32.5 | 1.3 |
To achieve the objectives previously outlined, the following types of activities will be used:
1. Theoretical lectures where instructors will present the main concepts
The objective of this activity is to present the fundamental notions of the subject, and to facilitate their learning through the analysis of examples, which will emphasise both intuitive aspects and applications and explanations in the field of Economics.
2. Practical classes where problem solving will be discussed
This activity has the purpose to answer doubts that students may have encountered during the resolution of the problems and to correct possible errors committed. The presentation of solutions by students will be prioritised, either orally as a first step in their discussion, or in written form.
3. Problem solving by students (independent work)
Each topic will have a list of associated problems, which the students will have to solve independently. This activity has a dual objective of allowing the student to demonstrate that he/she has assimilated the theoretical concepts and work tools presented in class and that he/she has acquired the necessary skills to solve exercises and problems.
4. Attending office hours
The student will have access to some tutorials with the teacher that presents the course, in order to address doubts that may have arisen during the study of the subject and in the resolution of the problems. Due to the use of mathematical symbols that this activity implies, the tutorials will be developed in person.
The proposed teaching methodology may undergo some modifications according to the restrictions imposed by the health authorities onon-campus courses.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Mid-term exam | 30% | 2 | 0.08 | CM09, CM10, CM11, CM12, CM13, CM14, CM18, CM21, KM07, KM12, KM19, SM05, SM06, SM07 |
| Continous assessment activities | 20% | 0 | 0 | CM09, CM10, CM11, CM12, CM13, CM14, CM18, CM21, KM07, KM12, KM19, SM05, SM06, SM07 |
| Final exam | 50% | 2 | 0.08 | CM09, CM10, CM11, CM12, CM13, CM14, CM18, CM21, KM07, KM12, KM19, SM05, SM06, SM07 |
This subject/module does not offer the option for comprehensive evaluation.
The evaluation of the course will be carried out in a continuous way, through partial assessments and a final exam. The type of activities and their relative weight in the final note is the following:
- Final exam: 50% of the final mark (it will include the totality of the syllabus)
- Mid-term exam: 30% of the final mark
- Continuous assessment activities: a total of 20% of the final mark
The final grade will be the weighted average of all the activities. The minimum mark for any activity is not set.
If, once applied the above mentioned percentage the mark achieved is 5 or higher, the course is considered as passed and this will not be subject to a new evaluation. In case of a grade less than 3.5, the student will have to sit it again in the following year. For those students who have obtained a grade that is equal to or greater than 3.5 and less than 5 there will be a re-take exam. The teachers of the subject will decide the modality of this re-take exam. This re-take exam is scheduled in the last week of the semester. The re-take exam grade will be qualitative and will only have two possible options: PASS or NO PASS. If the student obtains a PASS grade, it is considered that they have passed the subject with a maximum numerical grade equal to 5. If the student obtains a NO PASS score, they do not have passed the subject and the final grade will be equal to the one obtained before the re-take exam.
A student is considered to be \"Not Evaluated\" in the subject as long as he/she has not participated in any of the assessment activities. Therefore, it is considered that a student who carries out some components of the continuous assessment modality can no longer opt for a \"Not Evaluated\".
Students attending the subject for the second, third or fourth time have the option to follow the continuous modality or to sit directly and only the final exam, which will count 100% of the final grade. The choice of this last option must accordingly be notified to their teacher during the first weeks of the semester, prior to any of the continuous evaluation activities. Submission of any of such activities shall be understood as to implicitly waiving this option.
Students must be examined in the classroom assigned to the group where they are enrolled. Doing the exam in the classroom assigned to another group may entail invalidation of the exam and it will be classed as ‘Not-attended’.
Calendar of evaluation activities
The dates of the evaluation activities (midterm exams, exercises in the classroom, assignments, ...) will be announced well in advance during the semester.
The date of the final exam is scheduled in the assessment calendar of the Faculty.
\"The dates of evaluation activities cannot be modified, unless there is an exceptional and duly justified reason why an evaluation activity cannot be carried out. In this case, the degree coordinator will contact both the teaching staff and the affected student, and a new date will be scheduled within the same academic period to make up for the missed evaluation activity.\" Section 1 of Article 115. Calendar of evaluation activities (Academic Regulations UAB). Students of the Faculty of Economics and Business, who in accordance with the previous paragraph need to change an evaluation activity date must process the request by filling out an Application for exams' reschedule https://eformularis.uab.cat/group/deganat_feie/application-for-exams-reschedule
Grade revision process
After all grading activities have ended, students will be informed of the date and way in which the course grades will be published. Students will also be informed of the procedure, place, date and time of grade revision following University regulations.
Retake Process
\"To be eligible to participate in the retake process, it is required for students to have been previously been evaluated for at least two thirds of the total evaluation activities of the subject.\" Section 3 of Article 112 ter. The recovery (UAB Academic Regulations). Additionally, it is required that the student to have achieved an average grade of the subject between 3.5 and 4.9.
The date of the retake exam will be posted in the calendar of evaluation activities of the Faculty. Students who take this exam and pass, will get a grade of 5 for the subject. If the student does not pass the retake, the grade will remain unchanged, and hence, student will fail the course.
If a student cannot take the mid-term or final exam, the evaluator reserves the right to choose the format of the exam replacement, which may, for instance, be written or oral.
Irregularities in evaluation activities
In spite of other disciplinary measures deemed appropriate, and in accordance with current academic regulations, \"in the case that the student makes any irregularity that could lead to a significant variation in the grade of an evaluation activity, it will be graded with a 0, regardless of the disciplinary process that can be instructed. In case of various irregularities occur in the evaluation of the same subject, the final grade of this subject will be 0\". Section 10 of Article 116. Results of the evaluation. (UAB Academic Regulations).
The proposed evaluation activities may undergo some changes according to the restrictions imposed by the health authorities on on-campus courses.
No electronic device (computer, calculator, phone, tablet, smartwatch etc.) is authorized during any evaluation.
Bibliography
Main textbooks:
- Sydsaeter, K. and P.J. Hammond, Mathematics for Economic Analysis. London, Prentice Hall (1995). (available in UAB library, online)
- Sydsaeter, K. and P.J. Hammond, Essential Mathematics for Economic Analysis. Fourth edition. Pearson Education (2012). (available in UAB library, online)
Complementary textbooks:
- Anton, Howard, Irl C. Bivens, and Stephen Davis. Calculus: early transcendentals single variable. John Wiley & Sons, 2021.
- Alejandre, F., F. Llerena, i C. Villela, Problemes de matemàtiques per a econòmiques i empresarials, Editorial Media (1995).
- Chiang, A.C., Fundamental Methods of Mathematical Economics, McGraw-Hill. (2005).
- Hoffmann, L.D., G.L. Bradley, G., and K.H. Rosen, 2005, Applied Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill (2005).
- Alegre, P., L. Jorba, F.J. Orti, G. Rodriguez, J.B. Saez, T. Sancho i A. Terceño, Ejercicios Resueltos de Matemáticas Empresariales II. Editorial Alfacentauro, Madrid (2000).
Software
No special software will be used
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 10 | Catalan | first semester | morning-mixed |
| (TE) Theory | 20 | Catalan | first semester | morning-mixed |
| (TE) Theory | 50 | Catalan | first semester | afternoon |
| (PAUL) Classroom practices | 101 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 201 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 501 | Catalan | first semester | afternoon |