Mathematics Training in Engineering Degrees: An Intervention from Teaching Staff to Students
Abstract
:1. Introduction
Research Rationale and Research Questions
- How can the mathematical curriculum of an engineering program be adapted to include technological applications?
- How do teachers value this intervention?
- How do students value this intervention?
2. Materials and Methods
2.1. Teachers’ Intervention
2.2. Students’ Intervention
3. Results
3.1. Teachers’ Results
3.1.1. Teachers’ Mathematical Contents
3.1.2. Teachers’ Surveys Results
- Innovative problems.
- Examples with applications in different fields.
- Interesting works linked to social needs.
3.2. Students’ Results
3.2.1. Students’ Mathematical Contents
- –
- Analysis of alternating current circuits: an alternating current i(t) must be calculated in a node, knowing the values of three alternating currents in the same node. Kirchhoff’s current law is used, and currents are converted into the complex form.
- –
- Triphasic distribution: phase/neutral voltage and phase/phase voltage must be calculated in a triphasic distribution. To solve it, voltages are converted into the complex form, and phasor representation is used in order to explain the relation between phase/neutral voltage and phase/phase voltage.
- –
- RLC circuit: a circuit with resistance, inductance and capacitor is solved using the complex impedance.
- –
- Resonances: the conditions in which resonance is produced in a parallel circuit must be determined.
- –
- Annulation of reactive power: in this exercise, the capacity of a capacitor must be calculated which has to be in parallel with impedance so that the equivalent impedance is real. That means that reactive power disappears, and performance is optimized.
- Prove that it can be described by the following linear equation system:
- Find and interpret the compatibility conditions.
- In such case, prove that it is a 1-indeterminate system, and a solution basis of the homogeneous system is .
- How many traffic measures are needed to know (?
- Deduce that there exist solutions with and that there exists a unique solution with and some .
- Interpret the solutions with .
- To study the compatibility conditions of the system.
- To determine how many flows must be measured to know the global circulation of the system.
- If global circulation can be calculated measuring the flows of the four peripheric points.
- If global circulation can be calculated measuring the flows of the four intern points.
- To generalize the study to three branches with more the one interconnexion.
- Prove that E is a vector space of dimension 9 and that F is a subspace of E of dimension 4.
- Determinate a basis of F so that (I1, I2, I3, I4) are its coordinates.
- Prove that one of Kirchhoff’s equations is redundant; that is, if it is verified at 5 nodes, it must also be verified at the 6th node.
- –
- With all of the controls, as an addition of subspaces.
- –
- With any of the controls, as an intersection of subspaces.
- G + B = CYAN (C)
- R + B = MAGENTA (M)
- R + G = YELLOW
- R + G + B = WHITE
- MAGENTA + YELLOW = RED
- CYAN + YELLOW = GREEN
- CYAN + MAGENTA = BLUE
- CYAN + MAGENTA + YELLOW = BLACK
- –
- Stations A, B: 1/3 of buses goes to C; 1/3 of buses goes to D; 1/3 of buses remains for maintenance.
- –
- Station C (and respectively D): 1/4 of buses goes to A; 1/4 of buses goes to B; 1/2 of buses goes to D (and respectively C).
3.2.2. Students’ Surveys and Interviews Results
- Applications let students know that mathematics is necessary.
- These sessions achieve the goal to motivate students and let them realize that linear algebra has real applications.
- Context in mathematics increases the interest and the attention of students, both in university and in secondary school.
- Applications helped students learn better linear algebra concepts.
- What aspects do you asses more positively of these sessions?
- What applications have been more interesting? Why?
- How have these sessions influenced on your motivation and on your interest toward linear algebra?
- Have these sessions helped you understand mathematical concepts of the subject linear algebra? What applications? What concepts?
- After these sessions, do you consider that mathematics are more important and essential to the development of engineering degrees? How? Why?
- The sessions “Applications of Linear Algebra in Engineering” let students know real applications in different disciplines of engineering.
- Seeing all these applications let students know what they will be able to do in the following courses and it is very motivating.
- These applications let students realize of how important linear algebra is for engineering degrees and for their future profession.
- Interesting applications: complex numbers (electricity, economy), indeterminate compatible systems (roundabout traffic), vector subspaces (linear control systems), linear applications (change to italics, population fluxes), eigenvectors and eigenvalues (demographic control).
4. Discussion
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Session | Title | Date |
---|---|---|
1 | “Invitation to the Educative Renewal of Mathematics in Engineering degrees” | 10 April 2018 |
2 | “Network Flows” | 25 April 2018 |
3 | “Engagement with the First Course Students of Civil Engineering” | 15 May 2018 |
4 | “Mathematics of Google” | 23 May 2018 |
5 | “Numerical Factory: a Numerical Tasting about the Teaching of Mathematics in Engineering” | 5 June 2018 |
6 | “How Mathematical Tools help to Manufacture Mechanical Parts” | 3 October 2018 |
7 | “One Proposal for the Teaching of Mathematics in Computer Science” | 16 October 2018 |
8 | “Mathematical Applications in Elasticity and Resistance of Materials” | 7 November 2018 |
9 | “A Historically Problematic Relationship: Mathematics in Engineering” | 27 November 2018 |
10 | “Virtual Reality Applications for Biomedical Engineering” | 27 February 2019 |
11 | “Fundamental Mathematical Concepts and Tools in Electronic Engineering” | 21 March 2019 |
12 | “Modelling and Linear Ordinary Differential Equations Systems” | 10 April 2019 |
13 | “Determined Linear Systems for Consecutive Values of States” | 2 May 2019 |
14 | “Mathematical Concepts and Tools in Automatic” | 22 May 2019 |
15 | “Animated Mathematics” | 16 October 2019 |
16 | “Probabilities and Communication Theory: Random Walks in Graphs and Algorithms” | 2 December 2020 |
17 | “Cryptography: the Arithmetic of Large Numbers” | 17 March 2021 |
18 | “Mathematics at the Service of Engineering Attitudes” | 4 May 2021 |
Session | Title |
---|---|
1 | “Complex Numbers on the Study of Price Fluctuations” |
2 | “Complex Numbers on the Study of Alternating Current” |
3 | “Indeterminate Systems: Control Variables” |
4 | “Mesh Flushes: a Basis of Conservative Fluxes Vector Subspace” |
5 | “Addition and Intersection of Vector Subspaces in Discrete Dynamical Systems” |
6 | “Linear Applications and Associated Matrix” |
7 | “Basis Changes” |
8 | “Eigenvalues, Eigenvectors and Diagonalization in Engineering” |
9 | “Modal Analysis in Discrete Dynamical Systems” |
10 | “Difference Equations” |
Applications | Linear Algebra Contents |
---|---|
Roundabout traffic | Matrices and determinants. Equation systems. |
Electrical network | Equation systems. Vectorial spaces. Vectorial subspaces. Linear applications. |
Bus station | Discrete linear systems: contagious matrix, eigenvectors and eigenvalues. |
Google: webs classification | Discrete linear systems: contagious matrix, eigenvectors and eigenvalues, Gould accessibility index. |
Survey Question | Average |
---|---|
The assessment of academic aspects is positive | 4.56 |
The level of satisfaction regarding the speaker is positive | 4.62 |
General organization of the activity has been appropriate | 4.56 |
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López-Díaz, M.T.; Peña, M. Mathematics Training in Engineering Degrees: An Intervention from Teaching Staff to Students. Mathematics 2021, 9, 1475. https://doi.org/10.3390/math9131475
López-Díaz MT, Peña M. Mathematics Training in Engineering Degrees: An Intervention from Teaching Staff to Students. Mathematics. 2021; 9(13):1475. https://doi.org/10.3390/math9131475
Chicago/Turabian StyleLópez-Díaz, María Teresa, and Marta Peña. 2021. "Mathematics Training in Engineering Degrees: An Intervention from Teaching Staff to Students" Mathematics 9, no. 13: 1475. https://doi.org/10.3390/math9131475
APA StyleLópez-Díaz, M. T., & Peña, M. (2021). Mathematics Training in Engineering Degrees: An Intervention from Teaching Staff to Students. Mathematics, 9(13), 1475. https://doi.org/10.3390/math9131475