| Language of instruction : English |
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Sequentiality
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Advising sequentiality bound on the level of programme components
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Group 1 |
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Following programme components are advised to also be included in your study programme up till now.
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Calculus 1 (3376)
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4.0 stptn |
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Calculus 2 (3323)
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4.0 stptn |
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Computer Labs for Mathematics (4550)
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5.0 stptn |
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Linear algebra (3983)
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4.0 stptn |
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Numerical methods 1 (1805)
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4.0 stptn |
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Numerical methods 2 (3238)
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4.0 stptn |
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Programming and algorithmic thinking (3725)
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5.0 stptn |
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Or group 2 |
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Following programme components are advised to also be included in your study programme up till now.
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Calculus 1 (4543)
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4.0 stptn |
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Calculus 2 (3323)
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4.0 stptn |
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Computer Labs for Mathematics (4550)
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5.0 stptn |
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Linear algebra (3983)
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4.0 stptn |
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Numerical methods 1 (1805)
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4.0 stptn |
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Numerical methods 2 (3238)
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4.0 stptn |
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Programming and algorithmic thinking (3725)
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5.0 stptn |
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| Degree programme | | Study hours | Credits | P2 SBU | P2 SP | 2nd Chance Exam1 | Tolerance2 | Final grade3 | |
 | Bachelor of Mathematics year 3 - pakket toegepaste wiskunde | Optional | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical |  |
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| | | Learning outcomes |
- EC
| EC 3: A graduate of the Bachelor of Mathematics programme has mastered the formal mathematical language and methodology. He/she is able to work at a sufficiently high level of abstraction. | | | - DC
| 3.1: A graduate of the Bachelor of Mathematics programme masters mathematical notation | | | - DC
| 3.2: A graduate of the Bachelor of Mathematics programme can understand abstract reasoning and its message | | | - DC
| 3.4: A graduate of the Bachelor of Mathematics programme can understand the consequences (implications) of abstract reasoning | - EC
| EC 4: A graduate of the Bachelor of Mathematics programme is able to understand a mathematical proof, he/she is able to judge whether an argument is correct and is able to understand which properties are used (in the context of the acquired knowledge). He/she can identify a gap or a redundant step in a proof or a calculation. | | | - DC
| 4.1: A graduate of the Bachelor of Mathematics programme can understand and assess the correctness of a mathematical proof or argument | | | - DC
| 4.3: A graduate of the Bachelor of Mathematics programme can recognize a gap (hole) or redundant step in a calculation or proof | | | - DC
| 4.4: A graduate of the Bachelor of Mathematics programme can improve a proof or calculation by removing redundant steps and errors, and/or by filling in gaps | - EC
| EC 5: A graduate of the Bachelor of Mathematics programme can apply the theories and methods to relatively simple mathematical problems (theoretical as well as computational). He/she can make and write down a mathematical line of reasoning by him/herself. | | | - DC
| 5.1: A graduate of the Bachelor of Mathematics programme can apply computational methods (e.g., integration, derivation of functions, variation of parameters, hypothesis testing, etc.) to solve simple mathematical problems | | | - DC
| 5.2: A graduate of the Bachelor of Mathematics programme can apply mathematical theories to analyze simple mathematical problems | | | - DC
| 5.3: A graduate of the Bachelor of Mathematics programme can, by using various proof techniques (e.g., direct/axiomatic proof, induction, incongruity, contraposition, counterexample, infinite descent), independently formulate and write a proof and mathematically correct argument within the material learned | - EC
| EC 6: A graduate of the Bachelor of Mathematics programme is able to integrate the acquired knowledge in new mathematical topics. He/she understands the connection between subjects. | | | - DC
| 6.1: A graduate of the Bachelor of Mathematics programme can recognize common mathematical and logical principles in various mathematical subfields | | | - DC
| 6.2: A graduate of the Bachelor of Mathematics programme can take a bird''s eye view of various mathematical topics and subfields | | | - DC
| 6.3: A graduate of the Bachelor of Mathematics programme understands the relationship between various topics | | | - DC
| 6.4: A graduate of the Bachelor of Mathematics programme can integrate principles learned in one topic into another, new topic | - EC
| EC 8: A graduate of the Bachelor of Mathematics programme had some skills in modelling.
| | | - DC
| 8.2: De bachelor wiskunde begrijpt eenvoudige natuurkundige beginselen en modellen | - EC
| EC 10: A graduate of the Bachelor of Mathematics programme has knowledge of a number of applications of mathematics. | | | - DC
| 10.1: A graduate of the Bachelor of Mathematics programme has knowledge of applications from the natural sciences | - EC
| EC 12: A graduate of the Bachelor of Mathematics programme has a basic knowledge of programming and is able to use common mathematical software (e.g.. Maple, Matlab). | | | - DC
| 12.3: A graduate of the Bachelor of Mathematics programme can work with mathematical software such as Matlab | - EC
| EC 13: A graduate of the Bachelor of Mathematics programme is familiar with English professional literature.
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| 13.1: A graduate of the Bachelor of Mathematics programme knows English names for various mathematical concepts in addition to Dutch | | | - DC
| 13.2: A graduate of the Bachelor of Mathematics programme comes into contact with international professional literature from various fields of mathematics | - EC
| EC 14: A graduate of the Bachelor of Mathematics programme has a critical attitude and a research attitude.
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| 14.1: A graduate of the Bachelor of Mathematics programme thinks critically about acquired information | - EC
| EC 16: A graduate of the Bachelor of Mathematics programme is able to work and plan independently, he/she is able to evaluate him/herself and is able to adjust his or her behaviour accordingly. | | | - DC
| 16.1: A graduate of the Bachelor of Mathematics programme can plan his/her studies and activities | | | - DC
| 16.2: A graduate of the Bachelor of Mathematics programme has insight into his/her learning process through self-evaluation | | | - DC
| 16.3: A graduate of the Bachelor of Mathematics programme can adjust his/her learning process if needed |
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| | EC = learning outcomes DC = partial outcomes BC = evaluation criteria |
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General Knowledge:
Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.
Behavior:
The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration (Quadrature), Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.
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Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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Lecture ✔
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Response lecture ✔
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Period 2 Credits 5,00
| Evaluation method | |
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| Written evaluaton during teaching periode | 50 % |
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| Oral evaluation during teaching period | 0 % |
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| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
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Second examination period
| Evaluation second examination opportunity different from first examination opprt | |
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| Explanation (English) | 100% oral exam |
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| Compulsory coursebooks (printed by bookshop) |
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- foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods.
- Numerical Methods in Scientific Computing,cursusboek
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| Compulsory course material |
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1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: F.J. Vermolen. Introduction into error analysis of finite element methods |
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| Master of Teaching in Sciences and Technology - Engineering and Technology choice for subject didactics math | Optional | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical | |
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| | | Learning outcomes |
- EC
| 5.4. The master of education is a domain expert SCIENCES: the EM has advanced knowledge and understanding of the domain disciplines relevant to the specific subject doctrine(s). |
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| | EC = learning outcomes DC = partial outcomes BC = evaluation criteria |
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General Knowledge:
Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.
Behavior:
The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration (Quadrature), Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.
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Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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Lecture ✔
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Response lecture ✔
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Period 2 Credits 5,00
| Evaluation method | |
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| Written evaluaton during teaching periode | 50 % |
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| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
|
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| Compulsory coursebooks (printed by bookshop) |
| |
- foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods.
- Numerical Methods in Scientific Computing,cursusboek
|
|
|
| Compulsory course material |
| |
1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: F.J. Vermolen. Introduction into error analysis of finite element methods |
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| Exchange Programme Mathematics | Optional | 135 | 5,0 | 135 | 5,0 | Yes | Yes | Numerical | |
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General Knowledge:
Elementary numerical techniques like numerical quadrature, Lagrangian Interpolation, Root finding. Elementary linear algebra like matrix addition - multiplication, eigenvectors, eigenvalues. Vector algebra like Stokes' Circulation Theorem, Gauss' Divergence Theorem. Elementary knowledge of ordinary differential equations, numerical integration, stability, consistence, convergence.
Behavior:
The student is able to perform elementary algebraic operations on matrices, such as addition, multiplication and solution of systems of equations (LU, Choleski, Gauss etc).
The student is able to use Numerical Integration (Quadrature), Interpolation, Iterative methods for nonlinear equations (such Newton-Raphson, Picard's Fixed Method).
The student is able to use numerical time-integration for initial value problems, and (s)he is able to assess mathematical issues like convergence, consistence and stability.
The student is able to compute eigenvalues, eigenvectors, eigenfunctions for matrices and elementary differential operators.
The student is able to integrate over curves, surfaces and volumes, and (s)he is able to apply Gauss' Divergence and Stokes' Circulation Theorems.
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|
|
|
Content: This course is an introduction to numerical methods for partial differential equations (PDEs). For each of the three important categories of PDEs (elliptic, parabolic, hyperbolic), we study basic properties and analyze suitable numerical methods (finite differences, finite volumes, finite elements). The student will use these methods to approximate the solution to a partial differential equation in order to simulate a process from the sciences (could be physics, biology, chemistry or engineering). Next to methodologies, mathematical issues regarding the reliability of the obtained approximations will be treated. These mathematical issues involve error analysis, consistency, stability and convergence.
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Lecture ✔
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Response lecture ✔
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Period 2 Credits 5,00
| Evaluation method | |
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| Written evaluaton during teaching periode | 50 % |
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|
| Additional information | A student has to take part in all the subexams. In case the student does not take part in one or more of the subexams, he/she will get a grade "N" ("examenonderdeel niet volledig afgelegd: ongewettigd afwezig voor onderde(e)len van de evaluatie") |
|
|
|
| Compulsory coursebooks (printed by bookshop) |
| |
- foutschatting eindige elementenmethode,This document describes an introduction to the error analysis of finite element methods.
- Numerical Methods in Scientific Computing,cursusboek
|
|
|
| Compulsory course material |
| |
1. Book: J van Kan, A Segal, FJ Vermolen. Numerical Methods in Scientific Computing. Delft Academic Press, second edition, 2014, ISBN 9789065623645
2. Lecture notes: F.J. Vermolen. Introduction into error analysis of finite element methods |
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1 Education, Examination and Legal Position Regulations art.12.2, section 2. |
| 2 Education, Examination and Legal Position Regulations art.16.9, section 2. |
3 Education, Examination and Legal Position Regulations art.15.1, section 3.
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| Legend |
| SBU : course load | SP : ECTS | N : Dutch | E : English |
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