Lorenz Halbeisen: Catalogue data in Spring Semester 2018

Name Prof. Dr. Lorenz Halbeisen
Address
Dep. Mathematik
ETH Zürich, HG G 51.5
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 633 84 60
E-maillorenz.halbeisen@math.ethz.ch
URLhttp://www.math.ethz.ch/~halorenz
DepartmentMathematics
RelationshipAdjunct Professor

NumberTitleECTSHoursLecturers
401-0252-00LMathematics II7 credits5V + 2UL. Halbeisen
AbstractContinuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content- Multivariable Differential Calculus:
functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence.

- Multivariable Integral Calculus:
multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications.

- Partial Differential Equations:
separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.
Lecture notesSee literature
Literature- Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley.
- Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.
Prerequisites / NoticeMathe-Lab (Assistance):
Tu 17-19, We 17-19, Fr 12-14 in Room HG E 41.
401-1010-00LThe Foundations of Analysis from a Philosophical and Historical Point of View Restricted registration - show details
Does not take place this semester.
Particularly suitable for students of D-MATH
Number of participants limited to 40
3 credits2SL. Halbeisen
AbstractAccompanying the courses in analysis, the beginning and development of analysis will be considered and discussed from a philosophical perspective. In particular, different approaches towards dealing with the problems sparked off by the infinitesimals will be studied. And finally, a short presentation of non-standard analysis will be given.
ObjectiveThis course aims at enabling the students to have a critical look at the basic philosophical premisses underlying analysis, to analyze them and to reflect on them.
NB. This course is part of the rectorate's critical thinking initiative.
401-3035-00LForcing: An Introduction to Independence Proofs8 credits3V + 1UL. Halbeisen
AbstractMit Hilfe der Forcing-Technik werden verschiedene Unabhaengigkeitsbeweise gefuehrt. Insbesondere wird gezeigt, dass die Kontinuumshypothese von den Axiomen der Mengenlehre unabhaengig ist.
ObjectiveDie Forcing-Technik kennenlernen und verschiedene Unabhaengigkeitsbeweise fuehren koennen.
ContentMit Hilfe der sogenannten Forcing-Technik, welche anfangs der 1960er Jahre von Paul Cohen entwickelt wurde, werden verschiedene Unabhaengigkeitsbeweise gefuehrt. Insbesondere wird gezeigt, dass die Kontinuumshypothese CH von den Axiomen der Mengenlehre ZFC unabhaengig ist. Weiter wird in Modellen von ZFC, in denen CH nicht gilt, die Groesse verschiedener Kardinalzahlcharakteristiken untersucht. Zum Schluss der Vorlesung wird ein Modell von ZFC konstruiert, in dem es (bis auf Isomorphie) genau n Ramsey-Ultrafilter gibt, wobei n fuer irgend eine nicht-negative ganze Zahl steht.
Lecture notesIch werde mich weitgehend an mein Buch "Combinatorial Set Theory" halten, aus dem einige Kapitel aus Part III & IV behandelt werden.
Literature"Combinatorial Set Theory: with a gentle introduction to forcing" (Springer-Verlag 2017)

http://www.springer.com/de/book/9783319602301
Prerequisites / NoticeVoraussetzung ist die Vorlesung "Axiomatische Mengenlehre" (Herbstsemester 2017) bzw. die entsprechenden Kapitel aus meinem Buch.
401-9983-00LMentored Work Subject Didactics Mathematics A Restricted registration - show details
Mentored Work Subject Didactics in Mathematics for TC and Teaching Diploma.
2 credits4AM. Akveld, K. Barro, A. Barth, L. Halbeisen, M. Huber, N. Hungerbühler, A. F. Müller, C. Rüede
AbstractIn their mentored work on subject didactics, students put into practice the contents of the subject-didactics lectures and go into these in greater depth. Under supervision, they compile tuition materials that are conducive to learning and/or analyse and reflect on certain topics from a subject-based and pedagogical angle.
ObjectiveThe objective is for the students:
- to be able to familiarise themselves with a tuition topic by consulting different sources, acquiring materials and reflecting on the relevance of the topic and the access they have selected to this topic from a specialist, subject-didactics and pedagogical angle and potentially from a social angle too.
- to show that they can independently compile a tuition sequence that is conducive to learning and develop this to the point where it is ready for use.
ContentThematische Schwerpunkte
Die Gegenstände der mentorierten Arbeit in Fachdidaktik stammen in der Regel aus dem gymnasialen Unterricht.

Lernformen
Alle Studierenden erhalten ein individuelles Thema und erstellen dazu eine eigenständige Arbeit. Sie werden dabei von ihrer Betreuungsperson begleitet. Gegebenenfalls stellen sie ihre Arbeit oder Aspekte daraus in einem Kurzvortrag vor. Die mentorierte Arbeit ist Teil des Portfolios der Studierenden.
Lecture notesEine kurze Anleitung zur mentorierten Arbeit in Fachdidaktik wird
zur Verfügung gestellt.
LiteratureDie Literatur ist themenspezifisch. Die Studierenden beschaffen sie sich in der Regel selber (siehe Lernziele). In besonderen Fällen wird sie vom Betreuer zur Verfügung gestellt.
Prerequisites / NoticeDie Arbeit sollte vor Beginn des Praktikums abgeschlossen
werden.
401-9984-00LMentored Work Subject Didactics Mathematics B Restricted registration - show details
Mentored Work Subject Didactics in Mathematics for Teaching Diploma and for students upgrading TC to Teaching Diploma.
2 credits4AM. Akveld, K. Barro, A. Barth, L. Halbeisen, M. Huber, N. Hungerbühler, A. F. Müller, C. Rüede
AbstractIn their mentored work on subject didactics, students put into practice the contents of the subject-didactics lectures and go into these in greater depth. Under supervision, they compile tuition materials that are conducive to learning and/or analyse and reflect on certain topics from a subject-based and pedagogical angle.
ObjectiveThe objective is for the students:
- to be able to familiarise themselves with a tuition topic by consulting different sources, acquiring materials and reflecting on the relevance of the topic and the access they have selected to this topic from a specialist, subject-didactics and pedagogical angle and potentially from a social angle too.
- to show that they can independently compile a tuition sequence that is conducive to learning and develop this to the point where it is ready for use.
ContentThematische Schwerpunkte
Die Gegenstände der mentorierten Arbeit in Fachdidaktik stammen in der Regel aus dem gymnasialen Unterricht.

Lernformen
Alle Studierenden erhalten ein individuelles Thema und erstellen dazu eine eigenständige Arbeit. Sie werden dabei von ihrer Betreuungsperson begleitet. Gegebenenfalls stellen sie ihre Arbeit oder Aspekte daraus in einem Kurzvortrag vor. Die mentorierte Arbeit ist Teil des Portfolios der Studierenden.
Lecture notesEine kurze Anleitung zur mentorierten Arbeit in Fachdidaktik wird zur Verfügung gestellt.
LiteratureDie Literatur ist themenspezifisch. Die Studierenden beschaffen sie sich in der Regel selber (siehe Lernziele). In besonderen Fällen wird sie vom Betreuer zur Verfügung gestellt.
Prerequisites / NoticeDie Arbeit sollte vor Beginn des Praktikums abgeschlossen
werden.
401-9985-00LMentored Work Specialised Courses in the Respective Subject with an Educational Focus Mathematics A Restricted registration - show details
Mentored Work Specialised Courses in the Respective Subject with an Educational Focus in Mathematics for TC and Teaching Diploma.
2 credits4AM. Akveld, K. Barro, A. Barth, L. Halbeisen, M. Huber, N. Hungerbühler, A. F. Müller, C. Rüede
AbstractIn the mentored work on their subject specialisation, students link high-school and university aspects of the subject, thus strengthening their teaching competence with regard to curriculum decisions and the future development of the tuition. They compile texts under supervision that are directly comprehensible to the targeted readers - generally specialist-subject teachers at high-school level.
ObjectiveThe aim is for the students
- to familiarise themselves with a new topic by obtaining material and studying the sources, so that they can selectively extend their specialist competence in this way.
- to independently develop a text on the topic, with special focus on its mathematical comprehensibility in respect of the level of knowledge of the targeted readership.
- To try out different options for specialist further training in their profession.
ContentThematische Schwerpunkte:
Die mentorierte Arbeit in FV besteht in der Regel in einer Literaturarbeit über ein Thema, das einen Bezug zum gymnasialem Unterricht oder seiner Weiterentwicklung hat. Die Studierenden setzen darin Erkenntnisse aus den Vorlesungen in FV praktisch um.

Lernformen:
Alle Studierenden erhalten ein individuelles Thema und erstellen dazu eine eigenständige Arbeit. Sie werden dabei von ihrer Betreuungsperson begleitet. Gegebenenfalls stellen sie ihre Arbeit oder Aspekte daraus in einem Kurzvortrag vor. Die mentorierte
Arbeit ist Teil des Portfolios der Studierenden.
Lecture notesEine Anleitung zur mentorierten Arbeit in FV wird zur Verfügung gestellt.
LiteratureDie Literatur ist themenspezifisch. Sie muss je nach Situation selber beschafft werden oder wird zur Verfügung gestellt.
Prerequisites / NoticeDie Arbeit sollte vor Beginn des Praktikums abgeschlossen werden.
401-9986-00LMentored Work Specialised Courses in the Respective Subject with an Educational Focus Mathematics B Restricted registration - show details
Mentored Work Specialised Courses in the Respective Subject with an Educational Focus in Mathematics for Teaching Diploma and for students upgrading TC to Teaching Diploma.
2 credits4AM. Akveld, K. Barro, A. Barth, L. Halbeisen, M. Huber, N. Hungerbühler, A. F. Müller, C. Rüede
AbstractIn der mentorierten Arbeit in FV verknüpfen die Studierenden gymnasiale und universitäre Aspekte des Fachs mit dem Ziel, ihre Lehrkompetenz im Hinblick auf curriculare Entscheidungen und auf die zukünftige Entwicklung des Unterrichts zu stärken. Angeleitet erstellen sie Texte, welche die anvisierte Leserschaft, in der Regel gymnasiale Fachlehrpersonen, unmittelbar verstehen.
ObjectiveThe aim is for the students
- to familiarise themselves with a new topic by obtaining material and studying the sources, so that they can selectively extend their specialist competence in this way.
- to independently develop a text on the topic, with special focus on its mathematical comprehensibility in respect of the level of knowledge of the targeted readership.
- To try out different options for specialist further training in their profession.
ContentThematische Schwerpunkte:
Die mentorierte Arbeit in FV besteht in der Regel in einer Literaturarbeit über ein Thema, das einen Bezug zum gymnasialem Unterricht oder seiner Weiterentwicklung hat. Die Studierenden setzen darin Erkenntnisse aus den Vorlesungen in FV praktisch um.

Lernformen:
Alle Studierenden erhalten ein individuelles Thema und erstellen dazu eine eigenständige Arbeit. Sie werden dabei von ihrer Betreuungsperson begleitet. Gegebenenfalls stellen sie ihre Arbeit oder Aspekte daraus in einem Kurzvortrag vor. Die mentorierte
Arbeit ist Teil des Portfolios der Studierenden.
Lecture notesEine Anleitung zur mentorierten Arbeit in FV wird zur Verfügung gestellt.
LiteratureDie Literatur ist themenspezifisch. Sie muss je nach Situation selber beschafft werden oder wird zur Verfügung gestellt.
Prerequisites / NoticeDie Arbeit sollte vor Beginn des Praktikums abgeschlossen
werden.
406-0251-AALMathematics I Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
6 credits13RL. Halbeisen
AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

2. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals.

3. Ordinary Differential Equations:
variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems.
Literature- Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall.
- Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley.
406-0252-AALMathematics II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
7 credits15RL. Halbeisen
AbstractContinuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content- Multivariable Differential Calculus:
functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence.

- Multivariable Integral Calculus:
multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications.

- Partial Differential Equations:
separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.
Literature- Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley.
- Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.
406-0253-AALMathematics I & II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
13 credits28RL. Halbeisen
AbstractMathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
Main focus of Mathematics II: multivariable calculus and partial differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

2. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals.

3. Ordinary Differential Equations:
variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems.

4. Multivariable Differential Calculus:
functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence.

5. Multivariable Integral Calculus:
multiple integrals, line and surface integrals, work and flow, Gauss and Stokes theorems, applications.

6. Partial Differential Equations:
separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.
Literature- Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall.
- Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley.
- Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley.
- Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.