Lorenz Halbeisen: Catalogue data in Autumn Semester 2021

Name	Prof. Dr. Lorenz Halbeisen
Field	Logic and Set Theory
Address	Dep. Mathematik ETH Zürich, HG G 51.5 Rämistrasse 101 8092 Zürich SWITZERLAND
Telephone	+41 44 633 84 60
E-mail	lorenz.halbeisen@math.ethz.ch
URL	http://www.math.ethz.ch/~halorenz
Department	Mathematics
Relationship	Adjunct Professor and Privatdozent

Number	Title	ECTS	Hours	Lecturers
401-2003-00L	Algebra I The two-semester course Algebra I / Algebra II is offered for the last time in its current version in the Autumn Semester 2021 / Spring Semester 2022.	7 credits	4V + 2U	L. Halbeisen
Abstract	Introduction and development of some basic algebraic structures - groups, rings, fields.
Objective	Introduction to basic notions and results of group, ring and field theory.
Content	Group Theory: basic notions and examples of groups, subgroups, factor groups, homomorphisms, group actions, Sylow theorems, applications Ring Theory: basic notions and examples of rings, ring homomorphisms, ideals, factor rings, euclidean rings, principal ideal domains, factorial rings, applications Field Theory: basic notions and examples of fields, field extensions, algebraic extensions, applications
Literature	Karpfinger-Meyberg: Algebra, Spektrum Verlag S. Bosch: Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag S. Lang, Algebra, Springer Verlag A. Knapp: Basic Algebra, Springer Verlag J. Rotman, "Advanced modern algebra, 3rd edition, part 1" http://bookstore.ams.org/gsm-165/ J.F. Humphreys: A Course in Group Theory (Oxford University Press) G. Smith and O. Tabachnikova: Topics in Group Theory (Springer-Verlag) M. Artin: Algebra (Birkhaeuser Verlag) R. Lidl and H. Niederreiter: Introduction to Finite Fields and their Applications (Cambridge University Press)
401-3033-00L	Gödel's Theorems	8 credits	3V + 1U	L. Halbeisen
Abstract	Die Vorlesung besteht aus drei Teilen: Teil I gibt eine Einführung in die Syntax und Semantik der Prädikatenlogik erster Stufe. Teil II behandelt den Gödel'schen Vollständigkeitssatz Teil III behandelt die Gödel'schen Unvollständigkeitssätze
Objective	Das Ziel dieser Vorlesung ist ein fundiertes Verständnis der Grundlagen der Mathematik zu vermitteln.
Content	Syntax und Semantik der Prädikatenlogik Gödel'scher Vollständigkeitssatz Gödel'sche Unvollständigkeitssätze
Literature	L. Halbeisen and R. Krapf: Gödel's Theorems and Zermelo's Axioms: a firm foundation of mathematics, Birkhäuser-Verlag, Basel (2020)
401-9983-00L	Mentored Work Subject Didactics Mathematics A Mentored Work Subject Didactics in Mathematics for TC and Teaching Diploma.	2 credits	4A	M. Akveld, K. Barro, A. Barth, L. Halbeisen, N. Hungerbühler, C. Rüede
Abstract	In 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.
Objective	The 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.
Content	Thematische 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 notes	Eine kurze Anleitung zur mentorierten Arbeit in Fachdidaktik wird zur Verfügung gestellt.
Literature	Die 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 / Notice	Die Arbeit sollte vor Beginn des Praktikums abgeschlossen werden.
401-9984-00L	Mentored Work Subject Didactics Mathematics B Mentored Work Subject Didactics in Mathematics for Teaching Diploma and for students upgrading TC to Teaching Diploma.	2 credits	4A	M. Akveld, K. Barro, A. Barth, L. Halbeisen, N. Hungerbühler, C. Rüede
Abstract	In 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.
Objective	The 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.
Content	Thematische 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 notes	Eine kurze Anleitung zur mentorierten Arbeit in Fachdidaktik wird zur Verfügung gestellt.
Literature	Die 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 / Notice	Die Arbeit sollte vor Beginn des Praktikums abgeschlossen werden.
401-9985-00L	Mentored Work Specialised Courses in the Respective Subject with an Educational Focus Mathematics A Mentored Work Specialised Courses in the Respective Subject with an Educational Focus in Mathematics for TC and Teaching Diploma.	2 credits	4A	M. Akveld, K. Barro, A. Barth, L. Halbeisen, N. Hungerbühler, A. F. Müller, C. Rüede
Abstract	In 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.
Objective	The 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.
Content	Thematische 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 notes	Eine Anleitung zur mentorierten Arbeit in FV wird zur Verfügung gestellt.
Literature	Die Literatur ist themenspezifisch. Sie muss je nach Situation selber beschafft werden oder wird zur Verfügung gestellt.
Prerequisites / Notice	Die Arbeit sollte vor Beginn des Praktikums abgeschlossen werden.
401-9986-00L	Mentored Work Specialised Courses in the Respective Subject with an Educational Focus Mathematics B 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 credits	4A	M. Akveld, K. Barro, A. Barth, L. Halbeisen, N. Hungerbühler, A. F. Müller, C. Rüede
Abstract	In 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.
Objective
406-0252-AAL	Mathematics II 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 credits	15R	L. Halbeisen
Abstract	Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations.
Objective	Mathematics 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 flux, Green, 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, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons).
406-0253-AAL	Mathematics I & II 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 credits	28R	L. Halbeisen
Abstract	Mathematics 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.
Objective	Mathematics 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	1. 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, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 3. Ordinary Differential Equations: separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional 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, Green, 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 - Early Transcendentals (Pearson Addison-Wesley). - Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons).
Prerequisites / Notice	Prerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative. Assistance: Tuesdays and Wednesdays 17-19h, in Room HG E 41.