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Program Contact:

Dierk Schleicher

Professor of Mathematics

dierk@jacobs-university.de

Research I, 115

+49 421 200 3213

 
 
 

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Modules

Where appropriate, several closely interconnected courses with an overarching set of learning goals are grouped into a module. Modules provide a higher level view into the curriculum structure to facilitate information and documentation. Note, however, that formal graduation requirements and the documentation of the learning process refer to credit points and grades attributed to the individual courses or lab units.


ESM FOR MATHEMATICS MAJORS

  Semester: 1-2
  Credit Points:  10

General Information

Students of Mathematics may either take Engineering and Science Mathematics courses (``regular variant'' of the curriculum) or ANALYSIS and LINEAR ALGEBRA (``advanced variant'' of the curriculum) during their first year of study. Following the advanced variant is recommended; students should consult with Mathematics faculty for advice.

Learning goals

  • Basic skills in differential and integral calculus, linear algebra, probability, and statistics
  • Problem solving skills
  • Training in abstract reasoning and symbolic manipulation
  • Ability to turn real-world problems into a concise mathematical question
  • Ability to interpret mathematical statements back into the problem domain

Courses

Take at least one course per semester from among the following.

120101
ESM 1A - Single Variable Calculus
120111
ESM 1B - Multivariable Calculus, ODE
120102
ESM 2A - Linear Algebra, Probability, Statistics
120112
ESM 2B - Linear Algebra, Fourier, Probability


GENERAL MATHEMATICS AND COMPUTATIONAL SCIENCE

  Semester: 1-2
  Credit Points:  15

General Information

This module is taken by all students who follow the regular track of the Mathematics and ACM Bachelor degrees. Students with a strong background in Mathematics should take ANALYSIS and LINEAR ALGEBRA in their first year.

Learning goals

  • Fluency in basic logic
  • Ability to construct rigorous and concise arguments
  • Problem solving skills
  • Confidence in formulating conjectures
  • Ability to turn real-world problems into a concise mathematical question
  • Ability to interpret mathematical statements back into the problem domain
  • Ability to build simple models that still capture the essence of a problem
  • Basic knowledge in using standard software tools

Courses

110101
General Mathematics and Computational Science I
110111
Symbolic Software Lab
110102
General Mathematics and Computational Science II
110112
Numerical Software Lab


ANALYSIS

  Semester: 3-4 (regular variant) or 1-2 (advanced variant)
  Credit Points:  15

General Information

This module provides the foundations in Mathematical Analysis for students of Mathematics and ACM. In addition, it may be an appropriate first year or second year choice for students particularly in Physics, Electrical Engineering and Computer Science. Consult with faculty from your major, and read the document ``How to choose Mathematics courses''.

The courses in this module have no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this module in their first year of study (``Advanced Track'' of the Mathematics curriculum). However, a familiarity with mathematical reasoning and proof (e.g. proof by induction or by contradiction) is assumed. The module GENERAL MATHEMATICS AND COMPUTATIONAL SCIENCE is designed for students who still need to develop this maturity.

Learning goals

  • Core skills in Analysis that every Mathematician needs
  • Working knowledge on series, differentiation and integration on $ R^n$
  • Develop these concepts in a rigorous manner and in sufficient generality to prepare the student for advanced work in mathematics.
  • Building a core set of examples and counterexamples for each concept area
  • Necessary skills needed for more advanced and specialized courses

Courses

100211
Analysis I
100212
Analysis II


LINEAR ALGEBRA

  Semester: 3-4 (regular variant) or 1-2 (advanced variant)
  Credit Points:  15

General Information

This module complements ANALYSIS in the fundamental education of the Mathematics major. Students of ACM should consider taking this module. It may also be an appropriate first year or second year choice for students particularly in Physics, Electrical Engineering and Computer Science. Consult with faculty from your major, and read the document ``How to choose Mathematics courses''.

The courses in this module have no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this module in their first year of study (``Advanced Track'' of the Mathematics curriculum). However, a familiarity with mathematical reasoning and proof (e.g. proof by induction or by contradiction), is assumed. The module GENERAL MATHEMATICS AND COMPUTATIONAL SCIENCE is designed for students who still need to develop this maturity.

Learning goals

  • Core skills in Linear Algebra that every mathematician needs
  • Ability to abstract linear structures in any application domain to studying linear maps on vector spaces
  • Ability to carry out concrete computations in this framework
  • Working knowledge of the fundamental algebraic structures, in preparation of the respective third year courses

Courses

100221
Linear Algebra I
100222
Linear Algebra II


PERSPECTIVES OF MATHEMATICS

  Semester: 3-4 (regular variant) or 1-2 (advanced variant)
  Credit Points:  5-10

General Information

While the mathematical core courses build the foundation for a solid mathematical knowledge, the courses in this module cover beautiful or interesting areas of mathematics which need not be part of a systematic education, but which show mathematics as a lively, active and varied subject, and which convey the spirit why mathematicians enjoy their field. The topics covered in each instance of a course vary, so that each course may be taken for credit more than once.

Learning goals

  • Ability to apply basic skills to larger, but well defined mathematical problems
  • Find and work with original literature
  • Mathematical writing and presentation skills

Courses

100291
Perspectives of Mathematics I
100292
Perspectives of Mathematics II


SPECIALIZED MATHEMATICS COURSES

  Semester: 5-6 (regular variant) or 3-6 (advanced variant)
  Credit Points:  varying

General Information

Third year courses in Mathematics are designed to give students a first in-depth look into a wide selection of specialization areas in Mathematics. They also refine and extend the fundamental concepts introduced in ANALYSIS and LINEAR ALGEBRA. The courses are designed to be as independent as possible, so that a flexible selection of courses is possible. Some spring semester courses will depend to a limited extent on fall semester courses, and students should consult the individual course descriptions for details.

Learning goals

  • Skills in various areas of Mathematics as are required for a successful entry to graduate programs in Mathematics, Applied Mathematics, Computational Science, and Financial Mathematics
  • Sound basis on which students can develop their further career goals
  • Experience with advanced concepts needed by research mathematicians
  • First contact with the various specialization areas in Mathematics
A detailed list of available courses is provided in Section 5 below.


GUIDED RESEARCH MATHEMATICS AND BSC THESIS

  Semester: 5-6
  Credit Points:  15

General Information

In this module, students work on a research project in a particular area of specialization within mathematics. A faculty member acts as a supervisor and works with the student in a small study group or on a one-on-one basis.

Guided research has three major components: Literature study, research project, and seminar presentation (including a written report). The Guided Research report in the spring semester will typically be the Bachelor's Thesis which is a graduation requirement for Jacobs University undergraduates.

Learning goals

  • Learn how to search and use research literature
  • Scientific writing skills
  • Ability to orally present a project and its results
  • Time management and organizational skills
  • First-hand research experience

Courses

100391
Guided Research Mathematics I
100392
Guided Research Mathematics II



 

 
Last updated 2014-08-07, 18:04. © Jacobs University Bremen. All rights reserved.