The Mathematics Curriculum in Fall 2015
Background
Beginning Fall 2015, Jacobs University is implementing a new
structure for all of its undergraduate majors. All curricula will
be organized in identicallysized modules, with a uniform structure
across the entire university. Among the important advantages are
 Students preserve the choice between two or even three degree
programs until the end of the first year;
 Every student may opt to study abroad for one semester, or do a
semesterlong internship in a company or research institute;
 Every student can select a minor subject among a variety of
subject areas.
The New Mathematics Curriculum
The most visible change in our program structure is that the two
degree programs Mathematics and Computational and Applied Mathematics (ACM) are merged into a single degree program. However, the choices
which existed before will continue, and in some cases be extended,
within the new structure.An explicit differentiation between pure and applied mathematics
will begin in the second year of study. Students may specialize
further in their third year. In addition, it is now possible to
select a minor subject which will become an official part of the
degree transcript. This leads to a large set of degree options
tailored toward individual strengths and interests and extends the
study options previously available. In particular, it is now
possible to study for a
 Bachelor of Mathematics,
 Bachelor of Mathematics with a minor in
Physics,
 Bachelor of Mathematics with a minor in Computer
Science,
 Bachelor of Mathematics with a minor in Economics and
Management,
 Bachelor of Mathematics with a minor in Electrical
and Computer Engineering.
Many more major/minor combinations are possible.The structure of the new curriculum is represented in the
following diagram. It represents a typical selection of modules and
possible choices. Jacobs University offers individual advising and
provides a number of options which deviate from the general scheme,
including the fasttracking of students with exceptional talents,
tailored study options for students with prior university
experience, or additional minor subjects addressing special
interests and talents.
Note: The structure graphics is a simplified version
of the Mathematics curriculum. It is designed to convey the essence
of the program structure, but cannot show every detail or study
option. Exact module and course names are subject to
change.
The Study Plan
Year 1
The first year is providing a sound foundation in Mathematics. At
the same time it allows to venture into two other subject areas, at
least one of which should be Physics or Computer Science as these programs provide additional exposure to mathematics in
action.At least one module is completely free to choose. Thus, it is
possible to study close to Mathematics by selecting Physics
and Computer Science, or venture into areas of independent
interest such as Social Sciences, Business,
Economics, Psychology, or Chemistry.
As part of the universitywide methods and skills education,
students are strongly encouraged to learn or improve their German
if German is not their mother tongue, or learn a third language if
they are already fluent in German.
Year 2
The second year continues the mathematics core education with one
module common to all mathematics students supplemented by
additional courses from the universitywide methods and skills
lineup. In addition, students select among a pure and an applied
mathematics module, and one module continuing one of the first year
choices outside of mathematics. This leads to the following
possibilities:
 A student taking both the pure and the applied mathematics
module will graduate with a Bachelor of Mathematics without a
minor.
 A student taking only one of either pure or applied mathematics
will continue another subject into the second year, typically
leading to a Bachelor of Mathematics with a minor.
Year 3
In the fifth semester, students may opt to study abroad, or do a
semesterlong internship in a company or in a research lab.
Students who stay on campus will take specialization courses and
become involved in oneone research with a faculty member or junior
academic staff.The sixth semester offers further specialization options, and
all students work on their Bachelor thesis project. Students with a
minor subject should take at least one specialization course in
their chosen minor.
Over the course of study, Jacobs University requires all
students to take one module worth of credits in the fields of
Business, Technology, and Society. The respective courses will
broaden the horizon beyond the immediate subject area of the chosen
major, and will provide valuable practical skills and concepts that
contribute to success in any one's professional or academic
career.
Modules and Courses
Year 1  Fundamental Mathematics
 General Mathematics: Foundational topics and methods (5
ECTS)
 Analysis II: Continuation of first semester
Calculus/Analysis (5 ECTS)
 Mathematical Software Lab: Mathematica and LaTeX (2.5
ECTS)
 Student Seminar (2.5 ECTS)
Year 2  Core Mathematics
 Linear Algebra II: Continuation of second semester
Linear Algebra (5 ECTS)
 Introductory Real Analysis: Lebesgue integration and
applications (5 ECTS)
 Numerical Methods (5 ECTS)
Year 2  Pure Mathematics
 Calculus on Manifolds: Manifolds and differential
forms (5 ECTS)
 Introduction to Complex Analysis (5 ECTS)
 Introduction to Algebra (5 ECTS)
Year 2  Applied Mathematics
 Applied Dynamical Systems + Lab: Nonlinear dynamical
systems with applications (5+2.5 ECTS)
 Stochastic Methods + Lab: stochastic modeling with
applications to finance (5+2.5 ECTS)
Year 3  Specialization Courses
 Algebra and Geometry
 Manifolds and Topology
 Number Theory
 Discrete Structures and Optimization
 Stochastic Processes and Finance
 Functional Analysis and Elliptic Operators
 Numerical Analysis and Scientific Computing
 Mathematical Modeling with PDEs
 Differential Equations and Dynamical Systems
 Topics in Mathematics (topics of current interest)
