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 identically-sized 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
semester-long 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
fast-tracking 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 university-wide 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 university-wide 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
semester-long internship in a company or in a research lab. Students
who stay on campus will take specialization courses and become
involved in one-one 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)