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Professors Professor in charge: Nuutti Hyvönen
Other professors: Chris Brzuska, Antti Hannukainen, Camilla Hollanti, Pauliina Ilmonen, Kaie Kubjas, Lasse Leskelä, Rolf Stenberg
Credits: 40–65 Extent: 55–65 ECTS (long major) or 40–45 ECTS (compact major)
Abbreviation: AM
Code: SCI3053

Objectives

The major in Applied Mathematics is designed for students interested in mathematical sciences and their application to other disciplines. It is based on a solid mathematical core that gives the student a broad set of skills for working on diverse mathematical problems. The major also includes an elective part that provides flexibility to orientate toward a master's thesis project in a chosen application area. A high proportion of students majoring in applied mathematics will continue their studies to a doctoral degree.

The importance of mathematical techniques is increasing in science and engineering as new fields employing sophisticated mathematical models are constantly emerging. The driving forces for such development are the ever-increasing computational resources, which should be used wisely and to their full power. This requires the education of mathematicians who are able to interact and collaborate with experts in application areas. The major in Applied Mathematics responds to this need.

Each student choosing Applied Mathematics as major is assigned a mentor among the faculty of the Department of Mathematics and Systems Analysis.
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Courses

Mathematical core (35 cr)

The student learns core skills in applied mathematics by taking seven courses in the following key areas: numerical analysis and computational methods, probability and statistics, discrete mathematics, and optimization.

Choose seven of the following ten courses.

...

Code

...

Name

...

ECTS credits

...

Period

...

Year

...

MS-E1050

...

Graph theory

...

5

...

I

...

1.

...

MS-E1110

...

Number theory

...

5

...

II

...

1.

...

MS-E1461

...

Hilbert spaces

...

5

...

I

...

1.

...

MS-E1600

...

Probability theory

...

5

...

III

...

1.

...

MS-E1651

...

Numerical matrix computations

...

5

...

I

...

Content and structure

The major in Applied Mathematics can be taken either as a long major (55–65 ECTS) or a compact major (40–45 ECTS). The student's personal academic advisor provides assistance in planning the curriculum details.

Mandatory studies (15 ECTS)

CODE

NAME

CREDITS

PERIOD

YEAR

MS-E1651

Numerical matrix computations

5

II

1

MS-E2112

Multivariate statistical analysis

5

III–IV

1

MS-E2122

Nonlinear optimization

5

I–II

1

Core studies (25–45 ECTS)

Select 25–45 credits for a long major or 25–30 credits for a compact major. In both cases, select at least one course from each of the three categories below.

Computational mathematics

CODE

NAME

CREDITS

PERIOD

YEAR

MS-E1142

Computational algebraic geometry

5

I (every other year)

1 or 2

MS-E1461

Hilbert spaces

5

I

1 or 2

MS-E1652

Computational methods for differential equations

5

II

I

1

.

or 2

MS-E1653

Finite element method

5

III-IV

III–IV

1

.

or 2

MS-E1654

Computational inverse problems

5

IV

1

.

or 2

Optimization

CODE

NAME

CREDITS

PERIOD

YEAR

MS-

E2112Multivariate statistical analysis

E2121

Linear optimization

5

III-IV

1.

I–II

1 or 2

MS-E2123

Integer optimization

5

III–IV (every other year)

1 or 2

MS-

E2139Nonlinear programming

E2134

Decision making and problem solving

5

II

III–IV

1

.

Specialization area (30 cr)

A personalized collection of mathematical courses and studies in a selected application area. The student is required to include some courses from an applied discipline, for example one related to engineering, computer science, or natural sciences. This part of the studies is designed under the guidance of the mentor. All specialization area studies can be chosen on an individual basis, or they can be composed of a minor and 5–10 credits of supporting mathematical courses.

Examples of possible course contents

Expand
titleI Mathematical core (“Numerical analysis”)

MS-E1050 Graph theory, MS-E1461 Hilbert spaces, MS-E1651 Numerical matrix computations, MS-E1652 Computational methods for differential equations, MS-E1653 Finite element method, MS-E1654 Computational inverse problems, MS-E2139 Nonlinear programming.

Possible specialization areas:

1. MS-E1740 Continuum mechanics 1, MS-E1741 Continuum mechanics 2, MS-E1742 Computational mechanics 1, MS-E1743 Computational mechanics 2, two courses in Structural Mechanics.

2. MS-E1740 Continuum mechanics 1, PHYS-E0413 Theoretical mechanics, a minor or a selection of courses in Applied Physics and/or Structural Mechanics.

3. MS-E1600 Probability theory, MS-E1602 Large random systems, a minor or a selection of courses in Applied Physics and/or Computer Science.

...

titleII Mathematical core (“Discrete mathematics and probability”)

MS-E1050 Graph theory, MS-E1110 Number theory, MS-E1600 Probability theory, MS-E1651 Matrix computations, MS-E1654 Computational inverse problems, MS-E2112 Multivariate statistical analysis, MS-E2139 Nonlinear programming.

Possible specialization areas:

1. MS-E1111 Galois theory, MS-E2146 Integer programming, a minor or a selection of courses in Computer Science.

2. MS-E1602 Large random systems, a minor or a selection of courses in Computer Science and/or Applied Physics.

...

or 2

Statistics and probability

CODE

NAME

CREDITS

PERIOD

YEAR

MS-E1600

Probability theory

5

III

1 or 2

MS-E1602

Large random systems

5

IV (every other year)

1 or 2

MS-E1603

Random graphs and network statistics

5

I

1 or 2

CS-E5710

Bayesian data analysis

5

I–II

1 or 2

Students taking a long major select in addition sufficiently many courses in mathematics or other mathematical sciences to obtain a total of 55–65 credits. Courses not in the below list of recommended courses may also be included with the consent of the professor in charge.

Recommended courses

CODE

NAME

CREDITS

PERIOD

YEAR

MS-E1050

Graph theory

5

I (2018-2019)
II (2019-2020)

1 or 2

MS-E1110

Number theory

5

II (2018-2019)
I (2019-2020)

1 or 2

MS-E1111

Galois theory

5

IV (every other year)

1 or 2

MS-E1687

Advanced topics in cryptography

5

III–IV

1 or 2

MS-E1742

Computational mechanics 1

5

I

1 or 2

MS-E1743

Computational mechanics 2

5

II

1 or 2

CS-E3190

Principles of algorithmic techniques

5

I–II

1 or 2

CS-E3210

Machine learning: Basic principles

5

I–II

1 or 2

CS-E4500

Advanced course in algorithms

5

III–IV

1 or 2

CS-E4510

Distributed algorithms

5

I–II

1 or 2

CS-E4320

Cryptography and data security

5

I–II

1 or 2

CS-E4530

Computational complexity theory

5

III–IV

1 or 2

CS-E4555

Combinatorics

5

III–IV

1 or 2

CS-E4580

Programming parallel computers

5

V

1 or 2

CS-E5740

Complex networks

5

I–II

1 or 2

CS-E5745

Mathematical methods for network science

5

III (every other year)

1 or 2

PHYS-E0412

Computational physics

5

III–V

1 or 2

PHYS-E0419

Dynamics of particles, fluids and solids

5

I-II

1 or 2