Applied Mathematics

Professors in charge: Nuutti Hyvönen, Antti Hannukainen, Camilla Hollanti, Pauliina Ilmonen, Lasse Leskelä, Rolf Stenberg
Credits: 40-65
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 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.

Content and structure

(i) 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.

The student must choose seven of the following ten courses:

Mathematical core (35 cr)

CODE

NAME

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

1.

MS-E1652

Computational methods for differential equations

5

II

1.

MS-E1653

Finite element method

5

III-IV

1.

MS-E1654

Computational inverse problems

5

IV

1.

MS-E2112

Multivariate statistical analysis

5

III-IV

1.

MS-E2139

Nonlinear programming

5

II

1.

 

(ii) A 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

I 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.

II 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.

3. MS-E1601 Brownian motion and stochastic analysis, MS-E1602 Large random systems, a selection of courses in Systems and Operations Research and/or Computer Science. 

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