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 everincreasing 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.Excerpt Include  


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
...
...
Graph theory
...
5
...
I
...
1.
...
...
Number theory
...
5
...
II
...
1.
...
...
Hilbert spaces
...
5
...
I
...
1.
...
...
Probability theory
...
5
...
III
...
1.
...
...
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 
Numerical matrix computations  5  II  1  
Multivariate statistical analysis  5  III–IV  1  
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 
Computational algebraic geometry  5  I (every other year)  1 or 2  
Hilbert spaces  5  I  1 or 2  
Computational methods for differential equations  5 
I  1 
or 2  
Finite element method  5 
III–IV  1 
or 2  
Computational inverse problems  5  IV  1 
or 2 
Optimization
CODE  NAME  CREDITS  PERIOD  YEAR 
Linear optimization  5 
IIIIV
1.I–II  1 or 2  
Integer optimization  5  III–IV (every other year)  1 or 2  
Decision making and problem solving  5 
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  

 
MSE1050 Graph theory, MSE1461 Hilbert spaces, MSE1651 Numerical matrix computations, MSE1652 Computational methods for differential equations, MSE1653 Finite element method, MSE1654 Computational inverse problems, MSE2139 Nonlinear programming. Possible specialization areas: 1. MSE1740 Continuum mechanics 1, MSE1741 Continuum mechanics 2, MSE1742 Computational mechanics 1, MSE1743 Computational mechanics 2, two courses in Structural Mechanics. 2. MSE1740 Continuum mechanics 1, PHYSE0413 Theoretical mechanics, a minor or a selection of courses in Applied Physics and/or Structural Mechanics. 3. MSE1600 Probability theory, MSE1602 Large random systems, a minor or a selection of courses in Applied Physics and/or Computer Science. 
...
title  II Mathematical core (“Discrete mathematics and probability”) 

MSE1050 Graph theory, MSE1110 Number theory, MSE1600 Probability theory, MSE1651 Matrix computations, MSE1654 Computational inverse problems, MSE2112 Multivariate statistical analysis, MSE2139 Nonlinear programming.
Possible specialization areas:
1. MSE1111 Galois theory, MSE2146 Integer programming, a minor or a selection of courses in Computer Science.
2. MSE1602 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 
Probability theory  5  III  1 or 2  
Large random systems  5  IV (every other year)  1 or 2  
Random graphs and network statistics  5  I  1 or 2  
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 
Graph theory  5  I (20182019)  1 or 2  
Number theory  5  II (20182019)  1 or 2  
Galois theory  5  IV (every other year)  1 or 2  
Advanced topics in cryptography  5  III–IV  1 or 2  
Computational mechanics 1  5  I  1 or 2  
Computational mechanics 2  5  II  1 or 2  
Principles of algorithmic techniques  5  I–II  1 or 2  
Machine learning: Basic principles  5  I–II  1 or 2  
Advanced course in algorithms  5  III–IV  1 or 2  
Distributed algorithms  5  I–II  1 or 2  
Cryptography and data security  5  I–II  1 or 2  
Computational complexity theory  5  III–IV  1 or 2  
Combinatorics  5  III–IV  1 or 2  
Programming parallel computers  5  V  1 or 2  
Complex networks  5  I–II  1 or 2  
Mathematical methods for network science  5  III (every other year)  1 or 2  
Computational physics  5  III–V  1 or 2  
Dynamics of particles, fluids and solids  5  III  1 or 2 