**Directors of the specialization**: Matti Lassas and Petri Ola

**Core courses**, recommended

MAST31002 Functional analysis (10 cr)

MAST30132 Introduction to Real and Fourier Analysis (5 cr)

**Specialization courses**, at least 10 cr from this list

MAST31402 Bayesian inversion (10 cr)

MAST31403 Integral equations (10 cr)

MAST31401 Inverse problems 1: convolution and deconvolution (5 cr)

MAST31010 Partial differential equations I (10 cr)

MAST31404 Introduction to wavelets (5 cr)

MAST31036 Convex analysis and optimization I (5 cr)

MAST31041 Convex analysis and optimization II (5 cr)

MAST30001** ****Master´s thesis seminar (5 cr)**

MAST31000 **Master´s thesis (30 cr) (the link includes grading scale and criteria)**

Other advanced courses from the list of core courses, mathematics and applied mathematics. statistics courses and/or courses from other programmes as approved in personal study plan.

Bachelor's level courses on differential equations and multivariable calculus are strongly recommended. If these were not done during the bachelor studies it is possible to include parts of them in the master's studies.

Matti Lassas and Petri Ola

Matti Lassas and Petri Ola

The studies begin by contacting one of the directors of the specialization in order to form a personal study plan.

Apart from the required core and specialization courses, the student can choose any advanced courses from all other specializations in mathematics and statistics. It is possible to include courses from different master’s programs such as physics, machine learning or computer science if they have sufficient mathematical content.

Topics in applied analysis vary from purely mathematical questions ranging from partial differential equations and differential geometry to numerical methods in applications. The aim of the studies is to obtain professional level in pure or applied mathematics needed in working in private and public sector, or continuing to Ph.D studies.

Example 1

This example concerns a student interested in a solid background in analysis, possibly with interests in applications, who is interested in moving go work in the private sector after completing his/her master degree (containing 55 cr. in mathematics + 30 cr. pro gradu + 5 cr. seminar + 30 cr. computer science or some other subject).

The student considered in the example did not do Vector analysis II or Differential equations II in the candidate studies so these courses need to included in the master studies.

**Year 1, Autumn:**

Vector analysis II, 5 cr

Fourier analysis I, 5 cr, or Introduction to wavelets, 5 cr, or Convex analysis and optimization I, 5 cr

Introduction to Real and Fourier Analysis, 5 cr

Functional Analysis, 10 cr

**Year 1, Spring:**

Inverse Problems courses, 5 +5 cr

Partial differential equations I, 10 cr

A course in data science or machine learning 10 cr

**Year 2, Autumn:**

Complex analysis I, 10 cr

Studies in data science and machine learning, 15-20 cr, Convex analysis and optimization II, 5 cr

Work on masters thesis (30 cr) and master’s thesis seminar ( 5cr) starts.

**Year 2, Spring:**

Master thesis (30 cr) and seminar (5 cr) completed

Studies in data science or machine learning (5 cr).

EXAMPLE 2

This example concerns a student who is interested in Applied analysis and who is interested in applying to graduate school after completing their master's degree. The example is based on the assumption that the student has chosen differential equations II and Vector analysis II courses in their candidate studies, but not Numerical linear algebra. Also, the student wants to study only mathematics but no other subjects in their master's studies (studies then contain 55+30 cr. math. + 30 cr. Pro gradu + 5 cr. seminar).

**Year 1, Autumn:**

Functional Analysis 10 cr

Fourier analysis I and II, 10 cr

Introduction to Real and Fourier Analysis, 5 cr

Numerical linear algebra 5 cr

**Year 1, Spring:**

Complex analysis I, 10 cr.

Partial differential equations I, 10 cr

Integral equations 10 cr

**Year 2, Autumn:**

Partial differential equations II, 10 cr or Convex analysis and optimization I and II (5 + 5 cr.)

Riemannian geometry, 10 cr

Master’s thesis (30 cr) and Master’s thesis seminar (5 cr) start.

**Year 2, Spring:**

Inverse problems courses, 5+5 cr,

Master’s thesis and Master’s thesis seminar are completed.