# Applied analysis

### Directors of the specialization

Matti Lassas and Petri Ola

### Persons responsible for discussing the study plans

Matti Lassas and Petri Ola

### Model study plans

#### 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.

Real analysis, 5 cr.

Functional Analysis 10 cr.

Minor subject 10 cr.

**Year 1, Spring:**

Fourier analysis I , 5 cr. or Introduction to Wavelets and Fourier analysis 5 cr.

Inverse Problems, 10 cr. or Bayesian Inverse Problems, 10 cr.

Partial differential equations I, 10 cr.

Minor subject 5 cr.

**Year 2, Autumn:**

Minor subject 15 cr.

Pro gradu work seminar starts

Pro gradu work starts

**Year 2, Spring:**

Pro gradu, 30 cr, completed + Pro gradu seminar 5 cr.

Complex analysis, 10 cr.

Minor subject 10 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 cf. Pro gradu + 5 cr. seminar).

**Year 1, Autumn:**

Functional Analysis 10 cr.

Topology II, 10 cr.

Real analysis I, 5 cr.

**Year 1, Spring:**

Fourier analysis I+II, 10 cr.

Partial differential equations I, 10 cr.

Introduction to differential geometry, 10 cr.

Topics in Probability I, 5 cr.

**Year 2, Autumn:**

Integral equations 10 cr.

Partial differential equations II, 10 cr.

Pro gradu seminar starts

Pro gradu work starts

**Year 2, Spring:**

Inverse Problems, 10 cr. or Bayesian Inverse Problems, 10 cr.

Pro gradu, 30 cr., completed + Pro gradu seminar 5 cr.