**Directors of the specialization: **Hans-Olav Tylli and Xiao Zhong

**Mandatory core courses**

MAST30132 Introduction to Real and Fourier Analysis (5 cr)

MAST31002 Functional analysis (10 cr)

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

MAST31006 Complex analysis I (10 cr)

MAST31008 Fourier analysis (5 cr)

MAST31010 Partial differential equations I (10 cr)

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

MAST30000 **Master´s thesis **(30 cr)** **(the link includes grading scale and criteria)

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

Personal study plan form (for Mathematics and Applied Mathematics):

Personal Study Plan

Hans-Olav Tylli and Xiao Zhong

Ilkka Holopainen, Hans-Olav Tylli and Xiao Zhong

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. It is recommended that the core courses (Introduction to Real and Fourier Analysis and Functional analysis) are taken in the Autumn of Year 1. The optional courses can be chosen freely, and the recommended total amount of credits in mathematics is at most 30 credit points per semester.

**Year 1, Autumn**

Differential equations II, 5 cr. (if not taken earlier)

Vector analysis II, 5 cr. (if not taken earlier)

Introduction to Real and Fourier Analysis , 5 cr. (core)

Functional analysis, 10 cr. (core)

Harmonic analysis, 10 cr. (optional)

Minor subject, 10 cr.

**Year 1, Spring**

Fourier analysis I, II, 10 cr. (optional)

Complex analysis I, 10 cr. (optional)

Partial differential equations I, 10 cr. (optional)

Real analysis II, 10 cr. (optional)

Introduction to differential geometry, 10 cr. (optional)

Spectral theory, 10 cr. (optional)

Minor subject 5 cr.

**Year 2, Autumn**

Minor subject 15 cr.

Optional analysis course, 10 cr. (depending on total credit points)

Master´s thesis seminar starts

Master´s thesis starts

**Year 2, Spring**

Master´s thesis 30 cr and Master´s thesis seminar 5 cr completed

Optional analysis course, 10 cr. (depending on total credit points)

Minor subject 10 cr.

This example concerns a student who is interested in analysis and who is interested in applying to graduate school after completing the master degree. The example is based on assumption that the student has chosen Vector analysis II and Differential equations II courses in his/her candidate studies. Also, the student wants to study only mathematics but no other subjects in his/her master studies (studies then contain 55+30 cr. math. + 30 cr. pro gradu + 5 cr. seminar). It is recommended that the core courses (Real analysis I and Functional analysis) are taken in the Autumn of Year 1. The optional courses can be chosen freely, and the recommended total amount of credits in mathematics is at most 30 credit points per semester.

**Year 1, Autumn**

Introduction to Real and Fourier Analysis , 5 cr. (core)

Functional analysis, 10 cr. (core)

Harmonic analysis, 10 cr. (optional)

optional advanced course, 5-10 cr.

**Year 1, Spring**

Fourier analysis I, II, 10 cr. (optional)

Complex analysis I, 10 cr. (optional)

Partial differential equations I, 10 cr. (optional)

Real analysis II, 10 cr. (optional)

Introduction to differential geometry, 10 cr. (optional)

Spectral theory, 10 cr. (optional)

**Year 2, Autumn**

Optional analysis course, 10 cr. (depending on total credit points)

Optional analysis course, 10 cr. (depending on total credit points)

Master´s thesis seminar starts

Master´s thesis work starts

**Year 2, Spring**

Master´s thesis 30 cr and Master´s thesis seminar 3 cr completed

Optional analysis course, 10 cr. (depending on total credit points)

Optional analysis course, 10 cr. (depending on total credit points)

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