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

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

Schedule and instructions of Analysis studies

Dir­ect­ors of the spe­cial­iz­a­tion

Hans-Olav Tylli and Xiao Zhong

Per­sons re­spons­ible for dis­cuss­ing the study plans

Ilkka Holopainen, Hans-Olav Tylli and Xiao Zhong

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. 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.

Ex­ample 2

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)