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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5054 MODULAR FORMS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics Mathematics

Course Objective

The aim of this course is to introduce the fundamental concepts in modular forms, and show its usage in the whole body of mathematics.

Learning Outcomes of the Course Unit

1   Will be able to use fundamental domains. 2   Will be able to modular forms. 3   Will be able to q-series. 4   Will be able to Fourier expansions. 5   Will be able to use applications of modular forms to other domains.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Fundamental domains 2 Modular groups 3 Modular forms and weights 4 Cusp forms 5 Fourier expansions 6 q-series 7 Eisenstein series 8 Midterm 9 Ramanujan tau function 10 Theta series 11 Dimension computations 12 Applications to sum of squares 13 Functional equation of the Riemann zeta function 14 Partition function, connections to elliptic curves and automorphic forms

Recomended or Required Reading

Textbook(s): [1] Serre J. P., A Course in Arithmetic, Springer, 1996. [2] Apostol, T., Modular Functions and Dirichlet Series in Number Theory, Springer, 1997. References: Materials: Instructor s notes and presentations

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 RPT REPORT 4 FIN FINAL EXAM 5 FCG FINAL COURSE GRADE MTE * 0.30 +ASG +RPT/2 * 0.30 +FIN * 0.40 6 RST RESIT 7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 +ASG +RPT/2 * 0.30 +RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

haydar.goral@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 4 3 3 2 2 2 4 3 3 3 LO.2 4 3 3 2 2 2 4 3 3 3 LO.3 4 3 3 2 2 2 4 3 3 3 LO.4 4 3 3 2 2 2 4 3 3 3 LO.5 4 3 3 2 2 2 4 3 3 3