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Theta Functions Course

Theta Functions Course
from 4 to 360h flexible workload
valid certificate in your country

What will I learn?

This course provides a structured journey through theta functions, starting from fundamental definitions and convergence properties, progressing to essential functional equations, transformation laws, and quasi-periodic behaviors. Participants will learn to represent lattices, develop elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and utilize uniqueness and dimension theorems, supported by detailed proofs, examples, and tips for accurate mathematical writing and referencing.

Elevify advantages

Develop skills

  • Master theta series convergence, including control of domains and holomorphic properties.
  • Derive key theta identities such as heat equation solutions, quasi-periodicity, and modular transformations.
  • Construct elliptic functions using theta quotients to achieve specific divisors.
  • Connect theta functions to Weierstrass ℘-function via poles, zeros, and field extensions.
  • Develop skills in rigorous mathematical exposition, lattice normalization, and precise source citation.

Suggested summary

Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.
Workload: between 4 and 360 hours

What our students say

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Very great course. Lots of rich information.
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