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Theta Functions Course

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

What will I learn?

This course provides a structured journey through theta functions, starting from fundamental definitions and convergence properties, advancing to essential functional equations, transformation laws, and quasi-periodicity. Participants will learn to encode lattices, build elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and leverage uniqueness and dimension theorems, supported by detailed proofs, examples, and tips for rigorous writing and proper citations.

Elevify advantages

Develop skills

  • Master theta series convergence, including control over domains and holomorphic properties.
  • Derive key theta identities such as the heat equation, quasi-periodicity, and modular S-transformation.
  • Construct elliptic functions using theta quotients to achieve specified divisors.
  • Analyze relations between theta functions and Weierstrass ℘-function via poles, zeros, and fields.
  • Develop skills in writing precise mathematical notes, normalizing lattices, and citing sources accurately.

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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Great course. Lots of valuable information.
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