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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, practical examples, and tips for accurate, rigorous writing and proper referencing.

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 by employing theta quotients to achieve specified divisors.
  • Connect theta functions to Weierstrass ℘-function through analysis of poles, zeros, and field extensions.
  • Develop skills in writing precise mathematical notes, normalising lattices, monitoring multipliers, and citing references accurately.

Suggested summary

Before starting, you can change the chapters and 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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