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Theta Functions Course

Theta Functions Course
4 to 360 hours 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 behaviours. Participants will learn to represent lattices, develop elliptic functions using theta quotients, connect them to the Weierstrass ℘-function, and utilise 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 of domains and holomorphic properties.
  • Derive essential theta identities such as heat equation solutions, quasi-periodicity, and modular transformations.
  • Construct elliptic functions via theta quotients to achieve specified divisors.
  • Link theta functions to Weierstrass ℘-function by analysing poles, zeros, and field extensions.
  • Develop skills in writing precise mathematical notes, normalising lattices, and citing references 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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