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Theta Functions Course

Theta Functions Course
flexible workload of 4 to 360h
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-periodicity. Participants will learn to represent lattices using theta functions, develop elliptic functions through theta quotients, connect them to the Weierstrass ℘-function, and utilise 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 over 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 by analysing poles, zeros, and field extensions.
  • Develop skills in writing precise mathematical notes, normalising lattices, and proper 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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