Theta Functions Course
This course provides mastery of theta functions, progressing from series definitions and convergence through to modular transformations and elliptic functions. Participants will construct explicit theta-quotient models, connect them to the Weierstrass ℘-function, and explore their applications in elliptic curves, modular forms, and physics, supported by clear proofs and examples.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course traces a focused journey through theta functions, from fundamental definitions and convergence to essential functional equations, transformation laws, and quasi-periodicity. Learners will encode lattices, build elliptic functions using theta quotients, link them to the Weierstrass ℘-function, and leverage uniqueness and dimension theorems, all with rigorous proofs, examples, and advice on precise exposition and source referencing.
Elevify advantages
Develop skills
- Master theta convergence: control series, domains, and holomorphic behaviour.
- Derive core theta identities: heat equation, quasi-periodicity, modular S-law.
- Build elliptic functions: use theta quotients to realise prescribed divisors.
- Relate theta to Weierstrass ℘: compare poles, zeros, and field generation.
- Write rigorous notes: normalise lattices, track multipliers, and cite sources.
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.What our students say
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