Dr Christoph Czichowsky

This course is available on the MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. This course is available with permission as an outside option to students on other programmes where regulations permit. This course uses controlled access as part of the course selection process. For information on controlled access courses, including eligibility, application processes, deadlines, and departmental contact details, please refer to the Controlled Access Courses webpage.

Students should submit a short statement indicating a) why they think the course is suitable for them given their background knowledge and b) their motivation for their choice.

Deadline for application: Due to the nature of the method of application, interested students should apply as soon as possible after the opening selection and no later than 10.00am on Friday 25 September.

Course lecturers will aim to make initial offers to students on LSE For You by Friday 25 September. 

All MSc Financial Mathematics and MPhil/PhD Mathematics students will be guaranteed a place if they select the course by the course selection deadline in Autumn Term. All other students for which this course is available will be selected based on a first come first served basis. 

This course is available as an outside option for students with a strong quantitative background after obtaining permission from the lecturers of the course. This includes for instance students from MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (Research)Students should submit a short statement indicating a) why they think the course is suitable for them given their background knowledge and b) their motivation for their choice.

Students are expected to have basic Python programming skills and good command of linear algebra and calculus.

This course consists of two parts. Part I explores the core mathematical principles and foundations that power Generative AI, including an in-depth study of Transformer architectures and Large Language Models (LLMs). Part II transitions from theory to practice, guiding participants through the design, implementation, and scaling of GenAI-driven systems.

• AI Fundamentals: Covers the history of the evolution of LLMs (GPT, Claude, Gemini), foundational models, and the current state and economic impact of GenAI adoption.
• The Math & Architecture: Focuses on linear algebra, probability, and the Transformer architecture, including multi-head attention and scaling laws.
• Training & Fine-Tuning: Explores pre-training, Supervised Fine-Tuning (SFT), and Parameter-Efficient Fine-Tuning (PEFT)/Low-Rank Adaptation (LoRA), along with hardware optimization (GPUs/TPUs) and model quantization.
• Agents & RAG: Deep dive into building Agentic Frameworks and agents using LangChain and Retrieval-Augmented Generation (RAG) for custom data.
• Systems & MCP: Covers production deployment (AWS), MLOps, and the integration of models with external tools via APIs and Model Context Protocol (MCP) standards.
• Ethics & Beyond: Examines AI ethics and data privacy alongside non-text models like GANs, Diffusion, and time-series forecasting.

Teaching arrangements
1.    Co-teaching: Konstantin Kuchenmeister (instructor) and Christoph Czichowsky (academic faculty).
2.    Lectures: Delivered by the instructor, and will be primarily delivered through two focused week-long sessions.
3.    Office hours: Weekly office hours by the instructor in person in Weeks 6 and 11 and via Zoom in Weeks 1 to 5 and 7 to 10. 
4.    Lecture recordings: Recorded and made available on request, with in-person attendance expected for interactive elements and cohort learning.
5.    Facilities / computing: Students require access to Python and a standard ML stack. Where feasible, practical work will be designed to run on modest hardware for core components; optional extensions may use cloud or shared compute if available within School policy.
6.    Classroom and schedule: 2 hours of lecture via zoom in Week 1, lectures and tutorials totaling to 20 hours in Week 6 and lectures and tutorials totaling to 8 hours in Week 11. 
 

Formative assessment takes the form of one homework problem and feedback on a presentation of the first part of the group project, both in Week 9.

1. Build a Large Language Model (from Scratch), Sebastian Raschka, ISBN-13: 978-1633437166,  ISBN-10: 1633437167

2. AI Engineering: Building Applications with Foundation Models, Chip Huyen, ISBN-13: 978-1098166304,  ISBN-10: 1098166302

Project (50%) in Autumn Term Week 10.

This component of assessment includes an element of group work.

Written test (50%) in Winter Term Week 1.

Students can take this course either as a course with an attendance certificate if they attend a sufficient number of hours of the teaching or as an assessed course where they take the summative assessment and receive a mark. Students have to indicate during the course selection in which way they would like to attend the course. The summative assessment of this course consists of a presentation on a group project (50%) in Week 11 of Autumn Term and a written exam (50%) in Week 1 of Winter Term.