2026 Shanghai Jiao Tong University Artificial Intelligence Summer School

Mathematics is the “language through which we converse with creation.” Its most prominent feature is abstraction, a quality that can intimidate many students but is precisely the true source of mathematics’ beauty. This course not only reveals the internal logic of mathematics itself, but also explores its fascinating connections with economics, logic, music theory, and other fields. It helps students understand why linear algebra, calculus, probability, and statistics are indispensable tools for almost every university discipline; what their connection to artificial intelligence really is; and what practical value this mathematical knowledge can bring. The course aims to help students learn to think like mathematicians: to grasp the core essence beneath complexity, identify patterns amid uncertainty, and appreciate the beauty and power that mathematical thinking brings to the human mind. For students about to move from high school to university, this course serves as an essential bridge between secondary-school mathematics and university-level thinking.

Design Rationale: Centered on “data and transformations in space,” this course guides students to understand the nature of linear algebra as a discipline that studies spatial structures, data representation, and mapping relationships. It connects abstract objects such as vectors, matrices, and spatial transformations with practical visualization, building mathematical intuition through the lens of spatial transformation and laying the foundation for understanding data representation and feature transformation in machine learning algorithms.

Core Knowledge Points:

1. Geometric meaning and algebraic representation of vectors: Understand that vectors can represent points and directions in space as well as real-world data. Using examples such as sound, images, and text, the course explains how data can be represented as a point in high-dimensional space and builds 2D/3D spatial intuition.
2. Matrices and linear transformations: Establish the perspective that “a matrix is a transformation” and understand the dual meaning of matrices as both data tables and tools for spatial transformation. Demonstrate how space rotates, scales, and projects under matrix transformations. Use visualization tools, such as Python plotting libraries or interactive geometry tools, to show how transformations change shapes in space.

Learning Outcomes:

1. Students will be able to understand, from the perspective of disciplinary development, how linear algebra serves as an underlying language of data representation and transformation that supports modern AI algorithms.
2. Students will develop a “spatial transformation” mindset and use visualization tools to intuitively understand the geometric effects of matrix operations on space.

Design Rationale: This course aims to cultivate students’ mathematical intuition for handling continuity and randomness. The calculus component emphasizes the geometric meaning of derivatives, while the probability component focuses on understanding uncertainty from an axiomatic perspective, laying a foundation for core machine learning concepts such as optimization algorithms, loss functions, data distributions, and Bayesian inference.

Core Knowledge Points:

1. Limits and derivatives: Introduce the idea of limits through instantaneous rates of change and understand the derivative as the essence of the “best linear approximation” of a function at a point. Master basic differentiation rules and their geometric meaning, namely the slope of a tangent line. Understand the foundation of gradient descent: derivatives determine the direction in which the function value decreases most rapidly.
2. Probability spaces and statistical distributions: Establish the concepts of sample spaces and events, and explore the expectation (mean) and variance (fluctuation) of random variables. Analyze the mathematical properties of the normal distribution and its prevalence in nature. Understand how statistical distributions describe patterns and variability in real-world data, and why they are a universal language for describing data noise and regularity.

Learning Outcomes:

1. Develop intuitive thinking about “local linearization”.
2. Become familiar with core symbols such as gradients and distribution functions, understand why gradient descent can be used as an optimization tool, and prepare the mathematical foundation for machine learning algorithms.

Design Rationale: This module assembles the mathematical tools from the first two modules to analyze classic machine learning algorithms while introducing state-of-the-art models.

Core Knowledge Points:

1. Introduction to AI, machine learning, and deep learning: Clarify core concepts and disciplinary boundaries.
2. Classic machine learning algorithms: Linear regression and logistic regression.
3. Deep neural networks: Simple neural network models, such as fully connected networks, and optimization methods, such as backpropagation.
4. Introduction to state-of-the-art models, such as large language models and generative models.

Learning Outcomes:

1. Master the basic concepts of foundational machine learning algorithms.
2. Understand the complete AI workflow of data feature extraction, model training, testing, and validation.

Project Topics: The summer school plans to offer several thematic tracks with fixed topics, such as AI for Science, AI for Goods, AI entrepreneurship, AI algorithm applications, AI finance, and AI large models. Students may also propose topics of personal interest. A formal topic selection discussion will be held on the afternoon of July 16, and final topics will be determined in connection with the machine learning curriculum. In project-based learning, each group, or every five students, will be assigned one teaching assistant. Teaching assistants will mainly be graduate or doctoral students of the course professors and will also support group assignments and tutorial sessions.

Python learning will be integrated into project-based learning. Traditional high school Python courses often stop at printing text and do not easily create a sense of achievement. This module will combine large language models to guide students in using prompts to generate front-end code and integrating it with Python back-end logic written by themselves, enabling truly agile division of work and real-time debugging capability.

Core knowledge points and practice in Python programming include:

1. Data processing and environment preparation: Review of Python fundamentals, including variables, functions, loops, and conditionals; data processing libraries, including basic use of NumPy and Pandas; and an introduction to data visualization, such as Matplotlib or Plotly.
2. AI-assisted programming and prompt engineering: The appropriate role of AI tools, such as GPT, in code generation; basic principles of prompt engineering; how to construct clear requirements, define function logic, find and fix bugs, and understand and identify hallucinations.
3. PBL agile development: Build an AI web application.
4. Demo roadshow and code review.

Learning Outcomes:

1. Master how to use large language models such as GPT as powerful development assistants and greatly lower the threshold for developing web applications.
2. Develop a complete project demo that can be interactively presented in a browser.
3. Further improve their Python skills and the understanding of vibe coding.

Project-Based Learning List

1. Applications of AI Algorithms｜Training the Diffusion Model From Noise to Creation: Training Diffusion Models for Image and Audio Generation
   Mentor: Dan Hu (Teaching Assistant: Zhang Li)
   Students will train diffusion models for image and speech generation and learn how conditional guidance is used in the training and sampling process.
2. AI and Generative Models｜AI and Generative Models: From Random Patterns to Neural Networks
   Mentor: Lei Li (Teaching Assistant: Lishuo Zhang)
   This course primarily introduces hands-on practice with simple generative models using Python. It will start with random numbers and basic pattern generation, covering NumPy arrays, Matplotlib visualisation, and the matrix representation of images. The course then moves on to the MNIST dataset, illustrating the architecture and training process of an autoencoder. Finally, it briefly introduces the core concepts behind modern generative models such as Flow Matching, helping students build a foundational understanding of current generative AI approaches.
3. AI for translation｜Design and Implementation of a Neural Network-Based Intelligent Translation System
   Mentor: Zheng Ma (Teaching Assistants: Jishen Peng, Chen Min)
   This project will guide students through the full process of training a small neural machine translation model from scratch on an online programming platform, using LSTM, seq2seq, and Transformer architectures to explore intelligent translation among Chinese, English, and Arabic. Students will work with publicly available bilingual parallel corpora to complete data preprocessing (tokenization, vocabulary building), model design (encoder-decoder structure), training, and inference. In practice, students will use Python and PyTorch to implement or simplify core Transformer components (self-attention, multi-head attention, positional encoding, etc.). They will also learn the “vibe coding” approach, leveraging large language models to assist in generating, debugging, and optimizing code, while monitoring loss curves and BLEU scores in real time to evaluate translation quality. After training, students will demonstrate translation results directly in Jupyter Notebooks—by inputting custom test sentences, visualizing output translations and attention weight maps to intuitively understand how the model aligns source and target languages. The final deliverables include a fully executable notebook, a code repository, and a brief experimental report. The primary goals are to deepen students’ understanding of neural machine translation principles and Transformer mechanisms, and to develop their ability to independently conduct deep learning experiments. No prior background in translation or NLP is required; basic Python knowledge is sufficient, and teaching assistants will provide step-by-step guidance throughout the project.
4. AI for Science｜“Mind Reading” Using Brain Waves
   Mentor: Shanshan Qin (Teaching Assistant: Zikai Fang)
   What you will do: In sci-fi movies, people type or control robotic arms with their “mind”—the technology behind it is called a brain-computer interface (BCI). In this project, you will build the smallest possible BCI from scratch: train an AI to determine, based solely on real human brainwaves, whether the person’s eyes are open or closed. What you will produce: ① A “mind-reading” mini-program (Demo) that runs in a browser; ② A complete code repository (GitHub); ③ A technical report plus a simplified research paper. Prerequisites: No background in neuroscience is required; no strong math skills needed. Just a basic knowledge of Python will do, and teaching assistants will guide you through the entire process.
5. AI for Science｜Quantum Computational Chemistry: Simulating the Ground-State Energy of the Hydrogen Molecule with VQE
   Mentor: Pei Zeng (Teaching Assistant: Jiayi Tang)
   This project uses the Variational Quantum Eigensolver (VQE) to simulate the ground-state energy of the hydrogen molecule, giving students a hands-on experience of quantum computing applications in molecular simulation. Building on established quantum computing software packages and sample programs, students will vary the interatomic distance of hydrogen using Python, run quantum circuits, and plot the potential energy curve of the molecule. By locating the minimum point on the curve, they will estimate the equilibrium bond length of the hydrogen molecule and compare it with classical calculation results. The project emphasizes developing students’ abilities to use computational tools for scientific experimentation, data analysis, and result interpretation. The final deliverables include a working program, visualisation outputs, and a brief research report.
6. AI for Science｜Intelligent Transportation System
   Mentor: Hepeng Zhang (Teaching Assistants: Tianjian Peng, Zhangyong Zhang)
   This project involves a group of high school students using programmable cars and a traffic simulation table to conduct an exploratory study of autonomous driving. Each car is equipped with three types of sensors—line-following, ultrasonic, and AI vision—to mimic the perceptual capabilities of real vehicles. The line-following sensor enables the car to move automatically along the track; the ultrasonic sensor detects obstacles ahead and triggers timely stops to avoid collisions; and the built-in vision screen supports one-click training to recognize traffic lights and directional signs, allowing the car to stop at red lights, turn automatically upon recognizing road signs, and give voice prompts. The team will test and optimize the car’s performance on the traffic simulation table. The final goal is to produce a fully self-driving physical car, while also compiling experimental data, a project report, and a demonstration video. Combining knowledge from physics and information technology, the project offers an intuitive understanding of the fundamental principles of autonomous driving, and helps students develop hands-on building skills, basic programming abilities, and collaborative problem-solving capabilities in a team setting.

This course takes students into frontier technology laboratories and well-known technology companies to experience real research and work environments firsthand. Students will have the opportunity to observe actual R&D processes in fields such as artificial intelligence, robotics, chips, and biocomputing; communicate with corporate technical experts and R&D personnel; and understand the complete path by which a technology moves from laboratory prototype to industrial product.

In the AI protein design section, including a visit to Matwings Technology, students will enter the company, communicate face-to-face with experts, take part in course learning, and engage with leading scientists and frontier technology research. They will enter a hyper-realistic laboratory, use AI like engineers to design entirely new proteins, hand them over to automated factory equipment for synthesis, and finally receive a customized figurine made from recycled plastic degraded by proteins. From algorithm to physical object, students will fully experience a future-oriented mode of learning.

Learning Focus: The course aims to broaden students’ technological horizons, stimulate their interest in scientific research and engineering practice, and provide intuitive reference points for future major selection and career planning.

1. SJTU exploration: By visiting iconic locations at SJTU, students will experience the campus culture and academic atmosphere of a century-old university and learn about SJTU’s historical heritage and innovative spirit through on-site exploration.
2. In-depth briefing on Shanghai Jiao Tong University’s international student admissions policy: Admissions representatives will provide detailed introductions to application requirements, scholarship policies, program choices, and campus support services for international students, helping students plan their path to study in China in advance.