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MATHEMATICS

Calculus

InstructorZhenping

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Mastering AI Agents: Architecture, Autonomy, and Applications

In the rapidly evolving landscape of artificial intelligence, the paradigm is shifting from passive language models to active, autonomous decision-makers. This course provides a comprehensive foundation into the world of AI Agents—systems capable of perceiving their environment, reasoning through complex tasks, and executing actions to achieve specific goals.

Introduction to Artificial Intelligence

This courseware is designed to guide you through the fundamentals of AI in a clear and approachable way. You will explore what AI truly is, how it works, and what opportunities and challenges lie ahead—all without needing a background in advanced mathematics.

Numerical Computation and Optimization Theory

This course provides a rigorous introduction to numerical computation methods and optimization theory, focusing on the mathematical foundations and algorithmic techniques used to solve complex computational problems. It bridges theory and practice by equipping students with the tools necessary to design efficient and reliable numerical algorithms. Key topics include numerical linear algebra, iterative methods, nonlinear equation solving, numerical integration and differentiation, and error analysis. On the optimization side, the course covers unconstrained and constrained optimization, convex optimization, gradient-based methods, duality theory, and large-scale optimization techniques. Students will gain hands-on experience implementing numerical algorithms and optimization methods, with applications in machine learning, engineering, economics, and scientific computing. Emphasis is placed on computational efficiency, stability, and convergence analysis.

Calculus

Calculus is a foundational mathematics course that introduces students to differential and integral calculus through practical applications and computational problem-solving. The course covers limits, derivatives, integrals, and their applications to optimization, related rates, area calculations, and volume computations. Students will master fundamental techniques including differentiation rules, integration methods, the Fundamental Theorem of Calculus, and series expansions. Through hands-on implementations using computational tools like Python, students will solve real-world problems in physics, engineering, economics, and data science, including motion analysis, optimization problems, and mathematical modeling. Students will explore how calculus principles underpin machine learning algorithms, including gradient descent optimization, back propagation in neural networks, and probability distributions in AI models.

Discrete Mathematics

This course introduces the fundamental mathematical structures used in computer science and data analysis. Over eight weeks, students will progress from the basics of propositional logic and number theory to advanced topics in combinatorics, discrete probability, and graph theory. The curriculum is designed to bridge the gap between abstract mathematical proofs and real-world applications, providing students with the analytical tools necessary to understand complex algorithms and modern AI workflows.

Probability and Statistics

This course introduces the fundamental concepts of probability and statistics that form the foundation of Artificial Intelligence and data-driven decision making. Students will learn how to model uncertainty, analyze data, interpret statistical results, and apply quantitative methods to support AI and machine learning applications.

Linear Algebra

Linear Algebra is a fundamental mathematics course that introduces students to vector spaces, matrices, and linear transformations through computational applications and real-world problem-solving. The course covers vector operations, matrix algebra, determinants, eigenvalues and eigenvectors, linear independence, and basis transformations. Students will master essential techniques including Gaussian elimination, matrix factorizations, least squares methods, and dimensionality reduction algorithms. Through hands-on implementations using Python libraries like NumPy, SciPy, and scikit-learn, students will tackle practical problems in computer graphics, data analysis, signal processing, and optimization. Students will explore how linear algebra forms the mathematical foundation of artificial intelligence, including principal component analysis, singular value decomposition in recommendation systems, and matrix operations in neural network computations.

Deep Learning in Practice

Welcome to Deep Learning in Practice, an intensive, hands-on journey designed to bridge the gap between theoretical machine learning and real-world AI deployment. This course bypasses the abstract equations to focus heavily on building, training, and optimizing production-grade neural networks. Throughout the curriculum, you will dive straight into industry-standard frameworks like PyTorch and TensorFlow. You will master the core architectures driving today’s technological revolution, including Convolutional Neural Networks (CNNs) for computer vision, Recurrent Neural Networks (RNNs) and Transformers for Natural Language Processing (NLP), and Generative Adversarial Networks (GANs). Moving beyond model code, this course emphasizes the entire engineering lifecycle. You will learn critical practical skills: handling messy real-world datasets, implementing effective data augmentation, debugging training anomalies like vanishing gradients, and leveraging transfer learning to build powerfu

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Data Communication and Computer Network Security

AWAllen Wang

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