1

**Vector Spaces and Linear Transformations – Advanced Concepts

Description
  • Description: This day delves deep into the theoretical underpinnings of vector spaces. Focus on abstract vector spaces, subspaces, direct sums, quotient spaces, and their properties. Study linear transformations, including their kernel, image, rank-nullity theorem, and matrix representations. Explore change of basis and its implications for understanding linear transformations. - Resources/Activities: - Expected Outcomes: Solid understanding of abstract vector spaces, linear transformations, the rank-nullity theorem, and the significance of basis changes. Ability to apply these concepts to practical problems.
Available

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
2

**Eigenvalues, Eigenvectors, and Diagonalization – Deep Dive

  • Description: Focus on eigenvalues and eigenvectors. Understand their significance in analyzing linear transformations. Learn about eigenspaces, diagonalization, and conditions for diagonalizability. Study the spectral theorem (symmetric matrices), Jordan normal form (if time permits), and applications to differential equations and matrix exponentiation. - Resources/Activities: - Expected Outcomes: Mastery of eigenvalue and eigenvector concepts. Ability to diagonalize matrices and understand their implications. Ability to apply these concepts to real-world data science problems.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
3

**Multivariable Calculus – Gradient Descent and Optimization

  • Description: Deep dive into multivariable calculus concepts crucial for machine learning. Focus on partial derivatives, gradients, directional derivatives, the chain rule, and the Hessian matrix. Explore constrained and unconstrained optimization problems using Lagrange multipliers and gradient descent algorithms. Study Taylor expansions in multiple dimensions. - Resources/Activities: - Expected Outcomes: Solid understanding of multivariable calculus concepts, especially gradients, Hessians, and optimization algorithms. Ability to implement gradient descent and related optimization techniques.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
4

**Convex Optimization and its Applications

  • Description: Explore convex optimization – a cornerstone of machine learning. Understand convexity, convex sets, and convex functions. Study concepts such as duality, KKT conditions, and different optimization algorithms for convex problems (e.g., interior-point methods, proximal gradient methods). Explore the use of convex optimization in support vector machines (SVMs) and other machine learning models. - Resources/Activities: - Expected Outcomes: Deep understanding of convex optimization concepts, including convexity, duality, and different optimization algorithms. Ability to apply convex optimization to real-world data science problems.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
5

**Tensor Calculus and Its Importance for Deep Learning

  • Description: Introduce tensor calculus, extending the concepts of multivariable calculus to higher-order tensors. Study tensor products, contractions, and the chain rule for tensors. Understand how tensors are used in deep learning, particularly in neural networks. Explore how concepts like gradients are calculated for tensor-based operations. - Resources/Activities: - Expected Outcomes: Understanding of tensor calculus and its role in deep learning. Ability to use tensors and understand their role in modern deep learning frameworks.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
6

**Applications of Linear Algebra and Calculus in Data Science – Case Studies

  • Description: Analyze real-world data science projects. Apply the learned linear algebra and calculus concepts to solve complex problems. Focus on areas like recommender systems (SVD), dimensionality reduction (PCA), and time series analysis (e.g., Kalman filtering, state-space models). - Resources/Activities: - Expected Outcomes: Ability to apply linear algebra and calculus concepts to solve practical data science problems. Deepening of problem-solving skills and project management skills.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises
7

**Advanced Topics and Research Frontiers

  • Description: Explore advanced and current topics within linear algebra and calculus that are relevant to data science. Study topics such as: - Resources/Activities: - Expected Outcomes: Knowledge of advanced topics in linear algebra and calculus that are relevant to data science, and an understanding of the current research landscape.
Locked

Learning Objectives

  • Understand the fundamentals
  • Apply practical knowledge
  • Complete hands-on exercises

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