MATH E-23C: Mathematics for Computation and Data Science

Harvard University Extension School – Spring Term 2024

This is the second course in a challenging, semester-based sequence that follows MATH E-23A: Linear Algebra and Real Analysis I. As a student, I had the opportunity to deepen my understanding of real analysis, linear algebra, and multivariable calculus, with a focus on both theory and practical applications in data science and computation. One of the most rewarding aspects of the course was the chance to present mathematical proofs to my peers. Throughout the course, I worked on topics like vector spaces, eigenvectors, and integration techniques, applying them to real-world problems using R. This experience not only expanded my mathematical knowledge but also fueled my passion for teaching and helping others understand these concepts.

  • Lebesgue Integral
    Duration: 12:08
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    This proof extends the concept of integration through the Lebesgue Integral, providing a more general approach than Riemann integration. It is particularly useful for handling limits of sequences of functions and their convergence.

  • Projection Matrix for Subspace
    Duration: 10:14
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    Projection matrices play a crucial role in linear algebra, especially in least squares solutions and subspace projections. This proof demonstrates the construction of a projection matrix for a given subspace, showcasing its application in linear transformations and optimization.

  • Integrability and Sum of Integrals using Darboux Sums
    Duration: 19:06
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    Using Darboux sums, this proof establishes the integrability of functions by connecting Riemann sums with the concept of upper and lower sums. It also proves the sum of integrals, a foundational concept in real analysis and calculus.