Applied Mathematics
for AI and Data Science Cornell Certificate Program

Numerical computation often involves problems where exact solutions are difficult or impossible to calculate. Some equations lack closed-form solutions, some require summing infinite series, and others involve computationally expensive operations that exceed practical limits. Approximation, which is the process of estimating values instead of calculating exact ones, helps address these challenges by balancing precision with efficiency.

In this course, you will investigate how approximation allows you to solve real-world problems when exact computation falls short. You'll study core approximation topics, including error analysis, floating-point computation, and numerical techniques for derivatives and integrals. By the end of the course, you'll have gained experience in identifying and managing errors effectively, refining computational methods, and applying approximation techniques in fields such as engineering, physics, and machine learning, where precision and reliability are crucial.

Linear algebra provides the foundation for describing computational systems and tackling numerical problems. It is a robust and systematic framework used to represent, optimize, and solve linear systems, forming the backbone of machine learning, optimization, and data science workflows.

In this course, you will cover essential topics such as matrix operations, fundamental subspaces, projections, and singular value decomposition (SVD). You'll discover how to apply these tools to represent linear systems mathematically and computationally. By the end of the course, you'll have the experience to use linear algebra techniques confidently in real-world applications requiring precision and optimization.

Computational linear algebra offers a toolkit for solving high-dimensional problems across various fields, including machine learning, physics, and big data analytics. This course focuses on applied techniques, going beyond theory to teach practical methods such as LU and QR factorizations, least squares optimization, and principal component analysis (PCA).

You will engage directly with data-driven challenges, learning to compute efficiently, analyze complex datasets, and uncover actionable patterns that inform decisions in dynamic environments. By the end of this course, you'll have the tools to approach computational problems with clarity and confidence in real-world applications.

Probability and statistics form the mathematical foundation for making informed decisions in the face of uncertainty. These tools are integral to areas such as predictive modeling, data science, and machine learning, helping you analyze variability, identify patterns, and develop robust algorithms.

In this course, you will explore how to evaluate datasets, simulate random systems using Monte Carlo methods, and estimate model parameters using techniques like maximum likelihood estimation. Designed for computational applications, this course equips you to model uncertainty, analyze statistical properties, and apply data-driven insights to improve algorithms and workflows.

Optimization drives solutions across virtually every area of data science, machine learning, and predictive modeling. Whether powering recommendation systems, solving large-scale data matching, or refining algorithms, optimization provides the tools to make systems efficient and scalable.

In this course, you will explore key optimization techniques, including gradient descent algorithms, constrained and unconstrained methods, and stochastic approaches like stochastic gradient descent (SGD). You'll adapt these tools to address high-impact computational challenges with precision and confidence. By the end of the course, you'll understand optimization strategies that are essential for tackling real-world problems effectively.

Efficient computation and modeling are essential for solving complex numerical problems across various fields, including geospatial analysis and machine learning. This course introduces you to Python-based workflows for problem solving, where you will build structured computational pipelines, visualize datasets, and assess numerical algorithms in real-world contexts.

Through hands-on coding projects, you will tackle tasks such as optimization, simulation, and uncertainty analysis, developing practical expertise to solve complex problems in science, engineering, and industry. By course completion, you'll have the tools to design, implement, and refine reliable solutions for a variety of complex computational tasks.