MAD 4401

MAD 4401 – Introduction to Numerical Analysis (Spring 2026)

Ever wondered how a calculator really finds square roots, how computers solve
differential equations, or how we can trust numbers that come from messy real-world data?
MAD 4401 is where analysis meets algorithms: we study how to turn continuous mathematics
into computations a computer can actually do — and how to measure the error when it does.

What will we study?

The course focuses on numerical methods that power modern science, engineering,
and data analysis. Core topics include:

  • Error analysis and computer arithmetic (floating-point, round-off, and accuracy).
  • Root-finding methods such as bisection, Newton, and secant methods.
  • Interpolation and polynomial approximation (Lagrange, Newton forms, splines).
  • Least-squares ideas and simple linear regression for data fitting.
  • Numerical differentiation and integration (trapezoidal & Simpson rules, composites).
  • Numerical methods for initial value ODEs (Euler, Runge–Kutta, step-size and stability).

How will we learn?

MAD 4401 blends mathematical theory with hands-on computation:

  • Weekly homework to practice analysis and hand calculations.
  • Group computer labs where you implement algorithms (typically using Python or similar tools) and explore real data sets.
  • Discussion boards and in-class activities focused on explaining results and error behavior clearly and professionally.
  • Three midterm exams plus a cumulative final to synthesize the material.

Why might this course be a good fit for you?

  • You enjoy “how does this actually work on a computer?” questions, not just formulas on paper.
  • You want stronger intuition for error, approximation, and numerical stability — ideas that show up in modeling, data science, and scientific computing.
  • You are planning to use mathematics, science, or engineering in a setting where simulations and computation matter.

We use open-source numerical analysis texts, so you’ll always have digital access to the
primary references for the course.

Spring 2026 Syllabi

Full details about grading, policies, weekly schedules, and required materials are
available in the syllabi for each section.

Both sections cover the same core numerical analysis topics and use the same main
open-source textbook. Meeting times, exam logistics, and some activities differ, so be
sure to check the correct syllabus for your registered section.