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Learn Real Analysis online: university courses, full YouTube courses, and courses with free certificates, from the IITs, MIT, Harvard, Google, Microsoft and more.
Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions…
Johns Hopkins University
A data product is the production output from a statistical analysis. Data products automate complex analysis tasks or use technology to expand the utility of a data informed model, algorithm or inference. This course covers the basics of creating data products using Shiny, R packages, and interacti…
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed…
Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG This course gives an introduction to analysis, and the goal is twofold: 1. To learn ho…
Princeton University
Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis fo…
Escher's Print Gallery, and the tour of complex analysis it invites. Explore our virtual career fair: https://3b1b.co/talent Join channel supporters to see videos early: https://3b1b.co/support An equally valuable form of support is to share the videos. Home page: https://www.3blue1brown.com Origin…
Instructor: Paige Bright View the complete course: https://ocw.mit.edu/courses/18-s190-introduction-to-metric-spaces-january-iap-2023/ How do we go from real analysis on Euclidean space to more general settings? We use metric spaces! In this six-lecture course we develop the general theory of metri…
IBM
Vector databases provide the solid foundation required by large language models to deliver AI-powered similarity searches and recommendation systems for e-commerce recommendations, cybersecurity fraud detection, medical diagnostics, bioinformatics research, and other complex analysis tasks. Begin l…
MIT OpenCourseWare
This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts through a study of re…
Wesleyan University
This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dy…
MIT OpenCourseWare
Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implica…
University of Colorado Boulder
In this course, we will expand on vision as a cognitive problem space and explore models that address various vision tasks. We will then explore how the boundaries of these problems lead to a more complex analysis of the mind and the brain and how these explorations lead to more complex computation…
MIT OpenCourseWare
This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral…
University of Colorado Boulder
In this course, you will learn what a systems engineer does. Following the conceptual foundations from The Need for Systems Engineering, you will perform requirements analysis and functional analysis on engineering programs. You will learn how to perform a trade study using a methodical, quantitati…
MIT OpenCourseWare
This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation th…
MIT OpenCourseWare
Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality,…
Case Western Reserve University
The objective of this course is to teach the mathematical thinking processes that are used in all college-level math-theory courses (such as discrete math, abstract algebra, and real analysis, for example). The goal is to reduce the time and frustration involved in learning such courses and to prov…
