Dr. Eleftherios Gkioulekas -- faculty web page

Online Lecture Notes on Mathematics

I began hosting my Lecture Notes online since 2006. My goal is to provide free educational resources to anyone around the world that wishes to deeply master Mathematics. It is also my foremost aspiration to preserve a valuable teaching tradition that values and promotes clear mathematical communication skills and a genuine understanding of Mathematics.

Mathematics is inherently beautiful, and naturally attracts the interest of every student that has the inclination to become a good mathematician. Success in mastering mathematics requires, above everything else, a passion/love for the subject. That leads to hard work, patience, and never giving up. It helps, along the way, to have free educational resources that do not dumb down the content and that provide precise writing and complete arguments for proofs, examples, etc, in addition to theory and exercises. This Online Lecture Notes project is my modest contribution towards that end.

Most of the Online Lecture Notes below can be used as course textbooks or for independent study. They include fully solved examples and exercise sets. Most are still work-in-progress and have some rough edges, but many chapters are already in very good shape. If you are a student that has found the notes helpful, or an instructor that has used them in his teaching, or if you found any errors, I would like to hear from you. You may also like Paul's Online Math Notes and The Feynman Lectures on Physics.

For interested faculty, see my power-point presentation concerning this project. This project was made possible thanks to Wanchik's Writer.

College Algebra


Calculus 1

Calculus 2

Calculus 3

Math for Electrical Engineers

Intro Mathematics Proof

Linear Algebra

Discrete Structures

Ordinary Differential Equations

Real Analysis I

Mathematical Modeling

Other stuff

Business Algebra

Business Calculus


Old Notes from UCF

Finite Math (UCF)

Calculus 1 (late trancendentals)

Numerical Analysis

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