Stanford University - Introduction to Mathematical Thinking - Professor Keith Devlin - Mathematical thinking isn't the same as actually doing mathematics, as Devlin will describe. The goal of this course is to teach you to think mathematically and analytically—to think logically about a problem or puzzle and try to deduce the best approach based on the information available. The course starts at the beginning of February and comes in two flavors, the Extended version that's designed for college students interested in studying mathematics, and the shorter Basic version for people who just want to improve their critical and analytical thinking skills and apply what they've learned to their general and professional lives.
MIT - Dynamics - Professors David Gossard, Thomas Peacock, and J. Kim Vandiver - If you land at MIT interested in studying mechanical engineering, you first have to work your way through some of the basic mathematics that explains and describes how mechanical systems work. This course will help you do just that, and has the same rigor as the MIT class for undergraduates—you'll learn about the geometry of objects in motion, you'll learn to predict the movements of objects accurately, use tools like MATLAB to perform your calculations, and understand topics like torque and angular momentum—things you see every day, but may not be able to describe. You'll definitely be able to by the end of this course.
Udacity/San Jose State University - Visualizing Algebra - Professor Sandra DeSousa - Algebra can be a tricky topic, and this course will help you tackle and master it visually, with real world examples, puzzles to solve, and visual exercises for those of us who like to put our eyes on a problem instead of work in the abstract. The course is designed for people with no math background really. By the end of the course, you'll have a better feel for algebra and mathematics in general, and you'll be ready to tackle more complicated topics. Even if you're not, you'll find yourself more prepared to tackle other logical problems and analyzing patterns.
The Ohio State University - Calculus One - Professors Bart Snapp and Jim Fowler - If you've mastered algebra and you're eager for more of a challenge, or you want to embrace some of the mathematics that some of your favorite scientific topics are steeped in, this course is for you. You'll need some understanding of algebra to succeed in it, but beyond that, they'll take you through the basics of derivatives, integrals, functions and limits, and more. The course is designed as a first and easygoing introduction to calculus for people who haven't approached the topic before.