Recently I have read an article on Quartz about 200 universities that launched more than 600 free online courses. I have always believed that free courses are an incredible addition to the internet and education in general. I have used a lot of free courses in the past years and they have helped me learn and understand many concepts (not just mathematics). In this post I wanted to share with you some new free online courses on mathematics. Enjoy!

**Precalculus: the Mathematics of Numbers, Functions and Equations from University of Padova**

You’ll get familiar with the basic precalculus required for college or undergraduate-level studies. Through this course you’ll gain the foundation to support further mathematical studies, or improve your use of mathematics in everyday life. The object of this course is to actually learn, to the point of competence, a certain type of elementary but essential mathematics.

**Advanced Precalculus: Geometry, Trigonometry and Exponentials from University of Padova**

You’ll get to grips with more challenging precalculus topics: plane and solid geometry; logarithms and exponentials; equalities and inequalities; and trigonometric functions and identities. By the end of this course you’ll have gained the skills to support further mathematical studies.

**Calculus Applied! from Harvard University**

In this course, you will go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand ** how calculus and mathematical models play a role in their work**. With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.

**Differential Equations: 2×2 Systems from Massachusetts Institute of Technology**

Differential equations are the language of the models we use to describe the world around us. Most phenomena require not a single differential equation, but a system of coupled differential equations. In this course, you will develop the mathematical tool set needed to understand 2×2 systems of first order linear and nonlinear differential equations.

**Introduction to Graph Theory from University of California, San Diego**

In this course, you will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. You will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, you will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics.

**What is a Proof? from University of California, San Diego**

In this course they will try to convince you that this barrier is more frightening than prohibitive: most proofs are easy to understand if explained correctly, and often they are even fun. They provide an accompanied excursion in the “proof zoo” showing you examples of techniques of different kind applied to different topics. They will use some puzzles as examples, not because they are “practical”, but because discussing them you will learn important reasoning and problem solving techniques that are useful.

**Number Theory and Cryptography from University of California, San Diego**

In this short course, you will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!

**Delivery Problem from University of California, San Diego**

You’ll implement efficient programs for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. Also, you’ll implement several solutions for real world instances of the travelling salesman problem. While designing these solutions, you will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. You’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.

**More Fun with Prime Numbers from Kyoto University**

In this course, they will present several attractive topics on prime numbers. You will learn basic concepts of prime numbers from the beginning. You will also learn how to construct practical cryptosystems using prime numbers. Calculating with a pen and paper, you will explore the mysterious world of prime numbers. The course is designed to encourage you to attack unsolved problems, and hopefully, discover new laws of your own in the future!

I believe they all look great and tackle interesting topics. If you know of any other free online courses let us know. They are a wonderful step forward for education. Enjoy! Have a wonderful weekend. Also, if you have ideas for future blog posts, let us know. Don’t forget to check our last post: a short chronology on Paul Erdős. You can find us on Facebook, Tumblr, Google+, Twitter and Instagram. We will try to post there as often as possible.