Free Online Resources for Pre-Calculus and Calculus: Going Beyond the Basics

During my time as a teaching assistant in college, I often encountered a common complaint from students about a particular professor. He would teach the theoretical background and a few examples and then assign challenging homework, leaving some students floundering. These students often claimed they were not shown how to solve these problems. However, this misses the core point of mathematics, which is about logical reasoning, not merely solving problems.

The difficulty often lies not in the complexity of the problem per se, but in the number of steps required, each of which builds upon the fundamental concepts of the lesson. For example, difficult derivatives might require the application of the chain rule multiple times, an exercise that is more a series of repeated basic steps. Therefore, if you're struggling with tough problems, it might indicate that you don't have a solid grasp of the basics yet.

My suggestion is to tackle difficult problems yourself using the basics, rather than seeking out worked-out solutions. If you can't solve them, it means you need to deepen your understanding of the core concepts.

Effective Learning Tools and Platforms

One personal resource that stood out for me and many others is Khan Academy. It is a comprehensive platform for learning mathematics, ranging from pre-calculus to advanced calculus. However, some users might find that the pace of videos is too fast. If that's the case, you might want to explore other resources with a slower pace of explanation.

Khan Academy

Khan Academy is an excellent choice for anyone looking to learn mathematics on their own. The platform covers a wide range of topics, from basic arithmetic to advanced calculus, with video tutorials and practice exercises. The structure is very clear and the explanations are thorough, making it ideal for both beginners and advanced learners.

Massive Open Online Courses (MOOCs)

For a more structured and in-depth learning experience, you can explore MOOCs (Massive Open Online Courses) from platforms like edX and Coursera.

edX and Coursera

On edX, courses like Calculus 1A and 1B by MIT are highly recommended as they are designed to help you fall in love with calculus. MIT OCW (OpenCourseWare) offers great resources but might be less interactive and can be very academic. If you find these courses to be good, you might also want to explore Mathematics-1 from MIT OCW.

Diverse Learning Experiences

While MOOCs can be very effective, the way they are presented might not suit everyone. O'Reilly Learning and Coursera also have a variety of courses that can cater to different learning styles. For a gamified experience, try Brilliant, which offers interactive quizzes and problem sets.

Interactive and Fun Learning

If you prefer a more interactive and engaging learning experience, platforms like Mathsisfun and Cuemath can be very helpful. They provide step-by-step explanations, interactive tools, and a range of problems to help you practice and deepen your understanding.

Ultimately, the key to mastering mathematics is persistence and deep understanding. Utilize these resources to create a personalized learning plan that suits your needs. By focusing on the basics and challenging yourself through practice, you will find that the complex problems become easier to solve.

Summary

Khan Academy edX and Coursera Interactive MOOCs Brilliant and other interactive platforms

Keywords: Khan Academy, MOOCs, Interactive Learning, Pre-Calculus, Calculus