With this site, I intend to cover all mathematics required to solve practical problems beginning from counting to the most involved practical problems. My approach on each page is to cover each topic completely. This means I have not divided topics into year levels. My goal is to help you solve practical problems. As a consequence, many topics are covered in more detail than they typically are in school. For example, if a problem requires significant computation I will show computer code for the general case to perform the calculations rather than just providing a formula. I also focus on explaining why, and how to obtain results rather than just presenting the final answer.
I have also created several calculators or interactive demos to help you learn the topics, these calculators show all of the steps and can be found on the following pages:
- Counting
- Addition
- Subtraction
- Multiplication
- Time
- Division
- Quadratic factorization
- Any order polynomial factorization
- Sum of angles, double and triple angle trigonometric identities
- Polynomial division
I have also created a computer algebra system (CAS) that can help with many topics throughout the site. My CAS differs from other systems such as SymPy as it requires you to state what you would like to do to both sides of the equation or how you would like to rewrite part of the equation to achieve your goal. Computer Algebra Systems like SymPy require you to apply functions to achieve your goal so you need to learn how to program before you can use them well. This makes CAS like SymPy great to use after you understand algebra but not the best learning tool. My approach is aligned with how you perform algebra by hand therefore it can be used to learn algebra. To learn how to use it you can read about the general concepts of algebra and watch videos in this playlist. I also need to highlight understanding algebra is compulsory to be able to do anything useful with mathematics.
The following topics need to be understood to solve practical problems:
- Primary school mathematics
- Algebra
- Primary School Geometry
- Calculus
- Trigonometry and Geometry
- Numerical Mathematics
Understanding the above topics allows many real-world problems to be solved, such as analyzing the motion of projectiles.
Many of my students from primary school to university have found this website useful and I use it with them to help them understand what they are learning. I’m a private tutor contact me if you would like lessons or see about me for further information about tuition. Furthermore, some of the software I have written to explain concepts appears to be more functional than alternative commercial or free software currently available, see my automatic differentiation implementation as an example.
My plans for the development of this site are in the following order:
- Finish the Calculus section
- Complex numbers
- Other high school topics
- Add new applications potentially covering entire subject areas such as dynamics or structural analysis
A project I would like to work on but I am unlikely to be able to start any time in the near future is a computer algebra system that uses matrices as the base type. All computer algebra systems currently available use a variable to represent a single number rather than a Matrix. SymPy has very limited support for this but the syntax and what it does not support effectively make it unusable. I’ve heard Mathematica does support this but it is not free to use so I have not had any chance to test it or see how functional it is. My start on this project is my implementation of a traditional computer algebra system and the automatic differentiation implementation which with a matric symbolic class (does not exist) should allow the symbolic derivative of matrix functions.