10.4 Chapter Summary and Concluding Remarks
In this chapter we looked past algebra, opening the door to the idea that although algebra is extremely powerful, there are many problems whose solutions can't be found by algebraic techniques and require t numerical methods of solving equations. We also took a sneak peek into Calculus, otherwise known as the mathematics of change.
| Page | Summary |
|---|---|
| Introduction | For polynomials of degree 5 and higher, there's no "quadratic formula" type solution; in other words, there's no solution that involves roots, rational numbers, addition/subtraction, and multiplication/division! |
| The Interval Bisection Method | Not every equation can be solved using algebra! The Interval Bisection Method is one technique that can be used to solve an equation for which there is no algebraic way of solving it. To find the solution, we go through an iterative process, coming up with better and better estimates of the solution. |
| Introduction to Calculus | Calculus is the mathematics of change. While algebra solves static equations, equations in the world of calculus involve quantities that are in motion. This very important topic of mathematics was first developed to help us understand the motion of planets in the Universe. |
We hope that you've enjoyed your journey through algebra and along the way have picked up some general problem solving techniques that you can use in any class that requires analytical reasoning. Your thoughts mean a lot to us and if you have any suggestions regarding the text, please feel free to contact us.
