So the first week of lectures has ended. In **MAM1000** we have only dealt with sets and functions thus far, but in great detail using set builder and interval notation. In our first tutorial we have even started using parametric equations. **The Modulus(Absolute value) Function** had been added by the end of the week as well. Modulus function is nice to work with as the answer coming out of it must always be positive. If a variable (x) is shown in modulus it must be its non-negative version for example: if x in itself has a negative value then the value of x after modulus has been applied will be -x as this will then be a positive number. Similarly if x is positive then the output will be x. **|x|** is how modulus is written. We have now also learned that **|x+y|<=|x|+|y|**, this is called the **Triangle inequality** and is very important for future use. We have learned how to display an inequality in interval notation, **1<x<=5** can be written as **(1,5]**. A round bracket indicates that a value **is not** included whilst a square bracket indicates that it **is** included. We have learned to graph the modulus function as well, it is always situated above the x-axis as all the points on the graph must always have a non-negative y value. As you may have noticed I have focused extensively on the modulus function but this is purely because it is the latest we have learned about as well as my favourite part of the course so far.

Thank you for reading and I hope this might help anyone who is yet to fully grasp the concept of the absolute value function.

Aidan HornMarch 6, 2016 at 8:10 pmIndeed, I find the modulus function very useful even in third year. Last year in Linear Algebra and Real Analysis, it gave me a normed vector space, and this year we use it to define a Euclidean metric. I’m sure I will use it all the time next semester in my Complex Analysis course.

First year maths lecture notes subject links – MathemafricaMay 9, 2018 at 9:12 pm[…] The first week of lectures […]