# Learning to read complex math formulas

could anybody point me to a book or article where I could learn how to read formulas like this one:

I have no idea what that means.

• Your question is the same as asking for a book on how to read a sentence in an arbitrary natural language from somewhere on Earth. The best you can ask for is for the meaning of that particular equality and if you don't know what it means, you probably don't know the math needed to understand it. – Git Gud Jun 19 '13 at 18:00
• If you understand addition, subtraction, multiplication, and the square root, and the exponents, then presumably the hardest thing to understand about this expression is the summantion symbols $\sum$. Here is the wiki on that – rschwieb Jun 19 '13 at 18:35
• @ryudice I'm with you on not knowing math expressions such as this. While there is a few that have provided answers to this expression. It would be nice to have better direction or even an entry point in which to start this learning curve. I guess this was an ok starting point for me. But this is just reference to the meaning in english. School or a tutor would probably be best. web.efzg.hr/dok/MAT/vkojic/Larrys_speakeasy.pdf – Jason Foglia Oct 29 '16 at 16:40
• As already mentioned by @jason-foglia and samanv, this looks like a good book on how to read mathematical notations: Mathematical Notation: A Guide for Engineers and Scientists – maximpa Jan 12 '18 at 5:03
• The "Speak_easy.pdf" above no longer exists but I found it at englishlangkan.com/produk/… – Zhuinden Feb 6 '19 at 8:50

The following points may be helpful:

1. $i$ is used to index the various numerical values $x_i$ you have. Usually, unless specified otherwise, it is understood that $i$ ranges from $1$ to some finite value $n$.

Thus, in your example, you have $n$ observations each one of them is denoted by $x_i$.

2. $\bar{x}$ denotes the mean of the $n$ observations i.e.,

$$\bar{x} = \frac{x_1+x_2+\ldots+x_n}{n}$$

The same interpretation holds for $y_i$ and $\bar{y}$.

3. $\Sigma$ stands for sum and hence we could have re-written the mean as follows:

$$\bar{x} = \frac{x_1+x_2+\ldots+x_n}{n}=\frac{\Sigma_i{x_i}}{n}$$

I hope that helps decipher what is going on in the equation.

For this particular formula, any introductory statistics book will be a good start. Conceivably you won't have the background for this book, and then you would need to backtrack.

In particular, for this question you could look up "sigma summation notation," as that is the only really strange symbol here. The other symbols, such as $\bar x$, would need to be defined. The formula you asked about happens to be the formula to calculate Pearson's correlation coefficient, measuring how much change in one variable corresponds to change in the other. In this case, the values come from data points on the plane, and having a bar means an average (so $\bar x$ means the average of all the $x$).

• Typed from my tablet, sorry – davidlowryduda Jun 19 '13 at 18:10

This comprehensive pdf could be useful: Handbook for Spoken Mathematics

It represents the mathematical symbols and explains how to read them.

for example:

https://ibb.co/cjturF

We are talking here about two points (data sets) $(x_1,\ldots, x_n)$, $\>(y_1,\ldots, y_n)$. Here the $x_i$ are to be interpreted as measurements of a quantity $x\in{\mathbb R}$, and similarly for the $y_i$. For some "unknown" reason a new origin $\bar x$ on the $x$-axis and a a new origin $\bar y$ on the $y$-axis is chosen, and you are actually interested in the quantities $$\xi_i:=x_i-\bar x,\quad \eta_i:=y_i-\bar y\qquad(1\leq i\leq n)\ .$$ In terms of the new coordinates $\xi_i$, $\>\eta_i$ your quantity $r$ appears as $$r={\sum\nolimits_i\xi_i\>\eta_i\over\sqrt{\sum\nolimits_i\xi_i^2}\sqrt{\sum\nolimits_i\eta_i^2}}={\xi\cdot\eta\over|\xi|\ |\eta|}=\cos\phi\ ,$$ where $\phi$ is the angle between the vectors $\xi$, $\>\eta\in{\mathbb R}^n$, measured in the $2$-dimensional plane spanned by $\xi$ and $\eta$.

That particular summation example is actually called "Template Matching", and it is usually used to compare sections of an image to a template in order to search for an object or shape. The summation is made from 0 to n - 1, where n is the number of elements or pixels in the template. The normalised result is a value between -1 and 1 signifying the closeness with which the section matches the template.