When we speak of mums, we're referring to any of many species belonging to the genus Chrysanthemum, of which there are well over a hundred. The word "Chrysanthemum" is both the Latin name and the English name, which often is not the case.
If you make a cross-section of the above flower, here is what you see:
That picture shows how the disk flowers are stacked on their bottoms atop the platform-like receptacle. At the right you can see that better. Also, at the base of each disk flower you can see the future "seeds," which are actually special composite-flower fruits known as achenes. Once the flowers are pollinated, the achenes will enlarge and harden. When you buy "mum seeds" for sowing in your garden, you buy those achenes.
As is typical of composite flowers, the Chrysanthemum's flower heads arise from a cuplike collection of scale-like bracts, like the ones at the right. In some composite species the bracts are very slender and in others very wide, sometimes they are other than green, and sometimes they are arranged in just one series so that they stand side-to-side instead of overlapping like those above. You can see that the Chrysanthemum's bracts are in three or more series and overlap.
On our Composite Flower Page, down at the bottom, you see that at the top of many composite-flower achenes, there is a pappus. In some kinds of composite flowers the pappus is composed of needle-like hairs, as shown on the Composite Flower Page. Other pappuses are composed of feathery bristles, sharp teeth, scales, or maybe crown-like (like little cups at the achene top), and sometimes there are no pappuses at all. Atop Chrysanthemum achenes there are scale-like cups, or no pappuses at all. In the image at the left you can see that our Chrysanthemum species bears no pappus. Also in that image, note the Y-shaped stigma arising from the flowers' centers. The stigma is the part of the female pistil on which pollen germinates.
Here are some books you might be interested in, from Amazon.com: