Haydn lived through and helped contribute to an extraordinary period for the cultivation of symphony orchestras. In this 18th century, the instruments used went from just string to horns, oboes clarinets, and more. He also went from writing three movement symphonies to four movement symphonies, as the three movement custom disappeared. In the 19th century the boundaries of symphony orchestras were being expanded by Beethoven. He even wrote a five movement symphony. Others too kept find new and creative ways to expand the boundaries of symphony orchestras, and continued to add new and more instruments to the orchestra. Throughout the twentieth century symphonies underwent even further creative expansion in the style and content of the symphonies being written.
Mozart began as a child prodigy and composed at a young age, whereas Beethoven mostly focused on mastering his skill at the instruments at a young age. Beethoven was almost seen as the successor of Mozart, mostly because of his career taking off soon after Mozart had passed away. Beethoven's early work was very similar to Mozart's in style, but as he matured be began to go off in his own directions.
The instruments used and the size of the orchestra are similar to that of a classical symphony. Also, the movement ends in a tonic key, which was typical for classical works.
The mood of the symphony is very pensive and has moments of tension and relaxation. These are traits of the romantic era. Also the use of strings is another trait.
Charles Ives was the American Composer who wrote “London Bridge Is Fallen Down”. Part of the success of this song is how he added dissonant harmonies to a familiar tune. The repurposing of an old familiar tune shows his connection to his european roots.
Still distinguished himself by being an african american. This did not help him out any though. It was difficult for him to be taken seriously for a long time. In the symphony from the Listening Assignment, the first movement has a nice blues theme. The third movement features a banjo, which was a popular instrument for African American slaves.
Copland had a keen intelligence and an interest beyond nationalism. He liked to use indigenous American materials, like folk music or cowboy tunes as a baseline for some of his music. Copland believed in writing practical music, which sometimes caused him to tone down the complexity of some of his music.
Gershwin always tried to incorporate jazz like effects in his music. This gave it a very unique sound, and flair. It is said that he bridged the gap between popular and art music. Due to the artful nature of his music, but also the flair and jazz it was hard for him not to stand out. He very much liked the works of some classical composers.
Cage found himself drawn to the Eastern Asian culture, and things like Zen Buddhism. This helped liberate him from some of the Western traditions that limited other composers.This allowed him to create some unique pieces of music and stand out from other composers. 
Zwilich directed the people performing her music to perform in the Baroque style. This contributed to the uniqueness of her music (At the time) and showed her commitment to her European roots.
