Honors Calculus III
Honors Calculus III was an accelerated and advanced version of the typical Calculus III course offered by the University of Cincinnati, covering a variety of topics including sequences & series, systems of coordinates, lines & planes, and vector-valued functions. A key factor in differentiating (get it?!) this class from the typical Calculus III class was an emphasis on understanding the theorems behind the calculus and the proofs of those theorems. One unique aspect of our learning process came in the form of extended homework; each week we were given two to four questions and asked to respond by providing formal proofs. I had never before encountered this kind of math homework; in addition to working out the math problems in numbers, we had to present our solutions with words. Our professor told us that he thought it was important to learn to successfully convey complicated mathematical concepts with uncomplicated English. By the end of the course, I definitely felt as though I had learned how to write math using words as well as numbers. This will be a valuable skill going forward as no doubt it is important for engineers not only to develop ideas but also to present them - and more often than not, presentations aren't scribbles of numbers of a piece of loose-leaf paper!
Below on the left is the first page of one week's homework assignment. Download a PDF of the full assignment here. The idea was to make our responses resemble a textbook's explanation of a problem. The quality of my responses definitely increased dramatically as the quarter progressed. On the right is a sample of my lecture notes. Notice that instead of simply giving us an equation for curvature, we explore how it is derived. This leads to a much more fundamental understanding of calculus concepts. (JPEG)
Below on the left is the first page of one week's homework assignment. Download a PDF of the full assignment here. The idea was to make our responses resemble a textbook's explanation of a problem. The quality of my responses definitely increased dramatically as the quarter progressed. On the right is a sample of my lecture notes. Notice that instead of simply giving us an equation for curvature, we explore how it is derived. This leads to a much more fundamental understanding of calculus concepts. (JPEG)