Overview:
All of our engineering and mathematics majors, including those in secondary education, are required to take the Math 1 – Math 4 sequence. In these four classes, consisting of a total of 18 credit hours, we cover many of the topics seen in the first two years of a traditional curriculum - including differential and integral calculus, multivariable calculus, differential equations, and linear algebra. We also cover topics not usually seen early, if at all: discrete dynamical systems, partial differential equations, probability, and statistics.
Integrated Mathematical Themes:
Rather than covering these topics in separate courses, we strive to help the students see the continuum of mathematics by exploring, either in passing or in detail, the connections between topics as they naturally arise. Students revisit concepts at different times and from multiple perspectives, satisfying the pedagogical goal of spiraling to help with their comprehension and retention of material. In this way, the connections among topics drive the mathematical abstraction for students. Even though we have chosen a very applied program, this core curriculum could be used as a foundation for an upper division sequence in pure mathematics.
Applications Oriented:
Applications increase the average student’s interest level and help them solidify abstractions. Through the use of real-world examples, Interactive Lively Application Projects (ILAPs), and independent projects, we encourage our students to understand both the big picture as well as the theoretical detail. Our entire program, including the upper division courses, is built upon this principle. In order to graduate with a mathematics degree from Carroll College, our students must complement their mathematics courses with a cognate concentration in another field of interest (biology, business and economics, chemistry, computer science, engineering, environmental science, secondary education, or individualized).
Technology Enriched:
The appropriate use of technology both in the classroom and in the lab has helped shape our curriculum. Rather than being an “add-on”, we view technology as an integral part of our curriculum, helping to shape both what and how we teach. We have seen that technology has allowed us to introduce topics, such as Fourier series and the heat equation, that students would not normally see in the first two years of their education.
Student Centered:
In designing our curriculum, we have concentrated on the three pedagogical goals above while keeping the student at the center of all activities. Our new curriculum keeps our students actively engaged in their learning and gives them the foundation they will need to move on in mathematics or engineering. In focusing on communication skills, we have our students work in groups, prepare reports, and make presentations.