An Advanced Mathematics Curriculum
Mathematics is the cornerstone of science and technology. Historically speaking, whenever societies have neglected research into basic mathematics they have start to hemorrhage the understanding of how and why things are the way they are.
Calculus has been discovered time and again in a nascent form. In Classical Greece Archimedes formulated The Method, an early treatise on calculus hundreds of years before Jesus was born. Similar strides were made in ancient cultures in Africa, China, and the Middle East. We know this because, in each of these areas, relatively exact formulae for the area of a circle (along with various other formulae from antiquity) were available. This can only be obtain with a form of early integral Calculus!
While skills in algebra and calculus are potentially utilitarian and important, the heart of mathematics is proof- the ability to demonstrate the absolute truth of a statement within a logically consistent reasoning system. One of our main focuses is to expose students to high level mathematics and for the students to see how these mathematics have given rise to the modern world. Newton’s calculus is still paying dividends today: the Apollo space program mostly relied on calculations that can be derived from it! However, newer and more modern branches of math are essential in our evidence life. GPS is deeply tied to differential geometry. Fractal geometry gave us modern cell phone antennas. Scheduling algorithms are related to both modern statistics and game theory. Machine learning rest on top of the theory of linear algebra and special functions. Students at Aegis will be exposed to all of these areas. The core mathematics curriculum will cover
- Calculus 1, 2, and 3
- Complex Analysis
- Differential Geometry
- Game Theory
- Linear Algebra
- Machine Learning
- Modern Algebra
- Number Theory
with a special emphasis on proof. Additional electives will be offered on topics like functional analysis and fractal geometry.